Space-Efficient Vertex Separators for Treewidth

Abstract For n -vertex graphs with treewidth $$k = O(n^{1/2-\epsilon })$$ k = O ( n 1 / 2 - ϵ ) and an arbitrary $$\epsilon >0$$ > 0 , we present a word-RAM algorithm to compute vertex separators using only O ( ) bits of working memory. As application our algorithm, give (1)-approximation for tree decomposition. Our computes decomposition in $$c^k (\log \log n) ^* n$$ c log ∗ time some constant $$c > 0$$ . Together the result Banerjee et al. (Proceedings 21st international conference on computing combinatorics (COCOON 2015). LNCS, vol 9198, Springer, pp 349–360, 2015. https://doi.org/10.1007/978-3-319-21398-9_28 are able solution all monadic-second-order problems (MSO) $$O(n + \tau (k) \cdot p _{p} n)$$ + τ · p $$O(\tau n^{2 (2/\log p)})$$ where k is given graph, parameter $$2 \le ≤ $$\tau $$ function depending MSO formula. We finally use obtained by solve Vertex Cover Independent Set Dominating MaxCut q - Coloring polynomial as long graph smaller than $$c' ′ problem dependent $$0< c' < 1$$ <