Threshold dominating cliques in random graphs and interval routing

Authors:
Yong Gao
Affiliations:
Department of Computer Science, Irving K. Barber School of Arts and Sciences, University of British Columbia Okanagan, Kelowna, Canada V1V 1V7
Venue:
Journal of Discrete Algorithms
Year:
2009

Citing 7
Cited 1

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A survey on interval routing

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An exact algorithm for the minimum dominating clique problem

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IJCAI'05 Proceedings of the 19th international joint conference on Artificial intelligence
Random instances of W[2]-complete problems: thresholds, complexity, and algorithms

SAT'08 Proceedings of the 11th international conference on Theory and applications of satisfiability testing
An improved interval routing scheme for almost all networks based on dominating cliques

ISAAC'05 Proceedings of the 16th international conference on Algorithms and Computation

The complexity of connected dominating sets and total dominating sets with specified induced subgraphs

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Abstract

The existence of (shortest-path) interval routing schemes for random graphs that use at most one interval label per edge is an open problem posed in [C. Gavoille, D. Peleg, The compactness of interval routing for almost all graphs, SIAM J. Computing 31 (3) (2001) 706-721]. In this paper, we show that for any random graph G(n,p) with edge probability p0.765, there exists an interval routing scheme that uses at most one label per edge and has an additive stretch 1. In doing so, we provide an interesting construction of such an interval routing scheme for graphs that have a 12-threshold dominating clique, and establish a general result on the existence of threshold dominating cliques in random graphs.