Nisse, N., Rapaport, I., & Suchan, K. (2012). Distributed computing of efficient routing schemes in generalized chordal graphs. Theor. Comput. Sci., 444, 17–27.
Abstract: Efficient algorithms for computing routing tables should take advantage of particular properties arising in large scale networks. Two of them are of special interest: low (logarithmic) diameter and high clustering coefficient. High clustering coefficient implies the existence of few large induced cycles. Considering this fact, we propose here a routing scheme that computes short routes in the class of kchordal graphs, i.e., graphs with no induced cycles of length more than k. In the class of kchordal graphs, our routing scheme achieves an additive stretch of at most k – 1, i.e., for all pairs of nodes, the length of the route never exceeds their distance plus k – 1. In order to compute the routing tables of any nnode graph with diameter D we propose a distributed algorithm which uses O(log n)bit messages and takes O(D) time. The corresponding routing scheme achieves the stretch of k – 1 on kchordal graphs. We then propose a routing scheme that achieves a better additive stretch of 1 in chordal graphs (notice that chordal graphs are 3chordal graphs). In this case, distributed computation of routing tables takes O(min{Delta D, n}) time, where Delta is the maximum degree of the graph. Our routing schemes use addresses of size log n bits and local memory of size 2(d1) log n bits per node of degree d. (c) 2012 Elsevier B.V. All rights reserved.
