The backup 2-center and backup 2-median problems on trees

  • Authors:

  • Hung-Lung Wang;Bang Ye Wu;Kun-Mao Chao

  • Affiliations:

  • Department of Computer Science and Information Engineering, National Taiwan University, Taipei, Taiwan 106;Department of Computer Science and Information Engineering, National Chung Cheng University, Min-Hsiung, Chiayi, Taiwan 621;Dept. of Comp. Sci. and Info. Eng., Natnl. Taiwan Univ., Taipei and Grad. Inst. of Biomed. Electr. and Bioinfo., Natnl. Taiwan Univ., Taipei and Grad. Inst. of Netwkg. and Multimedia, Natnl. Taiwa ...

  • Venue:
  • Networks
  • Year:
  • 2009

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Abstract

In this paper, we are concerned with the problem of deploying two servers in a tree network, where each server may fail with a given probability. Once a server fails, the other server will take full responsibility for the services. Here, we assume that the servers do not fail simultaneously. In the backup 2-center problem, we want to deploy two servers at the vertices such that the expected distance from a farthest vertex to the closest functioning server is minimum. In the backup 2-median problem, we want to deploy two servers at the vertices such that the expected sum of distances from all vertices to the set of functioning servers is minimum. We propose an O(n)-time algorithm for the backup 2-center problem and an O(n log n)-time algorithm for the backup 2-median problem, where n is the number of vertices in the given tree network. © 2008 Wiley Periodicals, Inc. NETWORKS, 2009