Abstract
We study a covering problem motivated by spatial models in crowdsourcing markets, where tasks are ordered according to some geographic or temporal criterion. Assuming that each participating bidder can provide a certain level of contribution for a subset of consecutive tasks, and that each task has a demand requirement, the goal is to find a set of bidders of minimum cost, who can meet all the demand constraints. Our focus is on truthful mechanisms with approximation guarantees against the optimal cost. To this end, we obtain two main results. The first one, is a truthful mechanism that achieves a bounded approximation guarantee. This mechanism improves the state of the art, which is a mechanism with an arbitrarily large factor in worst case. The second one, concerns a class of instances that generalizes the minimum knapsack problem. Namely, we consider inputs with a constant number of tasks, for which we provide a truthful FPTAS. Finally, we also highlight connections of our problem with other well-studied optimization problems, out of which, we infer further conclusions on its (in)approximability.
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Notes
- 1.
It is convenient to highlight the dependence on \(\textbf{b}\), especially when arguing about truthful mechanisms in the remaining sections.
- 2.
For a similar reason, the 40-approximation for cmic by [11], which uses as a subroutine a primal-dual algorithm involving a “delete phase”, is non-monotone as well.
- 3.
Originally, the problem was defined using a semi-closed interval for each activity, but it is easy to see that defining it using a closed one instead, is equivalent and more convenient for our purposes.
- 4.
It becomes clear in the next subsection, that the dynamic programming procedure is only needed for integral cost values.
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Acknowledgement
This research was supported by the Hellenic Foundation for Research and Innovation. The first two authors were supported by the “1st Call for HFRI Research Projects to support faculty members and researchers and the procurement of high-cost research equipment” (Project Num. HFRI-FM17-3512) and the third author by the HFRI PhD Fellowship grant (Fellowship Num. 289).
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Markakis, E., Papasotiropoulos, G., Tsikiridis, A. (2022). On Improved Interval Cover Mechanisms for Crowdsourcing Markets. In: Kanellopoulos, P., Kyropoulou, M., Voudouris, A. (eds) Algorithmic Game Theory. SAGT 2022. Lecture Notes in Computer Science, vol 13584. Springer, Cham. https://doi.org/10.1007/978-3-031-15714-1_6
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