Permutation routing in double-loop networks: design and empirical evaluation

  • Authors:

  • Tomaž Dobravec;Borut Robič;Janez Žerovnik

  • Affiliations:

  • Faculty of Computer and Information Science, University of Ljubljana, Trzaska 25, 1000 Ljubljana, Slovenia;Faculty of Computer and Information Science, University of Ljubljana, Trzaska 25, 1000 Ljubljana, Slovenia;Faculty of Mechanical Engineering, University of Maribor, Smetanova 17, Maribor, Slovenia and Institute of Mathematics, Physics and Mechanics, Jadranska 19, Ljubljana, Slovenia

  • Venue:
  • Journal of Systems Architecture: the EUROMICRO Journal
  • Year:
  • 2003

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Abstract

A double-loop network is an undirected graph whose nodes are integers 0, 1,..., n - 1 and each node u is adjacent to four nodes u ± h1 (mod n), u ± h2(mod n), where 0 h1 h2 n/2. There are initially n packets, one at each of the n nodes. The packet at node u is destined to node π(u), where the mapping ω → π (u) is a permutation. The aim is to minimize the number of routing steps to route all the packets to their destinations. If l is the tight lower bound for this number, then the best known permutation routing algorithm takes, on average, 1.98l routing steps (and 2l routing steps in the worst-case).Because the worst-case complexity cannot be improved, we design four new static permutation routing algorithms with gradually improved average-case performances, which are 1.37l, 1.35l, 1.18l, and 1.12l. Thus, the best of these algorithms exceeds the optimal routing by at most 12% on average.To support our algorithm design we develop a program which simulates permutation routing in a network according to the given topology, routing model as well as communication pattern and measure several quality criteria. We have tested our algorithms on a large number of double-loop networks and permutations (randomly generated and standard).