An anytime assignment algorithm: From local task swapping to global optimality
 Lantao Liu,
 Dylan A. Shell
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The assignment problem arises in multirobot taskallocation scenarios. Inspired by existing techniques that employ task exchanges between robots, this paper introduces an algorithm for solving the assignment problem that has several appealing features for online, distributed robotics applications. The method may start with any initial matching and incrementally improve the current solution to reach the global optimum, producing valid assignments at any intermediate point. It is an anytime algorithm with a performance profile that is attractive: quality improves linearly with stages (or time). Additionally, the algorithm is comparatively straightforward to implement and is efficient both theoretically (complexity of \(O(n^3\lg n)\) is better than many widely used solvers) and practically (comparable to the fastest implementation, for up to hundreds of robots/tasks). The algorithm generalizes “swap” primitives used by existing task exchange methods already used in the robotics community but, uniquely, is able to obtain global optimality via communication with only a subset of robots during each stage. We present a centralized version of the algorithm and two decentralized variants that trade between computational and communication complexity. The centralized version turns out to be a computational improvement and reinterpretation of the littleknown method of Balinski–Gomory proposed half a century ago. Thus, deeper understanding of the relationship between approximate swapbased techniques—developed by roboticists—and combinatorial optimization techniques, e.g., the Hungarian and Auction algorithms—developed by operations researchers but used extensively by roboticists—is uncovered.
 Title
 An anytime assignment algorithm: From local task swapping to global optimality
 Journal

Autonomous Robots
Volume 35, Issue 4 , pp 271286
 Cover Date
 201311
 DOI
 10.1007/s1051401393512
 Print ISSN
 09295593
 Online ISSN
 15737527
 Publisher
 Springer US
 Additional Links
 Topics
 Keywords

 Multirobot task allocation
 Decentralized assignment
 Anytime algorithms
 Task swapping
 Industry Sectors
 Authors

 Lantao Liu ^{(1)}
 Dylan A. Shell ^{(1)}
 Author Affiliations

 1. Department of Computer Science and Engineering, Texas A&M University, College Station, TX, USA