Back to Search
Start Over
Deeper local search for parameterized and approximation algorithms for maximum internal spanning tree.
- Source :
-
Information & Computation . Feb2017, Vol. 252, p187-200. 14p. - Publication Year :
- 2017
-
Abstract
- The maximum internal spanning tree problem asks for a spanning tree of a given graph that has the maximum number of internal vertices among all spanning trees of this graph. In its parameterized version, we are interested in whether the graph has a spanning tree with at least k internal vertices. Fomin et al. (2013) [4] crafted a very ingenious reduction rule, and showed that a simple application of this rule is sufficient to yield a 3 k -vertex kernel, implying an O ⁎ ( 8 k ) -time parameterized algorithm. Using depth-2 local search, Knauer and Spoerhase (2015) [9] developed a (5/3)-approximation algorithm for the optimization version. We try deeper local search: We conduct a thorough combinatorial analysis on the obtained spanning trees and explore their algorithmic consequences. We first observe that from the spanning tree obtained by depth-3 local search, one can easily find a reducible structure and apply the reduction rule of Fomin et al. This gives an improved kernel of 2 k vertices, and as a by-product, a deterministic algorithm running in time O ⁎ ( 4 k ) . We then go even deeper by considering the spanning tree obtained by depth-5 local search. It is shown that the number of internal vertices of this spanning tree is at least 2/3 of the maximum number a spanning tree can have, thereby delivering an improved approximation algorithm with ratio 1.5 for the problem. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 08905401
- Volume :
- 252
- Database :
- Academic Search Index
- Journal :
- Information & Computation
- Publication Type :
- Academic Journal
- Accession number :
- 120278306
- Full Text :
- https://doi.org/10.1016/j.ic.2016.11.003