Trade-offs between selection complexity and performance when searching the plane without communication
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 sel...
| Main Authors: | , , , |
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| Other Authors: | |
| Format: | Article |
| Language: | en_US |
| Published: |
Association for Computing Machinery (ACM)
2016
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| Online Access: | http://hdl.handle.net/1721.1/100845 https://orcid.org/0000-0003-3045-265X https://orcid.org/0000-0003-1261-6681 |
| Summary: | 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. |
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