On multi-label linear interval routing schemes

Abstract

We consider linear interval routing schemes studied by [3, 5] from a graph-theoretic perspective. We examine how the number of linear intervals needed to obtain shortest path routings in networks is affected by the product, join and composition operations on graphs. This approach allows us to generalize some of the results of [3, 5] concerning the minimum number of intervals needed to achieve shortest path routings in certain special classes of networks. We also establish an X n 1=3 lower bound on the minimum number of intervals needed to achieve shortest path routings in the network considered.

Partial characterizations of networks supporting shortest path interval labeling schemes

“…the two copies of G 1 corresponding to the endpoints of Suppose that edge e Å (u 1 , u 2 ) √ E(G 0 ) has an edge the edge. In [13] It is a simple but tedious exercise to verify that the intervals, assigned above, take care of optimal routing between any pair of vertices in different copies of G 1 . Clearly, in each of the above cases, for any label in the graph G 0 , at most, one corresponding label is assigned to an edge in G Å n and 2°m°n.…”

“…Other networks such as trees, tori, and unit circular-arc graphs are in 1-IRS [6,13,15]. Conversely, not all graphs this method, each node is assigned a distinct label from the set {1, .…”

“…, n}. Links are bidirectional and are indiadmit 1 interval labelings [2,13,14]. In fact, for any large enough integer n, there is a network with n nodes vidually labeled with subintervals of the interval [1, n].…”

“…result does not apply to optimal schemes. There are many familiar kinds of networks that are known to be in 1-LIRS, A different approach to achieving compact tables, called interval routing, was proposed by Santoro and such as complete graphs, meshes, hypercubes, complete bipartite graphs [13], and proper interval graphs [6]. Khatib [15].…”

Compact Routing Schemes for Dynamic Ring Networks

“…The design of routing schemes that minimize the space devoted to routing tables in a network is an active area of research [3], [7], [10]- [16], [18]- [21]. Most of the research done in this area has concerned static networks and has focused on the tradeoffs between the space required for routing tables and the quality of the routing paths the tables defined.…”