The compactness of interval routing

The compactness of interval routing

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Article ID: iaor20002816
Country: United States
Volume: 12
Issue: 4
Start Page Number: 459
End Page Number: 473
Publication Date: Oct 1999
Journal: SIAM Journal on Discrete Mathematics
Authors: ,
Keywords: graphs
Abstract:

The compactness of a graph measures the space complexity of its shortest path routing tables. Each outgoing edge of a node x is assigned a (pairwise disjoint) set of addresses, such that the unique outgoing edge containing the address of a node y is the first edge of a shortest path from x to y. The complexity measure used in the context of interval routing is the minimum number of intervals of consecutive addresses needed to represent each such set, minimized over all possible choices of addresses and all choices of shortest paths. This paper establishes asymptotically tight bounds of n/4 on the compactness of an n-node graph. More specifically, it is shown that every n-node graph has compactness at most n/4 + o(n), and conversely, there exists an n-node graph whose compactness is n/4 – o(n). Both bounds improve upon known results.

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