Automata, Languages and Programming
Volume 317 of the series Lecture Notes in Computer Science pp 105118
Dynamic programming on graphs with bounded treewidth
 Hans L. BodlaenderAffiliated withDept. of Computer Science, University of Utrecht
Abstract
In this paper we study the complexity of graph decision problems, restricted to the class of graphs with treewidth ≤k, (or equivalently, the class of partial ktrees), for fixed k. We introduce two classes of graph decision problems, LCC and ECC, and subclasses CLCC, and CECC. We show that each problem in LCC (or CLCC) is solvable in polynomial (O(n ^{ C })) time, when restricted to graphs with fixed upper bounds on the treewidth and degree; and that each problem in ECC (or CECC) is solvable in polynomial (O(n ^{ C })) time, when restricted to graphs with a fixed upper bound on the treewidth (with given corresponding treedecomposition). Also, problems in CLCC and CECC are solvable in polynomial time for graphs with a logarithmic treewidth, and in the case of CLCCproblems, a fixed upper bound on the degree of the graph.
Also, we show for a large number of graph decision problems, their membership in LCC, ECC, CLCC and/or CECC, thus showing the existence of O(n ^{ C }) or polynomial algorithms for these problems, restricted to the graphs with bounded treewidth (and bounded degree). In several cases, C=1, hence our method gives in these cases linear algorithms.
For several NPcomplete problems, and subclasses of the graphs with bounded treewidth, polynomial algorithms have been obtained. In a certain sense, the results in this paper unify these results.
Keywords
Treewidth partial ktrees graph decision problems restrictions of NPcomplete problems polynomial time algorithms dynamic programming local condition compositions Title
 Dynamic programming on graphs with bounded treewidth
 Book Title
 Automata, Languages and Programming
 Book Subtitle
 15th International Colloquium Tampere, Finland, July 11–15, 1988 Proceedings
 Pages
 pp 105118
 Copyright
 1988
 DOI
 10.1007/3540194886_110
 Print ISBN
 9783540194880
 Online ISBN
 9783540392910
 Series Title
 Lecture Notes in Computer Science
 Series Volume
 317
 Series ISSN
 03029743
 Publisher
 Springer Berlin Heidelberg
 Copyright Holder
 SpringerVerlag
 Additional Links
 Topics
 Keywords

 Treewidth
 partial ktrees
 graph decision problems
 restrictions of NPcomplete problems
 polynomial time algorithms
 dynamic programming
 local condition compositions
 Industry Sectors
 eBook Packages
 Editors
 Authors

 Hans L. Bodlaender ^{(1)}
 Author Affiliations

 1. Dept. of Computer Science, University of Utrecht, P.O. Box 80.012, 3508 TA, Utrecht, the Netherlands
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