The file distribution problem for processor networks

Abstract

We investigate the segmentation problem for files in a network, as introduced in [3], for the case of regular interconnection networks. The strict segmentation problem can be reduced to the problem of finding a strong coloring of the network with d+1 colors, where d is the degree of the network. We prove that a strong coloring with d+1 colors is possible for the d-dimensional hypercube if and only if d=2ⁱ − 1 for some i>0, for the d-dimensional torus of size l ₁ × ... × _d whenl _i mod q=0, 1 ≤ i ≤ d, if d=2ⁱ-1 for some r>0, for the Cube-Connected Cycles CCC _d if and only if d>2, d ≠ 5, for the directed shuffle-exchange network, for the directed 4-pin shuffle network and for the chordal ring network, for some chord lengths and numbers of nodes. The results show in which instances perfect segmentations are possible for classical regular processor interconnection networks. Some results for other (almost) regular interconnection networks are included.

This work was supported by the ESPRIT II Basic Research Actions program of the EC under contract No. 3075 (project ALCOM).