Algorithmic Meta-theorems for Restrictions of Treewidth
2012 (English)In: Algorithmica, ISSN 0178-4617, Vol. 64, 19-37 p.Article in journal (Refereed) Published
Possibly the most famous algorithmic meta-theorem is Courcelle's theorem, which states that all MSO-expressible graph properties are decidable in linear time for graphs of bounded treewidth. Unfortunately, the running time's dependence on the formula describing the problem is in general a tower of exponentials of unbounded height, and there exist lower bounds proving that this cannot be improved even if we restrict ourselves to deciding FO logic on trees.
We investigate whether this parameter dependence can be improved by focusing on two proper subclasses of the class of bounded treewidth graphs: graphs of bounded vertex cover and graphs of bounded max-leaf number. We prove stronger algorithmic meta-theorems for these more restricted classes of graphs. More specifically, we show it is possible to decide any FO property in both of these classes with a singly exponential parameter dependence and that it is possible to decide MSO logic on graphs of bounded vertex cover with a doubly exponential parameter dependence. We also prove lower bound results which show that our upper bounds cannot be improved significantly, under widely believed complexity assumptions. Our work addresses an open problem posed by Michael Fellows.
Place, publisher, year, edition, pages
2012. Vol. 64, 19-37 p.
Vertex cover, Max-leaf number, MSO logic, Courcelle's theorem
IdentifiersURN: urn:nbn:se:kth:diva-112832DOI: 10.1007/s00453-011-9554-xISI: 000304395100003OAI: oai:DiVA.org:kth-112832DiVA: diva2:587570
QC 201304232013-01-142013-01-142013-04-23Bibliographically approved