The k-Leaf Spanning Tree problem admits a klam value of 39

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Abstract

The klam value of an algorithm that runs in time O (f(k)) is the maximal value k such that f(k) < 1020. Given a graph G and a parameter k, the k-Leaf Spanning Tree (k-LST) problem asks if G contains a spanning tree with at least k leaves. This problem has been extensively studied over the past three decades. In 2000, Fellows et al. [FSTTCS’00] asked whether it admits a klam value of 50. A steady progress towards an affirmative answer continued until 5 years ago, when an algorithm of klam value 37 was discovered. Our contribution is twofold. First, we present an O (3.188k)-time parameterized algorithm for k-LST, which shows that the problem admits a klam value of 39. Second, we rely on an application of the bounded search trees technique where the correctness of rules crucially depends on the history of previously applied rules in a non-standard manner, encapsulated in a “dependency claim”. Similar claims may be used to capture the essence of other complex algorithms in a compact, useful manner.

Original languageEnglish
Title of host publicationCombinatorial Algorithms - 26th International Workshop, IWOCA 2015, Revised Selected Papers
EditorsWilliam F. Smyth, Zsuzsanna Liptak
PublisherSpringer Verlag
Pages346-357
Number of pages12
ISBN (Print)9783319295152
DOIs
StatePublished - 1 Jan 2016
Externally publishedYes
Event26th International Workshop on Combinatorial Algorithms, IWOCA 2015 - Verona, Italy
Duration: 5 Oct 20157 Oct 2015

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume9538
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349

Conference

Conference26th International Workshop on Combinatorial Algorithms, IWOCA 2015
Country/TerritoryItaly
CityVerona
Period5/10/157/10/15

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