Embedding Graphs with Bounded Treewidth into Optimal Hypercubes
نویسندگان
چکیده
In this paper, we present a one-to-one embedding of a graph with bounded treewidth into its optimal hypercube. This is the first time that embeddings of graphs with a very irregular structure into hypercubes are investigated. The dilation of the presented embedding is bounded by , where denotes the treewidth of the graph and denotes the maximal degree of a vertex in the graph. The given embedding is a generalization of our method to embed arbitrary binary trees into their optimal hypercubes given in [HM93]. Moreover, if the given graph has constant treewidth or is represented by a tree-decomposition of width , this embedding can be efficiently implemented on the optimal hypercube itself.
منابع مشابه
Embedding Graphs with Bounded Treewidth into Their Optimal Hypercubes
In this paper, we present a one-to-one embedding of a graph with bounded treewidth into its optimal hypercube. This is the first time that embeddings of graphs with a highly irregular structure into hypercubes are investigated. The presented embedding achieves dilation of at most 3 log d+ 1 t + 1 + 8 and nodecongestion of at most O d dt 3 , where t denotes the treewidth of the graph and d denot...
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