A fast parallel algorithm for finding a most reliable source on a general ring-tree graph with unreliable edges

Authors:
Wei Ding;Guoliang Xue
Affiliations:
Zhejiang Water Conservancy and Hydropower College, Hangzhou, Zhejiang, China;Department of Computer Science and Engineering, Arizona State University, Tempe, AZ
Venue:
COCOA'11 Proceedings of the 5th international conference on Combinatorial optimization and applications
Year:
2011

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Abstract

Given an unreliable communication network, we aim to find a most reliable source (MRS) on the network, which maximizes the expected number of nodes that are reachable from it. Although the problem of finding an MRS on general graphs is #P-hard, it is tractable in several types of sparse graphs. The ring-tree graph is such a kind of sparse graph that not only has the capability of failure tolerance but also holds an underlying tree topology which facilitates network administration. In this paper, we are concerned with unreliable general ring-tree graphs in which each edge has an independent operational probability while all nodes are immune to failures. We first design a complementary dynamic programming algorithm and then develop a parallel algorithm based on the underlying tree for finding an MRS on the network.