The ANTS problem

Abstract

We introduce the Ants Nearby Treasure Search (ANTS) problem, which models natural cooperative foraging behavior such as that performed by ants around their nest. In this problem, k probabilistic agents, initially placed at a central location, collectively search for a treasure on the two-dimensional grid. The treasure is placed at a target location by an adversary and the agents' goal is to find it as fast as possible as a function of both k and D, where D is the (unknown) distance between the central location and the target. We concentrate on the case in which agents cannot communicate while searching. It is straightforward to see that the time until at least one agent finds the target is at least $\Omega$(D + D 2 /k), even for very sophisticated agents, with unrestricted memory. Our algorithmic analysis aims at establishing connections between the time complexity and the initial knowledge held by agents (e.g., regarding their total number k), as they commence the search. We provide a range of both upper and lower bounds for the initial knowledge required for obtaining fast running time. For example, we prove that log log k + $\Theta$(1) bits of initial information are both necessary and sufficient to obtain asymptotically optimal running time, i.e., O(D +D 2 /k). We also we prove that for every 0 \textless{} \textless{} 1, running in time O(log 1-- k $\times$(D +D 2 /k)) requires that agents have the capacity for storing $\Omega$(log k) different states as they leave the nest to start the search. To the best of our knowledge, the lower bounds presented in this paper provide the first non-trivial lower bounds on the memory complexity of probabilistic agents in the context of search problems. We view this paper as a "proof of concept" for a new type of interdisciplinary methodology. To fully demonstrate this methodology, the theoretical tradeoff presented here (or a similar one) should be combined with measurements of the time performance of searching ants.Comment: arXiv admin note: text overlap with arXiv:1205.454

Limits on reliable information flows through stochastic populations

“…As such, our theorems are general enough to constrain the performances of a vast class of computational systems regardless of their particulars or the specific computational algorithms which they apply. This generality stretches over to biology and can provide us with fundamental lessons regarding the limitations faced by distributed biological systems [ 24 – 26 ].…”

ANTS on a Plane

“…How can multiple simple searchers best find a target? Feinerman, Korman and others formalized this question by defining the ANTS (Ants Nearby Treasure Search) problem, where many searchers, all starting at a central location, seek a hidden target [9][10][11]. In this paper, we extend results on the ANTS problem in two key directions.…”

“…Table 1. A comparison of GoldenFA and the algorithms by Feinerman and Korman [10] (abbreviated as F&K). While the latter are not provably robust against adversarial crash failures, GoldenFA can efficiently handle all but one searchers to fail, even when these failures are scheduled by an adaptive adversary.…”

Evacuating Two Robots from a Disk: A Second Cut

“…A problem closely related to evacuation is the search problem. Especially the problem of finding a specific point on the line has received considerable attention, e.g., [2,3,16], and other works have focused on searching the plane, e.g., [15]. Another related problem is the rendezvous or gathering problem, where robots initially located at different points need to find each other [1,6,7,17,21].…”