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USC Computer Science Technical Reports, no. 962 (2015)

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USC Computer Science Technical Reports, no. 962 (2015)

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Content Real-TimeTaskAssignmentinHyper-LocalSpatial CrowdsourcingunderBudgetConstraints Hien To, Liyue Fan, Luan Tran, Cyrus Shahabi University of Southern California {hto,liyuefan,luantran,shahabi}@usc.edu ABSTRACT Spatial Crowdsourcing (SC) is a novel platform that engages individuals, groups and communities in the act of collect- ing, analyzing, and disseminating various types of spatial data. This method of data collection can signicantly re- duce cost and turnover time, and is particularly useful in case of environmental sensing, where traditional means fail to provide ne-grained eld data. In this study, we intro- duce a framework for crowdsourcing hyper-local informa- tion, in which only those workers who are already within the spatiotemporal vicinity of a task are eligible candidates to report data, e.g., the precipitation level at their area and time. In this setting, a subset of candidate workers whose size is constrained by a predened budget, can be activated to perform tasks. The challenge is to maximize task cov- erage under budget constraint, despite the dynamic arrivals of workers and tasks as well as their co-location relation- ship. We investigate two variants of the problem: xed and dynamic budgets. For each variant, we study the complex- ity of its o-line version and then propose eective methods for the online scenario that exploit the spatial and temporal knowledge acquired over time. Extensive experiments with real-world and synthetic datasets show the eectiveness and eciency of our proposed framework. 1. INTRODUCTION With the ubiquity of smart phones and wireless network bandwidth improvements, every person with a mobile phone can now act as a multimodal sensor collecting and shar- ing various types of high-delity spatiotemporal data in- stantaneously. This new paradigm for data collection has various applications in environmental sensing [16], weather forecasting [8], disaster response [23], and transportation decision-making [6]. Specically, with a few recently devel- oped apps, such as mPING 1 , Creek Watch 2 and WeatherSig- nal 3 , individual users can report weather conditions, docu- 1 http://mping.nssl.noaa.gov/ 2 http://www.research.ibm.com/social/projects creekwatch.shtml 3 http://weathersignal.com ment wildlife, measure air quality, etc. The gathered data, often in the form of ne-tuned, real-time eld reports, oer a valuable addition (e.g., ground-truth data) to the satel- lite remote sensing and radar detection currently used by various large-scale research projects [9]. The collected data also provide real-time weather notications to the users who subscribe to the regions of their interest. Spatial crowdsourcing (SC) [13] oers an eective platform for the aforementioned data collection scenarios where data requesters can create spatial tasks dynamically and workers are assigned with tasks based on their locations and certain optimization objectives, such as distance traveled and max- imum assignment [22, 13], trust/reputation [14] and data quality [3]. Consider a scenario where a requester issues a set of rainfall observation tasks to the SC-server (Step 1 in Figure 1), where one task corresponds to a specic ge- ographical region represented by a circle in Figure 1. On the other hand, the workers report and continuously update their locations to the SC-server when they become available for performing tasks (Step 0). Subsequently, the SC-server crowdsources the tasks among the workers in the task region and sends the collected data back to the requester (Steps 2, 3). Apart from precipitation, e.g., rain, snow, drought, driz- zle, this framework can be generalized to collect other kinds of information, such as air pollution, light intensity, temper- ature, noise level, etc. SC-Server Workers Requesters 2. Selected workers 1. Hyper-local SC tasks Push Notification Service 3. Task notifications 0. Report locations A, +5 mins C B D E Figure 1: The spatial crowdsourcing framework. One major dierence between our applications and exist- ing SC paradigms [22, 20, 3, 13] is that workers are not required to travel to the task locations, which would en- courage participation and yield fast response. We denote this new paradigm as Hyper-Local Spatial Crowdsourcing. Furthermore, since the requested data, such as air pollu- tion and temperature, exhibit spatial/temporal continuity in measurement, workers available in close vicinity of the task location and request time are sucient to fulll that task. For example, worker B and C in Figure 1 are both eligible to report precipitation level at University of South- ern California (USC), and worker A who becomes available 5 minutes later is also qualied. The acceptable ranges of space and time can be specied by data requesters, from which the SC-server can nd the set of eligible workers for each task. In reality, the SC-server operates to maximize fullled tasks for revenue. However, it cannot assign every task to all eli- gible workers due to practical considerations, e.g., to avoid high communication cost for sending/receiving task noti- cations and worker irritation after receiving too many task notications. Furthermore, it is not necessary to select many workers for overlapping tasks. For example in Figure 1, the observation of worker A can be used for precipitation tasks at both USC and Los Angeles downtown (tasks shown in two circles). Apart from considering user reputation [14] for guaranteed data delivery, the goal of our paper is to maximize the num- ber of assigned tasks on the SC-server where only a given number of workers can be selected over a time period, i.e., under a \budget" constraint. When tasks and workers are known apriori, we can reduce the task assignment problem to the classic Maximum Coverage Problem and its variants. However, the main challenge with SC comes from the dy- namism of the arriving tasks and workers, which renders an optimal solution infeasible in the real-time scenario. In Figure 1, the SC-server is likely to activate worker D and either workerB orC for the two tasks, respectively, without knowing that a more favorable workerA is qualied for both tasks and will arrive in the near future. Previously devel- oped heuristics in literature [22, 20, 3, 13] do not consider the vicinity of tasks in space and time or the budget, thus cannot be applied to Hyper-Local SC. Due to the unforeseeable arrival time and location of tasks and workers, the dynamic allocation of the budget towards global optimization imposes another challenge for real-time applications. As one worker can be selected for tasks from dierent time periods (e.g., worker A in Figure 1), greed- ily optimizing within each time period does not guarantee global optimal solutions over the entire campaign. We con- sider two variations for budget allocation, i.e., given a budget for each time period or given a budget for the entire cam- paign, which enforce a constraint on the number of activated workers for each time period or for the entire campaign, re- spectively. The specic contributions of this paper are as follow. 1) We provide a formal denition of the Hyper-Local SC problem, where the goal is to maximize task coverage un- der budget constraints. To the best of our knowledge, we are the rst to study the problem. Two problem variants are investigated in the paper: one with a given budget for each time period, and the other with a given budget for the entire campaign. We study the problem complexity of both variants (assuming a clairvoyant server) and prove that they are NP-hard in the oine setting. 2) When a budget is specied for each time period, we pro- pose three heuristics in the online setting, i.e., Basic, Spatial and Temporal. The spatial heuristic favors the tasks that may not co-locate with the workers who will be available in the near future, while the temporal heuristic favors the tasks which will soon be expired. 3) When a budget is specied for an entire campaign, we devise an adaptive strategy based on the contextual ban- dit algorithm [15] to dynamically allocate budget over time. By utilizing the historical logs and introducing randomness, our strategy strikes a balance between exploitation and ex- ploration and captures the dynamic changes in the arriving patterns of workers and tasks. 4) We conduct extensive experiments with real-world and synthetic datasets. The empirical results conrm that our online solutions are ecient and increase the task coverage by 40% over the baseline approach, thus can enable a wide range of SC applications. The remainder of this paper is organized as follows. Section 2 shows the related work. Section 3 presents the preliminar- ies of our SC framework and denes notations for the hyper- local SC problem. In Section 4, we introduce the problem variant with a xed budget for each time period and present heuristics for the online case. In Section 5, we study the problem variant where a budget is given for the entire cam- paign and introduce adaptive budget allocation strategies. Section 6 reports our experimental results while Section 7 concludes the paper and proposes future directions. 2. RELATED WORK Spatial Crowdsourcing (SC) has recently been attracting attention in both the research communities (e.g., [22, 1, 21, 20, 3, 24, 5, 7, 13]) and industry (e.g., TaskRabbit, Gigwalk [17]). A recent survey in this area can be found in [22], which distinguishes SC from related elds, includ- ing crowdsourcing, participatory sensing, volunteered geo- graphic information. In [13], a SC framework whose goal is to maximize the number of assigned tasks is proposed. In [21, 20], the authors introduce the problem of protecting worker location privacy in SC. This study proposes a frame- work that achieves dierentially-private protection guaran- tees. Recently in [3], Cheng et. al. study reliable task assignment in SC whose objective is to maximize both the condence of task completion and the diversity quality of the tasks. In contrast to our study, in [22, 3, 20, 5, 13], the workers need to travel to the tasks' locations, which may take a long time in rush hour. Consequently, the workers may reject their assigned tasks. In [24], an online spatial task assignment problem is suggested to maximize the num- ber of successful assignments. Meanwhile, distributed al- gorithm for task assignment is proposed in [1]. Recently, the problem of assigning and scheduling tasks for multiple workers that maximizes the number of assigned tasks is pro- posed in [7]. One of the challenges with crowdsourcing is to aggregate the workers' responses with varying degree of accuracy. One of the well-known mechanisms is majority voting, which accepts the result supported by the majority of workers. Another work aims to tackle the issue of trust by having tasks performed redundantly by multiple workers [3]. In the scope of this study, we assume that selected work- ers provide trustworthy data. If there are multiple reports for one task the SC-server will send all the corresponding results to the task requester. Crowdsourcing hyper-local information has been presented in both research (e.g., mPING [9]) and industry (e.g., mP- ing 4 , WeatherSignal 5 ). mPing is the state-of-the-art system for crowdsourcing weather reports; anyone with a smart- phone can report precipitation observations. However, mP- ing neglects to consider the cost of selecting workers to per- form tasks. Also, the task assignment in mPing is often sub- optimal as workers do not have a global system view. Work- ers typically choose nearby tasks to them, which may cause multiple workers to cover the same task unnecessarily while many other tasks remain uncovered. WeatherSignal uses phone sensors, such as temperature and humidity sensors, to measure local atmospheric conditions. Particularly, an algo- rithm was employed to translate phone battery temperature into the ambient temperature. However, the algorithm accu- racy is the main concern. In addition, WeatherSignal is re- stricted to the availability of phone sensors, which currently cannot detect various kinds of hyper-local information, such as air pollution, noise level, light intensity and precipitation level such as rain, snow, drought. Our proposed framework overcomes the aforementioned shortcomings by leveraging human power and server-side optimization of task coverage. 3. PRELIMINARIES We rst introduce concepts and notations used in this paper. A task is a query of certain hyper-local information, e.g., precipitation level at a particular location and time. For simplicity, we assume that the result of a task is in the form of a numerical value, e.g., 0=rain,1=snow,2=none 6 . Specif- ically, every task comes with a pre-dened region where any enclosed user can report data for that task. In this paper, we dene each task region as a circular space centered at the task location; however, task region can be extended to other shapes such as polygon or to represent geography such as district, city, county, etc. In real applications, the proper radius of the task region can be set by the requester. More- over, each task also species a valid time interval during which users can provide data. More formally, Definition 1 (Task). A taskt of form<l;r;s;> is a query at locationl, which can be answered by workers within a circular space centered at l with radius r. The parameter indicates the duration of the query: it is requested at time s and can be answered until time s +. We refer to s + as the \deadline" of task t. A task expires if it has not been answered before its deadline. Figure 2a shows the regions of six tasks, t 1 1 ;t 2 1 ;:::;t 6 1 . All tasks expire at time period 2 (i.e., they can be deferred to time period 2), represented by the dashed circles in Figure 2b. A worker can accept task assignments when he is online. 4 Developed by National Severe Storms Laboratory (NSSL) 5 weathersignal.com 6 Remote sensing techniques based on satellite images cannot dier- entiate between rain and snow 1 1 t t 1 4 2 1 t 2 1 w w 1 1 K 1 =1 t 1 3 t 1 5 t 1 6 (a) Time period 1 1 1 t t 1 4 2 1 t w 2 1 K 2 =1 t 1 3 t 1 5 t 1 6 (b) Time period 2 t 1 1 t 1 2 t 1 5 t 1 6 w 1 2 w 1 1 w 2 1 1 G 2 G t 1 4 t 1 3 (c) Bipartite graph Figure 2: Graphical example of worker-task coverage ( = 2). Sub- scripts represent time periods while superscripts mean ids. Definition 2 (Worker). A workerw of form<id;l>, is a carrier of a mobile device who can accept spatial task assignments. The worker can be uniquely identied by his id and his location is at l. Intuitively, a worker is eligible to perform a task if his lo- cation is enclosed in the task region. In Figure 2a, w 1 1 is eligible to perform t 1 1 ;t 2 1 and t 3 1 while w 2 1 is qualied to per- formt 1 1 ;t 4 1 ;t 5 1 andt 6 1 . Furthermore, a worker's report to one task can also be used for all other unexpired tasks whose task regions enclose the worker. As in Figure 2b, online worker w 1 2 is eligible to perform t 5 1 and t 6 1 , which are deferred from time 1. LetWi =fw 1 i ;w 2 i ;:::g denotes the set of available workers at timesi andTi =ft 1 i ;t 2 i ;:::g denotes the set of available tasks including tasks issued at time si and previously issued un- expired tasks. Below we dene the notions of worker-task coverage and coverage instance sets. Definition 3 (Worker-Task Coverage). Givenw j i 2 Wi, letC(w j i )Ti denotes the task coverage set ofw j i , such that for every t k i 2C(w j ), si <t k i :(s +) (1) jjw j i :lt k i :ljj2t k i :r (2) We also say the worker w j i covers the tasks t k i 2C(w j i ). An example of a coverage in Figure 2a is C(w 1 1 ) =ft 1 1 ;t 2 1 ;t 3 1 g. Definition 4 (Coverage Instance Set). At timesi, the coverage instance set, denoted by Ii is the set of worker- task coverage of form<w j i ;C(w j i )> for all workersw j i 2Wi. Time Coverage Instance Sets 1 f(w 1 1 ;<t 1 1 ;t 2 1 ;t 3 1 >); (w 2 1 ;<t 1 1 ;t 4 1 ;t 5 1 ;t 6 1 >)g 2 f(w 1 2 ;<t 5 1 ;t 6 1 >)g Table 1: The coverage instance set of the example in Figure 2. The coverage instance sets for the example in Figure 2 are illustrated in Table 1. For simplicity, we rst assume the utility of a specic task assignment is binary within the task region and before the deadline. That is, assignment to any worker within a task region before the deadline has utility 1, i.e. 1 successful assignment, and 0 otherwise. As a result, task t 5 1 and t 6 1 being answered by worker w 2 1 at time 1 is equivalent to it being answered by w 1 2 at time 2. The goal of our study is to maximize task assignment given a budget, despite the dynamic arrivals of tasks and workers. Now, we formally dene the notion of a budget. Definition 5 (Budget). Budget K is the maximum number of workers to select in a coverage instance set. In practice, budget K can capture the communication cost the SC-server incurs to push notications toK-selected work- ers (Step 3 in Figure 1), or the rewards paid to theK workers who provide data. 4. FIXED BUDGET We investigate the rst variant of the maximum task cover- age problem, in which a xed budget is given for each time period. We rst study the problem complexity of the o-line case and then propose heuristics for the online setting. 4.1 Offline Scenario Problem 1 (Fixed-budget Maximum Task Coverage). Given a set of time periods =fs1;s2;:::;sQg and a bud- get Ki for each si, the xed-budget maximum task coverage (MTC) problem is to select a set of workers Li at si, such that the total number of covered tasksj S Q i=1 S w j i 2L i C(w j i )j is maximized andjLijKi. This optimization problem is challenging since each worker is eligible for a subset of tasks. The fact that a task can be deferred to future time periods further adds to the complex- ity of the problem. With the following theorem, we proof that xed-budget oine MTC is NP-hard by a reduction from the maximum coverage with group budgets constraints problem (MCG) [2]. MCG is motivated by the maximum coverage problem (MCP) [10]. Consider a given Ig, we are given the subsetsS =fS1;S2;:::Smg of a ground setX and the disjoint setsfG1;G2;:::;G l g. Each Gi, namely a group, is a subset of S =fS1;S2;:::Smg. With MCG, we are given an integer k, and an integer bound ki for each group Gi. A solution to Ig is a subset H S such thatjHj k and jH\Gijki for 1il. The objective is to nd a solution such that the number of elements ofX covered by the sets in H is maximized. MCP is the special case of MCG [2]. Since MCP is known to be strongly NP-hard [10], by restriction, MCG is also NP-hard. Theorem 1. Fixed-budget oine MTC is NP-hard. Proof. We prove the theorem by a reduction from MCG [2]. That is, given an instance of the MCG problem, denoted by Ig, there exists an instance of the MTC problem 7 , de- noted by It, such that the solution to It can be converted to the solution of Ig in polynomial time. The reduction has two phases, transforming all workers/tasks across the entire 7 In this section, MTC refers to xed-budget MTC for short campaign to a bipartite graph, and mapping from MCG to MTC . First, we layout the tasks and workers as two set of vertices in a bipartite graph in Figure 2c. A worker w j i can cover a taskt k i if both spatial and temporal constraints hold, i.e., Equations 2 and 1, respectively. In Figure 2c, w 1 2 can covert 4 1 andt 5 2 , which are deferred froms1 tos2, represented by the dashed line. Thereafter, MTC can be stated as follows. Selecting the maximum Ki workers per group, each group represents a time period, such that the number of covered tasks is max- imized (i.e., jLij Ki). To reduce Ig to It, we show a mapping from Ig components to It components. For ev- ery elements in the ground set X in Ig, we create a task t j i (1jjXj). Also, for every set in S, we create a worker w j i with C(w j i = Sj ) (1 j m). Consequently, to solve It, we need to nd a subset Li Wi workers of maximum sizeKi in each group whose coverage is maximized. Clearly, if an answer to It is the set Li (1 i Q), the answer to Ig will be the set H S of maximum coverage such that jHjk = P Q i=1 Ki andjH\Gijki =Ki for 1iQ. As the transformation is bounded by the polynomial time to construct the bipartite graph, this completes the proof. By a reduction from the MCG problem, we can now use any algorithm that computes MCG to solve the MTC prob- lem. The solution to the example in Figure 2c isfw 1 1 ;w 1 2 g. It has been shown in [2] that the greedy algorithm gives 0.5-approximation for MCG and it is tight. However, this solution is not feasible in the online scenario where the server does not have knowledge about future tasks/workers. 4.2 Online Scenario The main challenges of spatial crowdsourcing are due to the dynamic arrivals of workers and tasks. The SC-server must select workers frequently and in real-time as new tasks and workers become available or as tasks are completed (or ex- pired) and workers leave the system. Since the clairvoyant assumption is not practical, the SC-server tries to optimize the worker selection locally at every period of time. How- ever, the optimization problem within each time period is not straightforward either. In fact, xed-budget online MTC is NP-hard by restriction. MTC for a single time snapshot (Q = 1) is NP-hard; thus, xed-budget online MTC is also NP-hard. MTC for one-time snapshot can be reduced from the maximum coverage problem (MCP) [10], MCPp MTC one-time snapshot. As MCP is strongly NP-hard, a greedy algorithm is proposed to achieve an approximation ratio of 0:63 [10]. The algo- rithm chooses a set at each stage that contains the largest number of uncovered elements. The results in [10] show that the greedy algorithm is the best-possible polynomial time approximation algorithm for MCP. As mentioned ear- lier, a global solution to online MTC is not feasible. Hence, our approach is to solve the MTC problem for every period of time with several heuristics, namely Basic, Spatial and Temporal. 4.2.1 Basic Heuristic The basic approach solves the online MTC problem by us- ing the greedy heuristic [11] for every time period. At each stage, Basic selects the worker that covers the maximum number of uncovered tasks, depicted in Lines 9-10 of Algo- rithm 1. For instance, in Figure 2a, w 1 1 is selected at the rst stage. At the beginning of each time period, Line 4 removes expired tasks being carried from the previous time period (Line 13). Thereafter, Line 5 adds uncovered un- expired tasks to current task set and assign new indices to tasks inU 0 i1 . Line 12 outputs the covered tasksCi per time period that will be used as the main performance metric in Section 6. The algorithm terminates when either running out of budget or all the tasks are covered (Line 9). Algorithm 1 Basic Algorithm 1: Input: worker set W i , task set T i , budgets K i 2: Output: selected workers L i 3: For each time period s i 4: Remove expired tasks U 0 i1 U i1 5: Update task set T i T i [U 0 i1 6: Remove tasks that do not enclose any worker T 0 i T i 7: Construct worker set W i , each w j i contains C(w j i ) 8: Init L i =fg, uncovered tasks R S w i 2W i C(w j i ) 9: WhilejL i j<K i andjRj> 0 10: Select w j i 2W i L i that maximizejC(w j i )\Rj 11: R RC(w j i ); L i L i +w j i 12: C i S w j i 2L i C(w j i ) 13: Keep uncovered tasks U i T 0 i C i 4.2.2 Spatial Heuristic The basic strategy treats all tasks equally without consider- ing the spatial characteristic of task locations. However, a task located in an area popular with workers is more likely to be covered in the future and vice versa. Therefore, tasks located in worker-sparse areas should have higher priorities to be assigned. Consequently, the priority of a worker is high if he covers a larger number of high priority tasks. The spatial \popularity" of a task location can be measured using Location Entropy [4], which captures the diversity of visits to a location. A location has a high entropy if many workers visit that location with equal probabilities. In con- trast, a location has a low entropy if there are only a few workers visiting. We extend the concept of location entropy to region entropy of the task. For a given task t, let Ot be the set of visits to task region R(t:l;r). Also, let Wt be the set of distinct workers that visited the task region oft, andOw;t be the set of visits that workerw has made to the location of taskt. The probability that a random draw from Ot belongs to Ow;t is Pt(w) = jO w;t j jO t j , which is the fraction of total visits to t that belong to workerw. The region entropy fort is computed as follows. RE(t) = X w2W t Pt(w)logPt(w) (3) We discretize the space using a 2D grid and pre-compute the entropies for each grid cell using aggregated historical data. By computing the region entropy of every uncovered task of a worker w j i , we associate to every worker a priority. priority(w j i ) = X t k i 2C(w j i )\R 1 1 +RE(t k i ) (4) where RE(t k i ) is calculated as Equation 3. Consequently, Spatial greedily selects the worker with maximum priority at each stage, as opposed to the worker that covers the max- imum number of uncovered tasks. Line 10 in Algorithm 1 can be modied to re ect the spatial priority of each worker. 4.2.3 Temporal Heuristic Another approach to prioritizing tasks is by their temporal urgency. The intuition is that a task that is further away from its deadline is more likely to be covered in the future, and vice versa. As a result, near-deadline tasks are more important than others and a worker that covers a large num- ber of soon-to-expire tasks should be preferred for selection. Similar to Equation 4, the priority of a workerw j i is dened based on the time-to-deadline for each of his covered tasks. priority(w j i ) = X t k i 2C(w j i )\R 1 t k i :(s +)i (5) Likewise, Line 10 in Algorithm 1 can be updated with the temporal priority for each worker as in Equation 5. We will empirically evaluate all heuristics in Section 6. 5. DYNAMIC BUDGET Another problem variant we investigate in the paper is more general, where a budget is given over the entire campaign. This scenario often results in higher task coverage. In Figure 2, the xed-budget method selects w 1 1 and w 1 2 and obtains the coverage of 5. However, the dynamic-budget variant yields higher coverage of 6 by selecting w 1 1 and w 2 1 . We study the problem complexity in the oine case and propose adaptive budget allocation strategies for the online scenario. 5.1 Offline Scenario Problem 2 (Dynamic-budget Maximum Task Coverage). The dynamic-budget MTC problem is similar to Problem 1, except the total budget is specied for the entire campaign K rather than for each time period, i.e., P Q i=1 jLijK. We rst investigate the oine case, where the server is clair- voyant about the future workers and tasks. With the follow- ing theorem, we prove that dynamic-budget oine MTC is NP-hard by reduction from the maximum coverage problem (MCP) [10]. Theorem 2. Dynamic-budget oine MTC is NP-hard. Proof. We prove the theorem by a reduction from MCP [10]. That is, given an instance of the MCP problem, denoted by Im, there exists an instance of the MTC problem 8 , denoted by It, such that the solution to It can be converted to the solution of Im in polynomial time. The reduction includes two steps, transforming all workers/tasks across the entire campaign to a bipartite graph, and mapping from MCP to 8 In this section, MTC refers to dynamic-budget MTC for short MTC . The rst step is similar to that of Theorem 1, in which the workers and tasks from the entire campaign are trans- formed into a bipartite graph as illustrated in Figure 2c. The mapping step can be considered as a special case of the proof in Theorem 1, in which there exists only one group of all budget. As the transformation is bounded by the poly- nomial time to construct the bipartite graph and MCP is strongly NP-hard, this completes the proof. 5.2 Online Scenario We propose adaptive strategies to dynamically allocate the total budgetK overQ time periods (KQ). When a bud- get is spent during a particular time period, the previously proposed heuristics, i.e., Basic, Spatial, Temporal, can be applied. 5.2.1 Adaptive Budget Allocation The simplest strategy, namely Equal, equally divides K to Q time periods; each has K=Q budget and the last time period obtains the remainder. However, Equal may over- allocate budget to the time periods with small numbers of tasks. Another strategy is to give each time period a budget that is proportional to the number of available tasks at that time periodjTij (i.e.,/ jT i j jTj K), wherejTj is the total number of tasks. However,jTj is unknown a priori andjTij does not provide insight on whether they can be optimally covered by available workers. To maximize task assignment, we need an approach that adaptively adjust the budget for each time period accord- ing to the dynamic arrivals of tasks and workers and their co-location. Toward that end, what is the indication of bud- get over/under-utilization? And how do we adapt to the changing coverage instance sets over time? To capture the aforementioned two aspects, we dene the following two no- tions. Delta budget, denoted as K , captures the current status of budget utilization, compared to a baseline budget strategy. Given a certain baselinefK base [i];i = 1;:::;Qg, K is the dierence between the aggregated baseline budget up to time i and the budget used so far. K = i X t=1 (K base [t])K used (6) We adopt the Equal strategy as a baseline. Another notion denoted as is delta gain, which represents the impor- tance of a worker being considered (i) compared to the ones selected in the past (i1). Formally, at time i, =ii1 (7) where i is the current gain, calculated from our heuristics (i.e., asjpriority(w j i )j with spatial and temporal heuristics) andi1 is the average gain of the last added workers from the previous time periods, i1 = 1 j1 P j1 t=1 t. Based on the contextual informationK and at each time period, we examine available workers one by one using a particular heuristic and decide whether to allocate budget 1 for each worker. Intuitively, when both K and are positive, i.e., the budget is under-utilized and a worker has higher gain than the historical average, the selection of the considered worker is favored. On the other hand, when both are negative, it is not worthwhile to spend the budget. The cases where one is positive and the other is negative are hard to judge as we prefer workers with higher gains but would also like to save budget for the future time periods. Our solution to the sequential decision problem is inspired by the well-know multi-armed bandit problem (MAB) [19], which has been widely studied and applied to decisions in clinical trials [18], online news recommendation [15], and portfolio design [12]. -greedy, which achieves a trade-o be- tween exploitation and exploration, proves to be often hard to beat by other MAB algorithms [25]. Hence, we propose an adaptive budget allocation, based on contextual -greedy algorithm [15]. We illustrate our solution in Figure 3. Figure 3: Work- ow for adaptive budget allocation. Contextual -greedy for Budget Allocation. For each worker selected by our heuristics, a binary decision to make is whether to allocate budget 1 to activate that worker. A YES decision corresponds to exploration, as the action will update our prior knowledge about gains of the selected work- ers while a NO decision corresponds to exploitation. In- tuitively, the best decision varies according to the circum- stances of each worker. The contextual -greedy algorithm allows us to specify an exploration-exploitation rate based on the worker's context, i.e.,K and . As depicted in Fig- ure 3, an i-greedy algorithm is activated corresponding to the context information, in which a YES decision is made with 1i probability and i probability for a NO deci- sion. The outline of our adaptive strategy is depicted in Algorithm 2. By default, 2 = 3 = 0:5 (uniform), while the YES/NO decisions are clearly made in the other cases (1 = 1;4 = 0). Algorithm 2 Adaptive Budget Algorithm (Adapt) 1: Input: W i , T i , total budgets K 2: Output: selected workers L i 3: Init R =T i ; used budget K used = 0; average gain i1 = 0 4: Budget allocation K equal [] with Equal strategy 5: For each time period s i 6: Perform Lines 4-8 from Algorithm 1 7: Remained budget K i =KK used 8: If i =Q, then K =K i fthe last time periodg 9: Otherwise, K = ( P i t=1 K equal [t])K used 10: WhilejL i j<K i and R is not empty: 11: Select w i in W i with highest i 12: Delta gain = i i1 13: If 0 and K 0 and rand(0;1) 1 , then break 14: If 0 and K > 0 and rand(0;1) 2 , then break 15: If > 0 and K > 0 and rand(0;1) 3 , then break 16: If > 0 and K 0 and rand(0;1) 4 , then break 17: K = K 1 18: Perform Line 11 from Algorithm 1 19: K used =K used +jL i jfupdate the budgetg 20: i = ( i1 (Q1)+ i )=Q 21: Perform Lines 12,13 from Algorithm 1 5.2.2 Historical Workload Algorithm 2 has been simplied by considering Equal as the baseline budget. Therefore, we propose to use the historical data to compute a baseline that captures the worker/task ar- rival patterns. Intuitively, human activity exhibits temporal patterns and understanding those patterns can predict the availability of workers. Musthag et al. [17] show the time-of- day usage pattern of workers in real mobile crowdsourcing applications. The activity peaks are between 4 to 7 pm when workers leave their day jobs. Similar patterns are observed in the data sets in Figure 4, which will be introduced in Section 6.1. Figure 4a shows the number of check-ins per hour in the Foursquare dataset. During weekdays, activ- ity presents three peaks: in the morning when people go to work, at lunchtime, and between 6 pm and 8 pm when they commute. During weekends, user activity presents one long-lasting plateau between noon and 10 pm. As for weekly patterns, we can observe peak activity during weekends in Gowalla dataset in Figure 4b. 100 200 300 400 500 600 700 Online worker count 0 100 1 49 97 145 193 241 289 337 Online worker count Time (hours) (a) Foursquare, 16x24 hours 400 600 800 1000 1200 1400 Online worker count 0 200 400 1 57 113 169 Online worker count Time (days) (b) Gowalla, 32x7 days Figure 4: The number of check-ins vary over time periods. As workers have activity patterns, we further improve Al- gorithm 2 by leveraging the optimal budget strategy in the recent past and use that as the baseline in Equation 6. The idea is to learn the budget allocation of from historical data, namely workload, using the solution to the dynamic-budget oine MTC problem and use the results to guide the future time periods. Consequently, we propose to improve Algo- rithm 2 by replacing Line 4 with the most recent optimal budget allocation, K prev []. 6. PERFORMANCE EV ALUATION We conducted several experiments on real-world and syn- thetic data to evaluate the performance of our proposed ap- proaches. Below, we rst discuss our experimental method- ology and then present our experimental results. 6.1 Experimental Methodology We used real-world data from location-based applications (Gowalla and Foursquare) that have been used in [22, 20, 13] to emulate spatial crowdsourcing (SC) workers and tasks, summarized in Table 2. Gowalla contains the check-in his- tory of users in a location-based social network. For our experiments, we used the check-in data over a period of 224 days in 2010, including more than 100,000 spots (e.g., restaurants), covering the state of California. We assumed that Gowalla users are SC workers, and their locations are those of the most recent check-in points. We also picked the granularity of a time period as one day. Consequently, all the users who checked in during a day as our available workers for that time period. At each time period, 1000 spa- tial tasks were randomly selected from the Gowalla venues. Likewise, Foursquare contains the check-in history of 45,138 users to 89,968 venues over 384 hours in the area of Pitts- burgh, Pennsylvania. Similarly, we used Foursquare users as Name #Tasks #Workers MTD 9 jsij Foursquare 89,968 45,138 (90/km 2 ) 16.6km 1 hour Gowalla 151,075 6,160 (35/km 2 ) 3.6km 1 day Table 2: Characteristics of real data. SC workers and venue locations as tasks. Last but not least, we developed a spatial crowdsourcing system namely iRain to collect weather information. Since the iRain dataset is relatively small, we generated a synthetic dataset with sim- ilar spatial distributions of workers and tasks (i.e., 1,355 workers and 385 tasks). The entire space is discretized into 200x200 grid, which are in forms of 2D histograms. For each time instance, we randomly create workers and tasks into grid cells proportional to their density, the locations are randomly distributed within each cell. We generated a range of datasets by combining the spa- tial worker/task distributions and their arrival rate. We needed to generate only task counts as the worker counts can be obtained from Gowalla (mean=991) and Foursquare (mean=291). To generate the number of available tasks (mean = 1000) for every time period, we used four functions: CONST, POISSON (default), ZIPFIAN and COSINE (Fig- ure 5). For example, Go-POISSON uses Gowalla for the spatial distributions and the worker arrival rate (Fig. 4b) and POISSON for the task arrival rate (Fig. 5a). iRain- POISSON uses iRain for the spatial distributions and POIS- SON for the arrival rates of workers and tasks. 800 850 900 950 1000 1050 1100 1 49 97 145 193 Task count Time period (a) POISSON 0 200 400 600 800 1000 1200 1400 1 49 97 145 193 Task count Time period (b) ZIPFIAN 0 500 1000 1500 2000 1 49 97 145 193 Task count Time period (c) COSINE Figure 5: Three samples of synthetic workload data. In all of our experiments, we varied the number of time periods Q2f7, 14, 28, 56g and the task duration 2f1, 2, 3, 4, 5, 6, 7, 8, 9, 10g. We varied the budget K2f28, 56,..., 3556g and the task radius r2f1, 2, 3, 4, 5, 6, 7, 8, 9, 10g km. For Foursquare, Q2f24, 48, 72, 96g and K2f24, 48,..., 3048g because we modeled a time period as one hour. Default values are shown in boldface. For Zipan decrease function, skew parameter s is set to 1. In xed- budget experiments, we set a budget for each time period to K=Q. All measured results are aggregated over 224=Q runs for Gowalla, and 384=Q runs for Foursquare. 6.2 Experimental Results We evaluate our solutions in terms of task coverage and rel- ative improvement measured by the coverage dierence di- vided by the coverage of the baseline approach. 6.2.1 Offline Solutions Monotonicity and Diminishing Return: We discuss two interesting properties of the solutions by Basic algo- rithm to the one-time snapshot MTC problem (i.e.,Q = 1). We observe that the number of covered tasks monotonically increases with plurality budget K as illustrated in Figure 6a. Also, Figure 6b shows the heavy-tailed distribution of the coverage gain of workers selected at each stage of Basic. 200 400 600 Coverage (Tasks) 0 1 21 41 61 81 Coverage (Tasks) Budget K (a) Monotonicity increase 10 15 20 25 30 35 Coverage Gain 0 5 1 21 41 61 81 Coverage Gain The Order of Selected Worker (b) Diminishing return Figure 6: Solutions of Basic for MTC instance, Gowalla. FixedO v.s. DynamicO: We compare the oine so- lutions to the two problem variants, FixedO (Section 4.1) and DynamicO (Section 5.1), using the greedy algorithm. Figure 7a illustrates the results for Go-POISSON by vary- ing the budget. As expected, higher budget yields higher coverage. However, the higher the budget, the smaller the relative improvement as shown in Figure 7b. This eect can be explained by the diminishing return property. That is, the coverage dierences among the algorithms are small in the case of high budget. 0 5000 10000 15000 20000 25000 30000 28 56 112 224 448 896 1792 3586 Coverage (Tasks) Budget K FixedOff DynamicOff (a) Vary K 0 1 2 3 4 5 28 56 112 224 448 896 1792 3586 Improvement(%) Budget K Relative (b) Vary K 0 2000 4000 6000 8000 10000 12000 14000 1 2 3 4 5 6 7 8 9 10 Coverage (Tasks) Delta (time periods) FixedOff DynamicOff (c) Vary 4000 6000 8000 10000 12000 14000 16000 Coverage (Tasks) FixedOff 0 2000 4000 1 2 3 4 5 6 7 8 9 10 Coverage (Tasks) Radius r (km) DynamicOff (d) Vary r Figure 7: Performance of oine solutions on Go-POISSON. We also evaluate the oine solutions by varying task dura- tion . As expected, Figure 7c shows that longer results in higher coverage. Also, the improvement of DynamicO over FixedO is larger when increases. The reason is that when tasks can be deferred to a wider range of future time periods, dynamic budget allocation becomes more eective. In Figure 7d, when r increases, every task can be covered by more workers, which yield higher coverage. We did not observe much dierence between xed budget and dynamic budget for Go-POISSON since the worker/task arrivals are stable. However, when there are peaks in arrival rate, such as in Go-ZIPFIAN, DynamicO shows more ad- vantage over FixedO (by up to 110% at = 1 in Figure 8). Unlike the result in Figure 7c, Figure 8a shows large improvements at = 1. The reason is that under the spiky workload, FixedO uses a xed amount of budget to the time periods with high spikes while DynamicO can allo- cates more budget to those time periods to cover more tasks. 0 100 200 300 400 500 600 1 2 3 4 5 6 7 8 9 10 Coverage (Tasks) Delta (time periods) FixedOff DynamicOff (a) Vary 0 100 200 300 400 500 600 700 800 1 2 3 4 5 6 7 8 9 10 Coverage (Tasks) Radius r (km) FixedOff DynamicOff (b) Vary r Figure 8: Performance of oine solutions on Go-ZIPFIAN. 6.2.2 Online Solutions The Performance of Heuristics: We evaluate the perfor- mance of the online heuristics from Section 4, Basic, Spatial and Temporal. Figures 9a shows the relative improvements of Spatial and Temporal over Basic on Go-POISSON. Spa- tial and Temporal yield 12% and 5% higher coverage than Basic at K = 28 and their performance converges as K in- creases. In addition, Figure 9b shows the results by varying task duration . As expected, the improvements of Spatial and Temporal are higher at larger while all techniques per- form similar at = 1. Similar trends can be observed when increasing the task radius r. Due to the superior perfor- mance, we will adopt Temporal from now on. 0 5000 10000 15000 20000 25000 28 56 112 224 448 896 1792 3586 Coverage (Tasks) Budget K Basic Temporal Spatial FixedOff (a) Vary K, Go-POISSON 0 5000 10000 15000 20000 1 2 3 4 5 6 7 8 9 10 Coverage (Tasks) Delta (time periods) Basic Temporal Spatial FixedOff (b) Vary , Go-POISSON Figure 9: Performance of heuristics in the xed-budget scenario. Adaptive Budget Strategy: We evaluate the performance of the adaptive algorithms in Section 5.2.1. EqualB refers to the algorithm that divides the budget equally to time periods and runs Basic, whereas AdaptB and AdaptT use Algorithm 2 with Basic and Temporal, respectively. Figures 10a and 10b show the improvements of AdaptT over AdaptB and EqualB by varying task duration . As expected, the higher, the larger improvements. Particularly, AdaptT im- proves EqualB by up to 12%. As AdaptT improves AdaptB, we hereafter show only the results of AdaptT. Figures 10c and 10d show similar results by varying task radius. Furthermore, to show the eectiveness of the adaptive al- gorithms in handling highly skew data, we evaluate AdaptT on Go-ZIPFIAN and Fo-ZIPFIAN. Figures 10e and 10f show the results by varyingr. AdaptT obtains up to 36% and 40% improvements at r = 1, correspondingly. Table 3 shows the results on the iRain dataset. The results show small improvement of AdaptT over EqualB (i.e., up to 6%). This can be explained by the fact that each task can only be performed by less than two workers in average. Historical Workload Improvement: We evaluate the performance of the workload strategy on real-world work- load data. Figures 11a and 11b show the results by varying K on Go-POISSON and Go-CONST, respectively. AdaptTW, 0 2000 4000 6000 8000 10000 12000 1 2 3 4 5 6 7 8 9 10 Coverage (Tasks) Delta (time periods) EqualB AdaptB AdaptT DynamicOff (a) Vary , Go-POISSON 0 5000 10000 15000 20000 1 2 3 4 5 6 7 8 9 10 Coverage (Tasks) Delta (time periods) EqualB AdaptB AdaptT DynamicOff (b) Vary , Fo-POISSON 0 2000 4000 6000 8000 10000 12000 14000 1 2 3 4 5 6 7 8 9 10 Coverage (Tasks) Radius r (km) EqualB AdaptT DynamicOff (c) Vary r, Go-POISSON 0 5000 10000 15000 20000 25000 1 2 3 4 5 6 7 8 9 10 Coverage (Tasks) Radius r (km) EqualB AdaptT DynamicOff (d) Vary r, Fo-POISSON 0 20 40 60 80 1 2 3 4 5 6 7 8 9 10 Coverage (Tasks) Radius r (km) EqualB AdaptT DynamicOff (e) Vary r, Go-ZIPFIAN 0 20 40 60 80 100 1 2 3 4 5 6 7 8 9 10 Coverage (Tasks) Radius r (km) EqualB AdaptT DynamicOff (f) Vary r, Fo-ZIPFIAN Figure 10: Performance of AdaptT in the dynamic-budget scenario. Radius EqualB AdaptB AdaptT 1 8932 9146 9396 5 24819 25102 25321 10 26859 27142 27442 Delta 1 18564 18716 19251 5 24620 24991 25112 10 24819 25156 25274 Table 3: The coverage of AdaptT on iRain-POISSON. K = 56;Q = 28. which uses historical optimal workload as the baseline bud- get strategy, marginally improves AdaptT on Go-POISSON. The reason is that POISSON distribution introduces ran- domness to the workload approach, which againsts the idea of leveraging the historical workload in AdaptTW. On the other hand, AdaptTW improves AdaptT by 7% on Go-CONST. We conclude that AdaptT outperforms EqualB, closing the gap between the equal-budget baseline and optimal oine solutions. AdaptTW further enhances AdaptT by using op- timal workload in the recent past. 4000 5000 6000 7000 28 56 112 224 448 896 1792 3586 Coverage (Tasks) Budget K EqualB AdaptT AdaptTW DynamicOff (a) Vary K, Go-POISSON 4000 5000 6000 7000 28 56 112 224 448 896 1792 3586 Coverage (Tasks) Budget K EqualB AdaptT AdaptTW DynamicOff (b) Vary K, Go-CONST Figure 11: Performance of AdaptTW on real-world data (Q = 7). Runtime Measurements: Figure 12 shows the run times of our online algorithms by varying the number of tasks per time period. We observe that with the increase in the num- ber of tasks, the runtime increases linearly. In addition, EqualB and AdaptT are shown to be very ecient (i.e., less than ten seconds), while the run time of AdaptTW is much higher (i.e., over 100 seconds) due to the overhead in learn- ing the optimal budget allocation in the recent past. 0.1 1 10 100 1000 500 1000 1500 2000 Runtime (seconds) The number of tasks EqualB AdaptT AdaptTW Figure 12: The average per-period run time on Go-CONST. 7. CONCLUSION AND FUTURE WORK In this paper, we introduced a framework for crowdsourcing hyper-local information, where tasks can be performed by workers within their spatiotemporal vicinity and the num- ber of assigned tasks can be maximized without exceeding the budget for activating workers. Two problem variants have been studied, one with a given budget at each time period, the other with a given budget for the entire cam- paign. We have shown that both variants are NP-hard in the oine case. In the online setting, several heuristics have been proposed, utilizing the spatial and temporal proper- ties of tasks. Also, an adaptive strategy has been proposed to dynamically allocate budget over time. According to our extensive experiments, AdaptTW, which merits the dynamic budget strategy with temporal and workload heuristics, was shown to be the best technique. As future work, we will extend the proposed framework to incorporate continuous utility functions where the utility of assignment decays depending on the distance from the worker to the task center. The intuition is that an assign- ment of a task to a nearby worker may yield higher util- ity than that of another worker farther from the task loca- tion. We will also consider non-uniform activation cost of the workers, which may represent the reputation or compen- sation demand of each worker. Finally, we will improve our heuristics by either linearly combining Spatial and Temporal or using multi-objective optimization. 8. REFERENCES [1] A. Alfarrarjeh, T. Emrich, and C. Shahabi. Scalable spatial crowdsourcing: A study of distributed algorithms. In Mobile Data Management (MDM), 2015 16th IEEE International Conference on, volume 1, pages 134{144. IEEE, 2015. [2] C. Chekuri and A. Kumar. Maximum coverage problem with group budget constraints and applications. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques, pages 72{83. Springer, 2004. [3] P. Cheng, X. Lian, Z. Chen, L. Chen, J. Han, and J. Zhao. Reliable diversity-based spatial crowdsourcing by moving workers. arXiv preprint arXiv:1412.0223, 2014. [4] J. Cranshaw, E. Toch, J. Hong, A. Kittur, and N. Sadeh. Bridging the gap between physical location and online social networks. In Proceedings of the 12th ACM international conference on Ubiquitous computing. ACM, 2010. [5] H. Dang, T. 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In Proceedings of the 19th international conference on World wide web, pages 661{670. ACM, 2010. [16] E. Malykhina. 8 apps that turn citizens into scientists. Scientic American, 2013. [17] M. Musthag and D. Ganesan. Labor dynamics in a mobile micro-task market. In Proceedings of the SIGCHI Conference on Human Factors in Computing Systems, pages 641{650. ACM, 2013. [18] W. H. Press. Bandit solutions provide unied ethical models for randomized clinical trials and comparative eectiveness research. Proceedings of the National Academy of Sciences, 106(52):22387{22392, 2009. [19] H. Robbins. Some aspects of the sequential design of experiments. In Herbert Robbins Selected Papers, pages 169{177. Springer, 1985. [20] H. To, G. Ghinita, and C. Shahabi. A framework for protecting worker location privacy in spatial crowdsourcing. Proceedings of the VLDB Endowment, 7(10), 2014. [21] H. To, G. Ghinita, and C. Shahabi. Privgeocrowd: A toolbox for studying private spatial crowdsourcing. 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Hien To, Liyue Fan, Luan Tran, and Cyrus Shahabi. "Real-time task assignment in hyper-local spatial crowdsourcing under budget constraints." Computer Science Technical Reports (Los Angeles, California, USA: University of Southern California. Department of Computer Science) no. 962 (2015).

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