The delivery man problem and cumulative matroids
Operations Research
STOC '94 Proceedings of the twenty-sixth annual ACM symposium on Theory of computing
Polynomial time algorithms for some minimum latency problems
Information Processing Letters
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Faster approximation algorithms for the minimum latency problem
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
Paths, Trees, and Minimum Latency Tours
FOCS '03 Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science
Approximation Algorithms for Orienteering and Discounted-Reward TSP
SIAM Journal on Computing
P-complete problems and approximate solutions
SWAT '74 Proceedings of the 15th Annual Symposium on Switching and Automata Theory (swat 1974)
The power of sequential single-item auctions for agent coordination
AAAI'06 proceedings of the 21st national conference on Artificial intelligence - Volume 2
Multiple agents maximum collection problem with time dependent rewards
Computers and Industrial Engineering
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We study multi-robot routing problems (MR-LDR) where a team of robots has to visit a set of given targets with linear decreasing rewards over time, such as required for the delivery of goods to rescue sites after disasters. The objective of MR-LDR is to find an assignment of targets to robots and a path for each robot that maximizes the surplus, which is defined to be the total reward collected by the team minus its total travel cost. We develop a mixed integer program that solves MR-LDR optimally with a flow-type formulation and can be solved faster than the standard TSP-type formulations but also show that solving MR-LDR optimally is NP-hard. We then develop an auction-based algorithm and demonstrate that it solves MR-LDR in seconds and with a surplus that is comparable to the surplus found by the mixed integer program with a 12 hour time limit.