The Computer Journal
The complexity of shortest path and dilation bounded interval routing
Theoretical Computer Science
Theoretical Computer Science
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Interval routing is a space-efficient method for point-to-point networks. For a survey of interval routing, one can refer to [C. Gavoille, A survey on interval routing, Theoret. Comput. Sci. 245 (2) (2000) 217-253 [1]]. The network in question is an undirected connected graph, G=(V,E), where V is the set of nodes, and E the set of the edges. G has n nodes and diameter D. In this paper, we will focus on the dilation analysis. In [S.S.H. Tse, F.C.M. Lau, An optimal lower bound for interval routing in general networks, in: Proc. 4th Internat. Colloquium on Structural Information and Communication Complexity (SIROCCO'97), 1997, pp. 112-124], by using one label, we have a lower bound of 2D-3, where D=8. In [C. Gavoille, On dilation of interval routing, Comput. J. 43 (1) (2000) 1-7 [7]], by using O(nDlog(n/D)) labels, the best known lower bound is @?32D@?-1, where D=2. In this paper, we modify the technique used in [S.S.H. Tse, F.C.M. Lau, Two lower bounds for multi-label interval routing, in: Proc. Computing: The Australasian Theory Symposium (CATS'97), 1997, pp. 36-43] and contribute with a better lower bound 32D by using O(logn) labels, where D=2 and even.