On the design of efficient ATM routing schemes
Theoretical Computer Science
Layouts for mobility management in wireless ATM networks
Discrete Applied Mathematics
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We study virtual path layouts in a very popular type of fast interconnection networks, namely asynchronous transfer mode (ATM) networks. One of the main problems in such networks is to construct path layouts that minimize the hop-number (i.e., the number of virtual paths between any two nodes) as a function of the edge congestion c (i.e., the number of virtual paths going through a link). In this paper we construct for any n vertex network H and any c a virtual path layout with hop-number $O(\frac{diam(H)\log\Delta}{\log c})$, where diam(H) is the diameter of the network H and $\Delta$ is its maximum degree. Involving a general lower bound from [E. Kranakis, D. Krizanc, and A. Pelc, Seventh IEEE Symposium on Parallel and Distributed Processing, IEEE Computer Society, 1995, pp. 662--668], we see that these hop-numbers are optimal for bounded degree networks with the diameter O(log n) for any congestion c. In the case of unbounded degree networks (with the diameter O(log n)) these hop-numbers are optimal for any $c\geq\Delta$. For instance, this gives optimal hop-numbers for hypercube related networks. Moreover, we improve known results for paths and meshes and prove optimal hop-numbers for hypercubes.