Time and energy in team-based search

N searchers are sent out by a source in order to locate a fixed object which is at a finite distance D, but the search space is infinite and D would be in general unknown. Each of the searchers has a finite random lifetime , and may be subject to destruction or failures, and it moves independently of other searchers, and at intermediate locations some partial random information may be available about which way to go. When a searcher is destroyed or disabled, or when it " dies naturally " , after some time the source becomes aware of this and it sends out another searcher, which proceeds similarly to the one that it replaces. The search ends when one of the searchers finds the object being sought. We use N coupled Brownian motions to derive a closed form expression for the average search time as a function of D which will depend on the parameters of the problem: the number of searchers, the average lifetime of searchers, the routing uncertainty, and the failure or destruction rate of searchers. We also examine the cost in terms of the total energy that is expended in the search.

Proceedings of the 2012 ACM symposium on Principles of distributed computing - PODC '12, 2012

We use distributed computing tools to provide a new perspective on the behavior of cooperative biological ensembles. We introduce the Ants Nearby Treasure Search (ANTS) problem, a generalization of the classical cow-path problem [10, 20, 41, 42], which is relevant for collective foraging in animal groups. In the ANTS problem, 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. We focus on trying to find what can be achieved if communication is limited or altogether absent. Indeed, to avoid overlaps agents must be highly dispersed making communication difficult. Furthermore, if the agents do not commence the search in synchrony, then even initial communication is problematic. This holds, in particular, with respect to the question of whether the agents can communicate and conclude their total number, k. It turns out that the knowledge of k by the individual agents is crucial for performance. Indeed, it is a straightforward observation that the time required for finding the treasure is Ω(D + D 2 /k), and we show in this paper that this bound can be matched if the agents have knowledge of k up to some constant approximation. We present a tight bound for the competitive penalty that must be paid, in the running time, if the agents have no information about k. Specifically, this bound is slightly more than logarithmic in the number of agents. In addition, we give a lower bound for the setting in which the agents are given some estimation of k. Informally, our results imply that the agents can potentially perform well without any knowledge of their total number k, however, to further improve, they must use non trivial information regarding k. Finally, we propose a uniform algorithm that is both efficient and extremely simple, suggesting its relevance for actual biological scenarios.

Lecture Notes in Computer Science, 2012

Initial knowledge regarding group size can be crucial for collective performance. We study this relation in the context of the Ants Nearby Treasure Search (ANTS) problem [24], which models natural cooperative foraging behavior such as that performed by ants around their nest. In this problem, k (probabilistic) agents, initially placed at some 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 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. It is easy to see that T = Ω(D + D 2 /k) time units are necessary for finding the treasure. Recently, it has been established that O(T) time is sufficient if the agents know their total number k (or a constant approximation of it), and enough memory bits are available at their disposal [24]. In this paper, we establish lower bounds on the agent memory size required for achieving certain running time performances. To the best our knowledge, these bounds are the first non-trivial lower bounds for the memory size of probabilistic searchers. For example, for every given positive constant ǫ, terminating the search by time O(log 1−ǫ k • T) requires agents to use Ω(log log k) memory bits. Such distributed computing bounds may provide a novel, strong tool for the investigation of complex biological systems.

Delta Journal of Science

The coordinated search problem faced by two searchers who start together from some point on the line in order to search for a lost target which randomly located on the line. In this paper the distribution of the lost target is symmetric around the point of the intersection of two lines, where the intersected point is a starting point of the motion of the searchers. There are four searchers start together the search for the lost target at the intersection point under this condition we defined the search plan and computed the expected value of the first meeting time between one of the searchers and the target. The search plan which minimized this first meeting time is studied. Finally we obtained some special cases for a search problems. An illustrative examples is given to demonstrate the applicability of this model.

Applied Mathematics, 2019

This paper presents the search technique for a lost target. A lost target is random walker on one of two intersected real lines, and the purpose is to detect the target as fast as possible. We have four searchers start from the point of intersection, they follow the so called Quasi-Coordinated search plan. The expected value of the first meeting time between one of the searchers and the target is investigated, also we show the existence of the optimal search strategy which minimizes this first meeting time.