Journal of Algorithms
A Linear-Time Algorithm for Finding Tree-Decompositions of Small Treewidth
SIAM Journal on Computing
Treewidth and Minimum Fill-in: Grouping the Minimal Separators
SIAM Journal on Computing
Improved approximation algorithms for minimum-weight vertex separators
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Spanners for bounded tree-length graphs
Theoretical Computer Science
Exact Algorithms for Treewidth and Minimum Fill-In
SIAM Journal on Computing
A parameterized algorithm for chordal sandwich
CIAC'10 Proceedings of the 7th international conference on Algorithms and Complexity
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We resolve the computational complexity of determining the treelength of a graph, thereby solving an open problem of Dourisboure and Gavoille, who introduced this parameter, and asked to determine the complexity of recognizing graphs of bounded treelength [6]. While recognizing graphs with treelength 1 is easily seen as equivalent to recognizing chordal graphs, which can be done in linear time, the computational complexity of recognizing graphs with treelength 2 was unknown until this result. We show that the problem of determining whether a given graph has treelength at most k is NP-complete for every fixed k 2, and use this result to show that treelength in weighted graphs is hard to approximate within a factor smaller than 3/2. Additionally, we show that treelength can be computed in time O*(1.8899n) by giving an exact exponential time algorithm for the Chordal Sandwich problem and showing how this algorithm can be used to compute the treelength of a graph.