A Graph Parameter That Matches the Resilience of the Certified Propagation Algorithm

Abstract

We consider the Secure Broadcast problem in incomplete networks. We study the resilience of the Certified Propagation Algorithm (CPA), which is particularly suitable for ad hoc networks. We address the issue of determining the maximum number of corrupted players $t^{\rm CPA}_{\rm max}$ that CPA can tolerate under the t-locally bounded adversary model, in which the adversary may corrupt at most t players in each player’s neighborhood. For any graph G and dealer-node D we provide upper and lower bounds on $t^{\rm CPA}_{\rm max}$ that can be efficiently computed in terms of a graph theoretic parameter that we introduce in this work. Along the way we obtain an efficient 2-approximation algorithm for $t^{\rm CPA}_{\rm max}$. We further introduce two more graph parameters, one of which matches $t^{\rm CPA}_{\rm max}$ exactly.

Work supported by ALGONOW project of the Research Funding Program THALIS, co-financed by the European Union (European Social Fund – ESF) and Greek national funds through the Operational Program “Education and Lifelong Learning” of the National Strategic Reference Framework (NSRF).