Designing networks with compact routing tables

Abstract

Abstract, Classes of network topologies are identified in which shortest-path information can be succinctly stored at the nodes, if they are assigned suitable names. The naming allows each edge at a node to be labeled with zero or more intervals of integers, representing all nodes reachable by a shortest path via that edge. Starting with the class of outerplanar networks, a natural hierarchy of networks is established, based on the number of intervals required. The outerplanar networks are shown to be precisely the networks requiring just one interval per edge. An optimal algorithm is given for determining the labels for edges in outerplanar networks.

On-line and dynamic algorithms for shortest path problems

“…in all cases where G has nice topological properties. As an example, consider outerplanar digraphs (q = 1), or planar digraphs which satisfy the k-interval property (k n and q = k) as they are defined in [15]. Another class of graphs with important applications are the graphs describing global area networks.…”

Improved Algorithms for Dynamic Shortest Paths

“…It defines a natural hierarchy of planar graphs [22] that appears to be very important since it generalizes outerplanar graphs (for which q = 1) and has been proved crucial in the design of space-efficient methods for message routing in communication networks [22]. Hence, our result is always competitive with the best previous ones, and it is better in all cases where q = o(n).…”

“…Hence, our result is always competitive with the best previous ones, and it is better in all cases where q = o(n). Classes of graphs with a small value of q are the planar graphs which satisfy the o(n)-interval property as they are defined in [22]. Yet another class of graphs are the graphs describing global area networks.…”

On multi-label linear interval routing schemes

“…A related problem is that of obtaining bounds on the LIRS numbers of other special classes of graphs. References [3][4][5] address this question for planar graphs, graphs of small genus and graphs with separators of constant size.…”

“…For other networks, they show that the scheme routes a message along a path whose length is at most twice the diameter of the network. Subsequent to [1], a number of other researchers have addressed the problem of obtaining optimal and nearoptimal labeling schemes for many classes of networks [3][4][5][6][7]. Reference [8] presents an example of a network which does not have an optimal interval labeling scheme.…”