Abstract
In this paper we refine the notion of tree-decomposition by introducing acyclic (R,D)-clustering, where clusters are subsets of vertices of a graph and R and D are the maximum radius and the maximum diameter of these subsets. We design a routing scheme for graphs admitting induced acyclic (R,D)-clustering where the induced radius and the induced diameter of each cluster are at most 2. We show that, by constructing a family of special spanning trees, one can achieve a routing scheme of deviation Δ ≤ 2R with labels of size O(log3 n / loglog n) bits per vertex and O(1) routing protocol for these graphs. We investigate also some special graph classes admitting induced acyclic (R,D)-clustering with induced radius and diameter less than or equal to 2, namely, chordal bipartite, homogeneously orderable, and interval graphs. We achieve the deviation Δ = 1 for interval graphs and Δ = 2 for chordal bipartite and homogeneously orderable graphs.
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Dragan, F.F., Lomonosov, I. (2004). On Compact and Efficient Routing in Certain Graph Classes. In: Fleischer, R., Trippen, G. (eds) Algorithms and Computation. ISAAC 2004. Lecture Notes in Computer Science, vol 3341. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30551-4_36
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DOI: https://doi.org/10.1007/978-3-540-30551-4_36
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