A Linear Time Algorithm for Computing the Most Reliable Source on a Tree with Faulty Vertices

  • Authors:

  • Wei Ding;Guoliang Xue

  • Affiliations:

  • Zhejiang Water Conservancy and Hydropower College, Hangzhou, China 310018;Department of Computer Science and Engineering, Arizona State University, Tempe, USA AZ 85287-8809

  • Venue:
  • COCOA '09 Proceedings of the 3rd International Conference on Combinatorial Optimization and Applications
  • Year:
  • 2009

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Abstract

Given an unreliable communication network, we seek for determining a vertex from the network, the expected number of vertices which connects to is maximum. Such vertex is named the most reliable source (MRS) on the network. The communication failures may occur to links or vertices of the network. The case was generally studied, where no failure happens to each vertex and each link has an independent operational probability. Practically, failures frequently happen to the vertices, including the transmitting fault and receiving fault. Recently, another case is proposed, where each link is steady and each vertex has an independent transmitting probability and receiving probability, and an $\mathcal{O}(n^2)$ time algorithm is presented for computing the MRS on such tree networks with n vertices. In this paper, we propose a faster algorithm for this case, whose time complexity is $\mathcal{O}(n)$.