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arXiv · 1907.00676

Space-Efficient Vertex Separators for Treewidth

Frank Kammer·Johannes Meintrup·Andrej Sajenko
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Abstract

For $n$-vertex graphs with treewidth $k = O(n^{1/2-\epsilon})$ and an arbitrary $\epsilon>0$, we present a word-RAM algorithm to compute vertex separators using only $O(n)$ bits of working memory. As an application of our algorithm, we give an $O(1)$-approximation algorithm for tree decomposition. Our algorithm computes a tree decomposition in $c^k n (\log \log n) \log^* n$ time using $O(n)$ bits for some constant $c > 0$. We finally use the tree decomposition obtained by our algorithm to solve Vertex Cover, Independent Set, Dominating Set, MaxCut and $q$-Coloring by using $O(n)$ bits as long as the treewidth of the graph is smaller than $c' \log n$ for some problem dependent constant $0 < c' < 1$.

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Frank Kammer, Johannes Meintrup, Andrej Sajenko. 2019-07-01. Space-Efficient Vertex Separators for Treewidth. https://arxiv.org/abs/1907.00676

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