| Co-Investigator(Kenkyū-buntansha) |
IWAMOTO Chuzo Hiroshima University, Faculty of Engineering, Associate Professor, 工学部, 助教授 (60274495)
MIYAZAKI Shuichi Kyoto University, Graduate School of Informatics, Research Associate, 情報学研究科, 助手 (00303884)
OKABE Yasuo Kyoto University, Graduate School of Informatics, Associate Professor, 情報学研究科, 助教授 (20204018)
KAWAKUBO Kazuo Fukuyama University, Faculty of Engineering, Associate Professor, 工学部, 助教授 (10186067)
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| Research Abstract |
Our model in this research is a distribution of N processors on a √<N>×√<N> mesh, where each processor is connected with four neighboring processors. Each processor has a constant queue size, namely, a processor can hold only a constant number of packets. At a unit step, each processor can send a packet to one of four neighbors.
We treat a permutation routing problem on the above model. In this problem, each processor initially holds a packet to be sent to another processor. No two processors hold packets whose destination is the same processor. Performance of algorithms is evaluated by the worst case completion time. Although the diameter of mesh is 2√<N>, the best known algorithm so far achieved only O(N) time, and it had been a long open problem whether it can be improved. In 1998, our research group developed an algorithm whose time complexity is O(N^<0.75>).
In this research, we improved the upper bound. First, we developed an O(√<N>) time algorithm using bit reversal permutation. However, constant coefficient was as big a 1000. To reduce it, we refined the bit reversal permutation and obtained a (2.954+ε)√<N> time algorithm.
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