Trade-offs between selection complexity and performance when searching the plane without communication

• Main Authors: Lenzen, Christoph (Contributor), Newport, Calvin Charles (Author), Lynch, Nancy Ann (Contributor), Radeva, Tsvetomira T. (Contributor)
• Other Authors: Massachusetts Institute of Technology. Computer Science and Artificial Intelligence Laboratory (Contributor), Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science (Contributor)
• Format: Article
• Language: English
• Published: Association for Computing Machinery (ACM), 2016-01-15T02:33:01Z.
• Subjects: Article
• Online Access: Get fulltext

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.
United States. Air Force Office of Scientific Research (Contract FA9550-13-1-0042)
National Science Foundation (U.S.) (Award 0939370-CCF)
National Science Foundation (U.S.) (Award CCF-1217506)
National Science Foundation (U.S.) (Award CCF-AF-0937274)
National Science Foundation (U.S.) (Award CCF 1320279)
Deutsche Forschungsgemeinschaft (Le 3107/1-1)
Ford Motor Company. University Research Program