A linear time algorithm for computing a most reliable source on a tree network with faulty nodes

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 85287-5406, United States
Venue:
Theoretical Computer Science
Year:
2011

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Abstract

Given an unreliable communication network, we seek for a node which maximizes the expected number of nodes that are reachable from it. Such a node is called a most reliable source (MRS) of the network. In communication networks, failures may occur to both links and nodes. Previous studies have considered the case where each link has an independent operational probability, while the nodes are immune to failures. In practice, however, failures may happen to the nodes as well, including both transmitting fault and receiving fault. Recently, another variant of the MRS problem is studied, where all links are immune to failures and each node has an independent transmitting probability and receiving probability, and an O(n^2) time algorithm is presented for computing an MRS on tree networks with n nodes. In this paper, we present a faster algorithm for this problem, with a time complexity of O(n).