Characterization of networks supporting multi-dimensional linear interval routing schemes

Abstract

An Interval Routing Scheme ( IRS) is a well-known, space efficient routing strategy for routing messages in a distributed network. In this scheme, each node of the network is assigned an integer label and each link at each node is labeled with an interval. The interval assigned to a link e at a node v indicates the set of destination addresses of the messages which should be forwarded through e at v . A Multi-dimensional Interval Routing Scheme ( MIRS) is a generalization of IRS in which each node is assigned a multi-dimensional label (which is a list of d integers for the d-dimensional case). The labels assigned to the links of the network are also multi-dimensional (a list of d 1-dimensional intervals). The class of networks supporting linear IRS (in which the intervals are not cyclic) is already known for the one-dimensional case (13th Annu. ACM Symp. Principles of Distributed Computing (PODC), ACM Press, New York, August 1994, pp. 216–224). In this paper, we generalize this result and completely characterize the class of networks supporting linear MIRS (or MLIRS) for a given number of dimensions d. We show that by increasing d, the class of networks supporting MLIRS is strictly expanded. We also give a characterization of the class of networks supporting strict MLIRS (which is an MLIRS in which the intervals assigned to the links incident to a node v , does not contain the label of v ).