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)
Graph searching and a min-max theorem for tree-width
Journal of Combinatorial Theory Series B
Selective families, superimposed codes, and broadcasting on unknown radio networks
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Capture of an intruder by mobile agents
Proceedings of the fourteenth annual ACM symposium on Parallel algorithms and architectures
The power of a pebble: exploring and mapping directed graphs
Information and Computation
Compact and localized distributed data structures
Distributed Computing - Papers in celebration of the 20th anniversary of PODC
Hundreds of impossibility results for distributed computing
Distributed Computing - Papers in celebration of the 20th anniversary of PODC
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
Oracle size: a new measure of difficulty for communication tasks
Proceedings of the twenty-fifth annual ACM symposium on Principles of distributed computing
Local MST computation with short advice
Proceedings of the nineteenth annual ACM symposium on Parallel algorithms and architectures
Decontamination of chordal rings and tori
IPDPS'06 Proceedings of the 20th international conference on Parallel and distributed processing
Distributed chasing of network intruders
SIROCCO'06 Proceedings of the 13th international conference on Structural Information and Communication Complexity
Tree exploration with an oracle
MFCS'06 Proceedings of the 31st international conference on Mathematical Foundations of Computer Science
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
Distributed computing with advice: information sensitivity of graph coloring
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
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
Journal of Parallel and Distributed Computing
Information and Computation
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Fraigniaud et al. [L. Blin, P. Fraigniaud, N. Nisse, S. Vial, Distributing chasing of network intruders, in: 13th Colloquium on Structural Information and Communication Complexity, SIROCCO, in: LNCS, vol. 4056, Springer-Verlag, 2006, pp. 70-84] introduced a new measure of difficulty for a distributed task in a network. The smallest number of bits of advice of a distributed problem is the smallest number of bits of information that has to be available to nodes in order to accomplish the task efficiently. Our paper deals with the number of bits of advice required to perform efficiently the graph searching problem in a distributed setting. In this variant of the problem, all searchers are initially placed at a particular node of the network. The aim of the team of searchers is to clear a contaminated graph in a monotone connected way, i.e., the cleared part of the graph is permanently connected, and never decreases while the search strategy is executed. Moreover, the clearing of the graph must be performed using the optimal number of searchers, i.e. the minimum number of searchers sufficient to clear the graph in a monotone connected way in a centralized setting. We show that the minimum number of bits of advice permitting the monotone connected and optimal clearing of a network in a distributed setting is @Q(nlogn), where n is the number of nodes of the network. More precisely, we first provide a labelling of the vertices of any graph G, using a total of O(nlogn) bits, and a protocol using this labelling that enables the optimal number of searchers to clear G in a monotone connected distributed way. Then, we show that this number of bits of advice is optimal: any distributed protocol requires @W(nlogn) bits of advice to clear a network in a monotone connected way, using an optimal number of searchers.