Interval routing is a space-efficient routing method for point-to-point communication networks. Themethod has drawn considerable attention in recent years because of its being incorporated into the design of a commercially available routing chip. Themethod is based on proper labeling of edges of the graphwith intervals. An optimal labelingwould result in routing of messages through the shortest...

Camponogara and Shima (2010) developed an ε-approximation algorithm (FPTAS) for the mobile agent routing problem in which a benefit function determines how visits to different sites contribute to the agent’s mission. The benefit is to be maximized under a time constraint. They reduced the problem to the constrained longest-path problem in a graph. In this note we present a modified FPTAS that i...

A bipartite graph is chordal bipartite if every cycle of length at least 6 has a chord in it. In this paper, we investigate the structure of $P_5$-free chordal bipartite graphs and show that these graphs have a Nested Neighborhood Ordering, a special ordering among its vertices. Further, using this ordering, we present polynomial-time algorithms for classical problems such as Hamiltonian cycle ...

Given a graph G, the longest path problem asks to compute a simple path of G with the largest number of vertices. This problem is the most natural optimization version of the well-known and well-studied Hamiltonian path problem, and thus it is NP-hard on general graphs. However, in contrast to the Hamiltonian path problem, there are only a few restricted graph families, such as trees, and some ...

In 1982 Laborde, Payan and Xuong [Independent sets and longest directed paths in digraphs, in: Graphs and other combinatorial topics (Prague, 1982) 173–177 (Teubner-Texte Math., 59 1983)] conjectured that every digraph has an independent detour transversal (IDT), i.e. an independent set which intersects every longest path. Havet [Stable set meeting every longest path, Discrete Math. 289 (2004) ...

Interval routing is a space-efficient method for point-to-point networks. The method has been incorporated in the design of a commercially available routing chip [7], and is a basic element in some compact routing methods (e.g., [4]). With up to one interval label per edge, the method has been shown to be nonoptimal for arbitrary graphs [9, 13], where optimality is measured in terms of the long...

Interval routing is a space-efficient routing method for computer networks. In this paper, all graphs are assumed to be planar graphs, unless specified otherwise. We have four upper bound results in this paper. First, for D ≥ 3, we prove the existence of an O(D)-IRS on arbitrary graphs whose longest path is bounded by D, where D is the diameter not less than three. With a little modification, w...