Minimizing the Maximum Delay for Reaching Consensus in Quorum-Based Mutual Exclusion Schemes

  • Authors:
  • Tatsuhiro Tsuchiya;Masatoshi Yamaguchi;Tohru Kikuno

  • Affiliations:
  • Osaka Univ., Toyonaka, Japan;Sumitomo Corp., Toyonaka, Japan;Osaka Univ., Toyonaka, Japan

  • Venue:
  • IEEE Transactions on Parallel and Distributed Systems
  • Year:
  • 1999

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Abstract

The use of quorums is a well-known approach to achieving mutual exclusion in distributed computing systems. This approach works based on a coterie, a special set of node groups where any pair of the node groups shares at least one common node. Each node group in a coterie is called a quorum. Mutual exclusion is ensured by imposing that a node gets consensus from all nodes in at least one of the quorums before it enters a critical section. In a quorum-based mutual exclusion scheme, the delay for reaching consensus depends critically on the coterie adopted and, thus, it is important to find a coterie with small delay. In [5], Fu introduced two related measures called max-delay and mean-delay. The former measure represents the largest delay among all nodes, while the latter is the arithmetic mean of the delays. She proposed polynomial-time algorithms for finding max-delay and mean-delay optimal coteries when the network topology is a tree or a ring. In this paper, we first propose a polynomial-time algorithm for finding max-delay optimal coteries and, then, modify the algorithm so as to reduce the mean-delay of generated coteries. Unlike the previous algorithms, the proposed algorithms can be applied to systems with arbitrary topology.