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On the Space Requirement of Interval Routing
July 1999 (vol. 48 no. 7)
pp. 752-757

Abstract—Interval routing is a space-efficient method for point-to-point networks. It is based on labeling the edges of a network with intervals of vertex numbers (called interval labels). An $M$-label scheme allows up to $M$ labels to be attached on an edge. For arbitrary graphs of size $n$, $n$ the number of vertices, the problem is to determine the minimum $M$ necessary for achieving optimality in the length of the longest routing path. The longest routing path resulted from a labeling is an important indicator of the performance of any algorithm that runs on the network. We prove that there exists a graph with $D=\Omega(n^{\frac{1}{3}})$ such that if $M\leq {\frac{n}{18D}}-O(\sqrt{\frac{n}{D}})$, the longest path is no shorter than $D+\Theta({\frac{D}{\sqrt{M}}})$. As a result, for any $M$-label IRS, if the longest path is to be shorter than $D+\Theta({\frac{D}{\sqrt{M}}})$, at least $M=\Omega({\frac{n}{D}})$ labels per edge would be necessary.

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Index Terms:
Compact routing, computational complexity, computer networks, distributed systems, graph theory, interval routing, optimization, shortest paths.
Citation:
Savio S.H. Tse, Francis C.M. Lau, "On the Space Requirement of Interval Routing," IEEE Transactions on Computers, vol. 48, no. 7, pp. 752-757, July 1999, doi:10.1109/12.780884
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