New Bounds for Oblivious Mesh Routing

We give two, new upper bounds for oblivious permutation routing on the mesh networks: Let N be the total number of processors in each mesh. One is an O(N) algorithm on the two-dimensional, √ N × √ N mesh with constant queue-size. This is the first algorithm which improves substantially the trivial O(N) bound for oblivious routing in the mesh networks with constant queue-size. The other is a 1.16 √ N + o( √ N) algorithm on the three-dimensional, N ×N ×N mesh with unlimited queue-size. This algorithm allows at most three bends in the path of each packet. If the number of bends is restricted to minimal, i.e., at most two, then the bound jumps to Ω(N) as was shown in ESA’97. Communicated by T. Nishizeki, R. Tamassia and D. Wagner: submitted January 1999; revised April 2000 and October 2000. A preliminary version of this paper was presented at the 6th European Symposium on Algorithms (ESA’98). Supported in part by Scientific Research Grant, Ministry of Japan, 09480055 and 08244105, and Kayamori Foundation of Information Science Advancement, Japan Supported in part by Scientific Research Grant, Ministry of Japan, 08244102 Supported in part by Scientific Research Grant, Ministry of Japan, 10780198 and 12780234, and The Telecommunications Advancement Foundation, Japan. K. Iwama et al., Oblivious Mesh Routing, JGAA, 5(5) 17–38 (2001) 18