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 , where b is the number of memory bits used by each agent and bounds the fineness of available probabilities (agents use probabilities of at least 1/2 ). 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 2 /n + D) · 2 O( ) for χ(A) ≤ 3 log log D + O(1), which is asymptotically optimal if ∈ 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 2−o(1) moves. This constitutes a sizable gap to the straightforward Ω(D 2 /n + D) lower bound.
The ANTS problem was further studied by Lenzen et al., who investigated the effects of bounding the memory as well as the range of available probabilities of the agents REF .
Trade-offs between selection complexity and performance when searching the plane without communication
PODC '14
Computer Science