Virtual Path Layouts in ATM Networks

Ladislav Stacho, Imrich Vrto
2000 SIAM journal on computing (Print)  
We study virtual path layouts in a very popular type of fast interconnection networks, namely ATM networks. One of the main problems in such networks is to construct path layout that minimizes the hop-number (i.e. the number of virtual paths between any two nodes) as a function of 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 the hop-number O( diam(H) log log c ), where diam(H)
more » ... is the diameter of the network H and is its maximum degree. Involving a general lower bound from 6] 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 . For instance, this gives optimal hop-numbers for hypercube related networks. Moreover, we improve known results for paths and meshes of Kranakis et al. 6]. Finally, we prove optimal hop-numbers for hypercubes.
doi:10.1137/s0097539796308151 fatcat:p46uhoj5qbhvzfxl6sgqw66ova