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 -