Information and Computation
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
Exploring unknown undirected graphs
Journal of Algorithms
Exploring Unknown Environments
SIAM Journal on Computing
Tree exploration with little memory
SODA '02 Proceedings of the thirteenth annual ACM-SIAM symposium on Discrete algorithms
Optimal Graph Exploration without Good Maps
ESA '02 Proceedings of the 10th Annual European Symposium on Algorithms
Distributed verification of minimum spanning trees
Proceedings of the twenty-fifth annual ACM symposium on Principles of distributed computing
Oracle size: a new measure of difficulty for communication tasks
Proceedings of the twenty-fifth annual ACM symposium on Principles of distributed computing
Tree exploration with logarithmic memory
SODA '07 Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms
Label-guided graph exploration by a finite automaton
ACM Transactions on Algorithms (TALG)
Memoryless search algorithms in a network with faulty advice
Theoretical 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
Remembering without memory: Tree exploration by asynchronous oblivious robots
Theoretical Computer Science
Local MST Computation with Short Advice
Theory of Computing Systems - Special Title: Parallelism on Algorithms and Architectures (SPAA); Guest Editors: Cyril Gavoille, Boaz Patt-Shamir and Christian Scheideler
Online computation with advice
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
Collaborative search on the plane without communication
PODC '12 Proceedings of the 2012 ACM symposium on Principles of distributed computing
Distributed computing with advice: information sensitivity of graph coloring
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
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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 [18], 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+D2/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 [18]. 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 ε, terminating the search by time O(log1−εk ·T) requires agents to use Ω(loglogk) memory bits. From a high level perspective, we illustrate how methods from distributed computing can be useful in generating lower bounds for cooperative biological ensembles. Indeed, if experiments that comply with our setting reveal that the ants' search is time efficient, then our theoretical lower bounds can provide some insight on the memory they use for this task.