Compact Routing Schemes for Generalised Chordal Graphs

Symmetry properties of chordal rings of degree 3

This paper presents the main properties of chordal rings of degree 3. This family of graphs is strongly related to circulant graphs, which are actually often called chordal rings too. The use of triangles in the plane to represent the vertices allows one to associate a plane tessellation to every chordal ring. By using this geometrical approach, we study the recognition and the isomorphism prob...

Compact Routing on Chordal Rings of Degree Four yLata

A chordal ring G(n; c) of degree 4 is a ring of n nodes with chords connecting each vertex i to the vertex (i + c) mod n. In this paper, we investigate compact routing schemes on such networks. We show a routing scheme for any such network that requires O(log n) bits of storage at each node, and O(1) time to compute a shortest path to any destination. This improves on the results of 16] which g...

Improved Compact Routing Scheme for Chordal Graphs

Distributed Computing of Efficient Routing Schemes in Generalized Chordal Graphs

Efficient algorithms for computing routing tables should take advantage of the particular properties arising in large scale networks. There are in fact at least two properties that any routing scheme must consider: low (logarithmic) diameter and high clustering coefficient. High clustering coefficient implies the existence of few large induced cycles. Therefore, we propose a routing scheme that...

Collective Tree Spanners of Graphs

In this paper we introduce a new notion of collective tree spanners. We say that a graph G = (V,E) admits a system of μ collective additive tree r-spanners if there is a system T (G) of at most μ spanning trees of G such that for any two vertices x, y of G a spanning tree T ∈ T (G) exists such that dT (x, y) ≤ dG(x, y) + r. Among other results, we show that any chordal graph, chordal bipartite ...