TY - GEN

T1 - The k-Leaf Spanning Tree problem admits a klam value of 39

AU - Zehavi, Meirav

N1 - Publisher Copyright:
© Springer International Publishing Switzerland 2016.

PY - 2016/1/1

Y1 - 2016/1/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=84961223791&partnerID=8YFLogxK

U2 - 10.1007/978-3-319-29516-9_29

DO - 10.1007/978-3-319-29516-9_29

M3 - Conference contribution

AN - SCOPUS:84961223791

SN - 9783319295152

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

SP - 346

EP - 357

BT - Combinatorial Algorithms - 26th International Workshop, IWOCA 2015, Revised Selected Papers

A2 - Smyth, William F.

A2 - Liptak, Zsuzsanna

PB - Springer Verlag

T2 - 26th International Workshop on Combinatorial Algorithms, IWOCA 2015

Y2 - 5 October 2015 through 7 October 2015

ER -