The Cost of Monotonicity in Distributed Graph Searching

Abstract. 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 nnode 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 info...

• Type: Conference
• Year: 2007
• Where: OPODIS
• Authors: David Ilcinkas, Nicolas Nisse, David Soguet
• Keywords: Blin Et Al, Distributed And Parallel Computing, OPODIS 2007, Searchers, Smallest Number