TY - JOUR

T1 - The ANTS problem

AU - Feinerman, Ofer

AU - Korman, Amos

N1 - Clore Foundation; Israel Science Foundation [833/15]; ANR project DISPLEXITY; ANR project PROSE; INRIA project GANG; European Research Council (ERC) under the European Union's Horizon research and innovation programme [648032]O.F., incumbent of the Shlomo and Michla Tomarin Career Development Chair, was partially supported by the Clore Foundation and the Israel Science Foundation (grant 833/15). A. K. was partially supported by the ANR projects DISPLEXITY and PROSE, and by the INRIA project GANG.; This project has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant agreement No 648032). O.F., incumbent of the Shlomo and Michla Tomarin Career Development Chair, was partially supported by the Clore Foundation and the Israel Science Foundation (grant 833/15). A. K. was partially supported by the ANR projects DISPLEXITY and PROSE, and by the INRIA project GANG.; This project has received funding from the European Research Council (ERC) under the European Union's Horizon 2020 research and innovation programme (grant agreement No 648032).

PY - 2017/6

Y1 - 2017/6

N2 - We introduce the Ants Nearby Treasure Search 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 unrestrictedmemory. 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 <epsilon <1, running in time O(log(1-epsilon) k . (D + D-2/k)) requires that agents have the capacity for storing Omega(log(epsilon) 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.

AB - We introduce the Ants Nearby Treasure Search 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 unrestrictedmemory. 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 <epsilon <1, running in time O(log(1-epsilon) k . (D + D-2/k)) requires that agents have the capacity for storing Omega(log(epsilon) 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.

U2 - https://doi.org/10.1007/s00446-016-0285-8

DO - https://doi.org/10.1007/s00446-016-0285-8

M3 - مقالة

SN - 0178-2770

VL - 30

SP - 149

EP - 168

JO - Distributed Computing

JF - Distributed Computing

IS - 3

ER -