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
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
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
An annotated bibliography on guaranteed graph searching
Theoretical Computer Science
Trade-offs between the size of advice and broadcasting time in trees
Proceedings of the twentieth annual symposium on Parallelism in algorithms and architectures
Fast Radio Broadcasting with Advice
SIROCCO '08 Proceedings of the 15th international colloquium on Structural Information and Communication Complexity
r3: Resilient Random Regular Graphs
DISC '08 Proceedings of the 22nd international symposium on Distributed Computing
Information and Computation
Online Computation with Advice
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
Fast radio broadcasting with advice
Theoretical Computer Science
Communication algorithms with advice
Journal of Computer and System Sciences
The cost of monotonicity in distributed graph searching
OPODIS'07 Proceedings of the 11th international conference on Principles of distributed systems
DISC'10 Proceedings of the 24th international conference on Distributed computing
Online computation with advice
Theoretical Computer Science
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Fraigniaud et al. (2006) 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 capture an invisible and arbitrarily fast fugitive 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. We show that the minimum number of bits of advice permitting the monotone connected clearing of a network in a distributed setting is O(n log n), where n is the number of nodes of the network, and this bound is tight. More precisely, we first provide a labelling of the vertices of any graph G, using a total of O(n log n) bits, and a protocol using this labelling that enables clearing G in a monotone connected distributed way. Then, we show that this number of bits of advice is almost optimal: no protocol using an oracle providing o(n log n) bits of advice permits the monotone connected clearing of a network using the smallest number of searchers.