Cost-Efficient Heterogeneous Worker Recruitment under Coverage Requirement in Spatial Crowdsourcing

With the progress of mobile devices and the successful forms of using the wisdom of crowds, spatial crowdsourcing has attracted much attention from the research community. The idea of spatial crowdsourcing is recruiting a set of available crowds to finish the spatial tasks located in crowdsourcing locations, e.g., landmarks, by using their handheld devices. This paper addresses the worker recruitment problem in spatial crowdsourcing under the coverage and workload-balancing requirements. The coverage constraint means that any crowdsourcing location should be visited by at least one of the recruited workers to satisfy the Quality-of-Service requirement, e.g., traffic monitoring or climate forecast. In addition, we argue that each crowdsourcing operation has a cost in reality, e.g., data traffic or energy consumption and the resource may be limited at each crowdsourcing location. The objective of this paper is to solve a Coverage and Balanced Crowdsourcing Recruiting (CBCR) problem, which ensures the coverage requirement and minimizes the maximum crowdsourcing cost for any crowdsourcing location. We prove that the CBCR problem is NP-hard in the general case. Then, we discuss the CBCR problem in the 1-D scenario. In the 1-D scenario, we first propose a directionally coverage scheme and further extend it to a Polynomial-Time Approximation Scheme (PTAS) to trade-off the computation complexity and the performance. The performance can be bounded to 2 + <inline-formula><tex-math notation="LaTeX">$\varepsilon$</tex-math><alternatives><mml:math><mml:mi>ɛ</mml:mi></mml:math><inline-graphic xlink:href="wang-ieq1-2865755.gif"/></alternatives></inline-formula>, where <inline-formula><tex-math notation="LaTeX">$\varepsilon$</tex-math><alternatives><mml:math><mml:mi>ɛ</mml:mi></mml:math><inline-graphic xlink:href="wang-ieq2-2865755.gif"/></alternatives></inline-formula> can be an arbitrary small value. Then, we found that there exists a sub-optimal structure, and thus the dynamic programming approach is proposed to find the optimal solution in the 1-D scenario. In the general 2-D scenario, we first prove that it has a sub-modular property and thus the naive greedy algorithm has an approximation ratio of <inline-formula><tex-math notation="LaTeX">$\ln n + 1$</tex-math><alternatives><mml:math><mml:mrow><mml:mo form="prefix">ln</mml:mo><mml:mi>n</mml:mi><mml:mo>+</mml:mo><mml:mn>1</mml:mn></mml:mrow></mml:math><inline-graphic xlink:href="wang-ieq3-2865755.gif"/></alternatives></inline-formula>. In addition, we propose a randomized rounding algorithm with an expectation bound of <inline-formula><tex-math notation="LaTeX">$O(\frac{\log n}{\log \;\log n})$</tex-math><alternatives><mml:math><mml:mrow><mml:mi>O</mml:mi><mml:mo>(</mml:mo><mml:mfrac><mml:mrow><mml:mo form="prefix">log</mml:mo><mml:mi>n</mml:mi></mml:mrow><mml:mrow><mml:mo form="prefix">log</mml:mo><mml:mspace width="0.277778em"/><mml:mo form="prefix">log</mml:mo><mml:mi>n</mml:mi></mml:mrow></mml:mfrac><mml:mo>)</mml:mo></mml:mrow></mml:math><inline-graphic xlink:href="wang-ieq4-2865755.gif"/></alternatives></inline-formula>. Extensive experiments on realistic traces demonstrate the effectiveness of the proposed algorithms.