Embedding Graphs with Bounded Treewidth into Their Optimal Hypercubes

Volker Heun, Ernst W. Mayr
2002 Journal of Algorithms  
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 denotes the maximal degree of a vertex in the graph. Provided that the graph is given by its
more » ... tion 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 log 2 n log log log 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 log 2 n d 2 + log n log log 2 n .  2002 Elsevier Science (USA)
doi:10.1006/jagm.2002.1217 fatcat:j2udl5lcufh3jekk54aax4upue