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• W2056539002 abstract "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 node-congestion of at most O(d(dt)3), where t denotes the treewidth of the graph and d denotes the maximal degree of a vertex in the graph. Provided that the graph is given by its tree-decomposition the embedding can be computed efficiently on the hypercube itself. In particular, the embedding of a graph with constant treewidth and constant degree can be computed in time O(log2(n)logloglog(n)log*(n)). For graphs with constant treewidth, a minimal tree-decomposition can be computed efficiently in parallel due to a result of Bodlaender and Hagerup. In this case, the embedding can be computed on the hypercube in time O(log2(n)(d2+log(n)loglog2(n)))." @default.
• W2056539002 created "2016-06-24" @default.
• W2056539002 creator A5032388168 @default.
• W2056539002 creator A5042305696 @default.
• W2056539002 date "2002-04-01" @default.
• W2056539002 modified "2023-09-25" @default.
• W2056539002 title "Embedding Graphs with Bounded Treewidth into Their Optimal Hypercubes" @default.
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• W2056539002 doi "https://doi.org/10.1006/jagm.2002.1217" @default.
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