TY - GEN

T1 - A 2k-vertex kernel for maximum internal spanning tree

AU - Li, Wenjun

AU - Wang, Jianxin

AU - Chen, Jianer

AU - Cao, Yixin

PY - 2015/1/1

Y1 - 2015/1/1

N2 - We consider the parameterized version of the maximum internal spanning tree problem: given an n-vertex graph and a parameter k, does the graph have a spanning tree with at least k internal vertices? Fomin et al. [J. Comput. System Sci., 79:1-6] crafted a very ingenious reduction rule, and showed that a simple application of this rule is sufficient to yield a 3k-vertex kernel for this problem. Here we propose a novel way to use the same reduction rule, resulting in an improved 2k-vertex kernel. Our algorithm applies first a greedy procedure consisting of a sequence of local exchange operations, which ends with a local-optimal spanning tree, and then uses this special tree to find a reducible structure. As a corollary of our kernel, we obtain a 4k·nO(1)-time deterministic algorithm, improving all previous algorithms for the problem.

AB - We consider the parameterized version of the maximum internal spanning tree problem: given an n-vertex graph and a parameter k, does the graph have a spanning tree with at least k internal vertices? Fomin et al. [J. Comput. System Sci., 79:1-6] crafted a very ingenious reduction rule, and showed that a simple application of this rule is sufficient to yield a 3k-vertex kernel for this problem. Here we propose a novel way to use the same reduction rule, resulting in an improved 2k-vertex kernel. Our algorithm applies first a greedy procedure consisting of a sequence of local exchange operations, which ends with a local-optimal spanning tree, and then uses this special tree to find a reducible structure. As a corollary of our kernel, we obtain a 4k·nO(1)-time deterministic algorithm, improving all previous algorithms for the problem.

KW - Kernelization algorithms

KW - Local-search

KW - Parameterized computation

UR - http://www.scopus.com/inward/record.url?scp=84951811884&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-21840-3_41

DO - 10.1007/978-3-319-21840-3_41

M3 - Conference article published in proceeding or book

SN - 9783319218397

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 495

EP - 505

BT - Algorithms and Data Structures - 14th International Symposium, WADS 2015, Proceedings

PB - Springer Verlag

T2 - 14th International Symposium on Algorithms and Data Structures, WADS 2015

Y2 - 5 August 2015 through 7 August 2015

ER -