Collaborative search on the plane without communication
Ofer Feinerman, Amos Korman (LIAFA, GANG), Zvi Lotker (UPD7),, Jean-S\'ebastien Sereni (MASCOTTE)

TL;DR
This paper studies a biologically inspired multi-agent search problem in the plane, analyzing how limited or no communication affects search efficiency and establishing bounds on the competitiveness of search algorithms based on knowledge of the number of agents.
Contribution
It provides tight bounds on search efficiency with and without knowledge of the number of agents, highlighting the importance of this knowledge in communication-limited environments.
Findings
Knowledge of the number of agents k is crucial for optimal search performance.
Without knowledge of k, no algorithm can be O(log k)-competitive.
A simple algorithm achieves O(log^{1+ε} k)-competitiveness when k is unknown.
Abstract
We generalize the classical cow-path problem [7, 14, 38, 39] into a question that is relevant for collective foraging in animal groups. Specifically, we consider a setting in which k identical (probabilistic) agents, initially placed at some central location, collectively search for a treasure in the two-dimensional plane. The treasure is placed at a target location by an adversary and the goal is to find it as fast as possible as a function of both k and D, where D is the distance between the central location and the target. This is biologically motivated by cooperative, central place foraging such as performed by ants around their nest. In this type of search there is a strong preference to locate nearby food sources before those that are further away. Our focus is on trying to find what can be achieved if communication is limited or altogether absent. Indeed, to avoid overlaps agents…
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