Information and Computation
A heuristic with worst-case analysis for minimax routing of two travelling salesmen on a tree
Discrete Applied Mathematics
Searching in an unknown environment: an optimal randomized algorithm for the cow-path problem
Information and Computation
(p-1)/(p+1)-approximate algorithms for p-traveling salemen problems on a tree with minmax objective
Discrete Applied Mathematics
Distributed Anonymous Mobile Robots: Formation of Geometric Patterns
SIAM Journal on Computing
The harmonic k-server algorithm is competitive
Journal of the ACM (JACM)
Exploring unknown undirected graphs
Journal of Algorithms
Exploring Unknown Environments
SIAM Journal on Computing
The power of a pebble: exploring and mapping directed graphs
Information and Computation
Tree exploration with little memory
Journal of Algorithms
Optimal graph exploration without good maps
Theoretical Computer Science
Coordination without communication: the case of the flocking problem
Discrete Applied Mathematics - Fun with algorithms 2 (FUN 2001)
Gathering of asynchronous robots with limited visibility
Theoretical Computer Science
Fault-Tolerant Gathering Algorithms for Autonomous Mobile Robots
SIAM Journal on Computing
Erratum: Distributed Anonymous Mobile Robots: Formation of Geometric Patterns
SIAM Journal on Computing
Networks
Optimal constrained graph exploration
ACM Transactions on Algorithms (TALG)
Online searching with turn cost
Theoretical Computer Science - Approximation and online algorithms
Tree exploration with logarithmic memory
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Cooperative Cleaners: A Study in Ant Robotics
International Journal of Robotics Research
Journal of Graph Theory
On a search problem related to branch-and-bound procedures
SFCS '86 Proceedings of the 27th Annual Symposium on Foundations of Computer Science
Undirected connectivity in log-space
Journal of the ACM (JACM)
SODA '09 Proceedings of the twentieth Annual ACM-SIAM Symposium on Discrete Algorithms
On the computational power of oblivious robots: forming a series of geometric patterns
Proceedings of the 29th ACM SIGACT-SIGOPS symposium on Principles of distributed computing
Multiple Random Walks in Random Regular Graphs
SIAM Journal on Discrete Mathematics
Tree exploration with logarithmic memory
ACM Transactions on Algorithms (TALG)
Tight bounds for the cover time of multiple random walks
Theoretical Computer Science
Toward more localized local algorithms: removing assumptions concerning global knowledge
Proceedings of the 30th annual ACM SIGACT-SIGOPS symposium on Principles of distributed computing
How many oblivious robots can explore a line
Information Processing Letters
FOCS '11 Proceedings of the 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science
Physarum can compute shortest paths
Proceedings of the twenty-third annual ACM-SIAM symposium on Discrete Algorithms
Exploring an unknown graph efficiently
ESA'05 Proceedings of the 13th annual European conference on Algorithms
Many random walks are faster than one
Combinatorics, Probability and Computing
Memory lower bounds for randomized collaborative search and implications for biology
DISC'12 Proceedings of the 26th international conference on Distributed Computing
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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 + D2/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 some information regarding k. Finally, we propose a uniform algorithm that is both efficient and extremely simple, suggesting its relevance for actual biological scenarios.