Graph Searching, Elimination Trees, and a Generalization of Bandwidth

13 years 9 months ago

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The bandwidth minimization problem has a long history and a number of practical applications. In this paper we introduce a natural extension of bandwidth to partially ordered layouts. We consider this extension from three main viewpoints: graph searching, tree decompositions and elimination orderings. The three graph parameters pathwidth, proﬁle and bandwidth related to linear layouts can be deﬁned by variants of graph searching using a standard fugitive. Switching to an inert fugitive, the two former parameters are extended to treewidth and ﬁll-in, and our ﬁrst viewpoint considers the analogous tree-like extension that arises from the bandwidth variant. Bandwidth also has a deﬁnition in terms of ordered path decompositions, and our second viewpoint extends this in a natural way to ordered tree decompositions. In showing that both extensions are equivalent we employ the third viewpoint of elimination trees, as used in the ﬁeld of sparse matrix computations. We call the res...

Fedor V. Fomin, Pinar Heggernes, Jan Arne Telle

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