Compact routing with slack

Michael Dinitz

Abstract: Given a weighted graph G=(V,E), a compact routing scheme is a distributed algorithm for forwarding packets from any source to any destination. The fundamental tradeoff is between the space used at each node and the stretch of the total route, measured by the multiplicative factor between the actual distance traveled and the length of the shortest possible route. We extend the normal definition with a slack parameter ε, which allows us to ignore up to εn2 of the shortest pairwise routes and give a guarantee on the remaining ones. For constant ε we give constant stretch, polylogarithmic space schemes in the name-dependent model and in the designer-port name-independent model, and give a lower bound that proves that such schemes do not exist in the fixed-port name-independent model. In the name-dependent model we also give a gracefully degrading scheme which works simultaneously for all ε > 0 and guarantees constant average stretch with polylog space.