The complexity of searching a graph
Journal of the ACM (JACM)
Monotonicity in graph searching
Journal of Algorithms
Recontamination does not help to search a graph
Journal of the ACM (JACM)
Capture of an intruder by mobile agents
Proceedings of the fourteenth annual ACM symposium on Parallel algorithms and architectures
Contiguous Search in the Hypercube for Capturing an Intruder
IPDPS '05 Proceedings of the 19th IEEE International Parallel and Distributed Processing Symposium (IPDPS'05) - Papers - Volume 01
Intruder capture in Sierpinski graphs
FUN'07 Proceedings of the 4th international conference on Fun with algorithms
SIROCCO'07 Proceedings of the 14th international conference on Structural information and communication complexity
Monotony properties of connected visible graph searching
WG'06 Proceedings of the 32nd international conference on Graph-Theoretic Concepts in Computer Science
Distributed chasing of network intruders
SIROCCO'06 Proceedings of the 13th international conference on Structural Information and Communication Complexity
Sweeping graphs with large clique number
ISAAC'04 Proceedings of the 15th international conference on Algorithms and Computation
Connected treewidth and connected graph searching
LATIN'06 Proceedings of the 7th Latin American conference on Theoretical Informatics
A Self-stabilizing Algorithm for Graph Searching in Trees
SSS '09 Proceedings of the 11th International Symposium on Stabilization, Safety, and Security of Distributed Systems
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Blin et al. (2006) proposed a distributed protocol that enables the smallest number of searchers to clear any unknown asynchronous graph in a decentralized manner. Unknown means that the searchers are provided no a priori information about the graph. However, the strategy that is actually performed lacks of an important property, namely the monotonicity. That is, the clear part of the graph may decrease at some steps of the execution of the protocol. Actually, the protocol of Blin et al. is executed in exponential time. Nisse and Soguet (2007) proved that, in order to ensure the smallest number of searchers to clear any n-node graph in a monotone way, it is necessary and sufficient to provide Θ(n log n) bits of information to the searchers by putting short labels on the nodes of the graph. This paper deals with the smallest number of searchers that are necessary and sufficient to monotoneously clear any graph in a decentralized manner, when the searchers have no a priori information about the graph. The distributed graph searching problem considers a team of searchers that is aiming at clearing any connected contaminated graph. The clearing of the graph is required to be connected, i.e., the clear part of the graph must remain permanently connected, and monotone, i.e., the clear part of the graph only grows. The search number mcs(G) of a graph G is the smallest number of searchers necessary to clear G in a monotone connected way in centralized settings. We prove that any distributed protocol aiming at clearing any unknown n-node graph in a monotone connected way, in decentralized settings, has competitive ratio Θ(n/lon n). That is, we prove that, for any distributed protocol P, there exists a constant c such that for any sufficiently large n, there exists a n-node graph G such that P requires at least c n/lon n mcs(G) searchers to clear G. Moreover, we propose a distributed protocol that allows O(n/log n) mcs(G) searchers to clear any unknown asynchronous n-node graph G in a monotone connected way.