One of the fundamental trade-o\ufb00s in compact routing schemes is between the space used to store the routing table on each node and the stretch factor of the routing scheme \u2013 the maximum ratio over all pairs between the cost of the route induced by the scheme and the cost of a minimum cost path between the same pair. All previous routing schemes required storage that is dependent on the diameter of the network. We present a new scale-free routing scheme, whose storage and header sizes are independent of the aspect ratio of the network. Our scheme is based on a decomposition into sparse and dense neighborhoods. Given an undirected network with arbitrary weights and n arbitrary node names, for any integer k \u2265 1 we present the \ufb01rst scale-free routing scheme with asymptotically optimal space-stretch tradeo\ufb00 that does not require edge weights to be polynomially bounded. The scheme uses e O(n1\/k) space routing table at each node, and routes along paths of asymptotically optimal linear stretch O(k).<\/p>\n","protected":false},"excerpt":{"rendered":"
One of the fundamental trade-o\ufb00s in compact routing schemes is between the space used to store the routing table on each node and the stretch factor of the routing scheme \u2013 the maximum ratio over all pairs between the cost of the route induced by the scheme and the cost of a minimum cost path […]<\/p>\n","protected":false},"featured_media":0,"template":"","meta":{"msr-url-field":"","msr-podcast-episode":"","msrModifiedDate":"","msrModifiedDateEnabled":false,"ep_exclude_from_search":false,"_classifai_error":"","msr-author-ordering":null,"msr_publishername":"","msr_publisher_other":"","msr_booktitle":"ACM Symposium on Parallel Algorithms and Architectures (SPAA)","msr_chapter":"","msr_edition":"ACM Symposium on Parallel Algorithms and Architectures 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