Abstract
We describe the first parallel algorithm with optimal speedup for constructing minimum-width tree decompositions of graphs of bounded treewidth. On n-vertex input graphs, the algorithm works in O((log n)2) time using O(n) operations on the EREW PRAM. We also give faster parallel algorithms with optimal speedup for the problem of deciding whether the treewidth of an input graph is bounded by a given constant and for a variety of problems on graphs of bounded treewidth, including all decision problems expressible in monadic second-order logic. On n-vertex input graphs, the algorithms use O(n) operations together with O(log nlog*n) time on the EREW PRAM, or O(log n) time on the CRCW PRAM.
This research was partially supported by the ESPRIT Basic Research Actions Program of the EU under contract No. 7141 (project ALCOM II).
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Bodlaender, H.L., Hagerup, T. (1995). Parallel algorithms with optimal speedup for bounded treewidth. In: Fülöp, Z., Gécseg, F. (eds) Automata, Languages and Programming. ICALP 1995. Lecture Notes in Computer Science, vol 944. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60084-1_80
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