Trade-offs between selection complexity and performance when searching the plane without communication
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Lynch_Trade-offs.pdf
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Author(s)
Lenzen, Christoph
Newport, Calvin Charles
Lynch, Nancy A.
Radeva, Tsvetomira T.
Date Issued
July 2014
Journal
Proceedings of the 2014 ACM symposium on Principles of distributed computing (PODC '14)
Publisher
Association for Computing Machinery (ACM)
Citation
Christoph Lenzen, Nancy Lynch, Calvin Newport, and Tsvetomira Radeva. 2014. Trade-offs between selection complexity and performance when searching the plane without communication. In Proceedings of the 2014 ACM symposium on Principles of distributed computing (PODC '14). ACM, New York, NY, USA, 252-261.
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Author's final manuscript
Abstract
We argue that in the context of biology-inspired problems in computer science, in addition to studying the time complexity of solutions it is also important to study the selection complexity, a measure of how likely a given algorithmic strategy is to arise in nature. In this spirit, we propose a selection complexity metric χ for the ANTS problem [Feinerman et al.]. For algorithm A, we define χ(A) = b + log l, where b is the number of memory bits used by each agent and l bounds the fineness of available probabilities (agents use probabilities of at least 1/2[superscript l]). We consider n agents searching for a target in the plane, within an (unknown) distance D from the origin. We identify log log D as a crucial threshold for our selection complexity metric. We prove a new upper bound that achieves near-optimal speed-up of (D[superscript 2]/n +D) ⋅ 2[superscript O(l)] for χ(A) ≤ 3 log log D + O(1), which is asymptotically optimal if l∈ O(1). By comparison, previous algorithms achieving similar speed-up require χ(A) = Ω(log D). We show that this threshold is tight by proving that if χ(A) < log log D - ω(1), then with high probability the target is not found if each agent performs D[superscript 2-o(1)] moves. This constitutes a sizable gap to the straightforward Ω(D[superscript 2]/n + D) lower bound.
MIT Department
Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
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DOI of Published Version
https://doi.org/10.1145/2611462.2611463
