TY - GEN
T1 - Max-cut above spanning tree is fixed-parameter tractable
AU - Madathil, Jayakrishnan
AU - Saurabh, Saket
AU - Zehavi, Meirav
N1 - Publisher Copyright: © 2018, Springer International Publishing AG, part of Springer Nature.
PY - 2018/1/1
Y1 - 2018/1/1
N2 - Every connected graph on n vertices has a cut of size at least n − 1. We call this bound the ‘spanning tree bound’. In the Max-Cut Above Spanning Tree (Max-Cut-AST) problem, we are given a connected n-vertex graph G and a non-negative integer k, and the task is to decide whether G has a cut of size at least n − 1 + k. We show that Max-Cut-AST admits an algorithm that runs in time O(8knO(1), and hence it is fixed parameter tractable with respect to k. Furthermore, we show that Max-Cut-AST has a polynomial kernel of size O(k5).
AB - Every connected graph on n vertices has a cut of size at least n − 1. We call this bound the ‘spanning tree bound’. In the Max-Cut Above Spanning Tree (Max-Cut-AST) problem, we are given a connected n-vertex graph G and a non-negative integer k, and the task is to decide whether G has a cut of size at least n − 1 + k. We show that Max-Cut-AST admits an algorithm that runs in time O(8knO(1), and hence it is fixed parameter tractable with respect to k. Furthermore, we show that Max-Cut-AST has a polynomial kernel of size O(k5).
UR - http://www.scopus.com/inward/record.url?scp=85048048614&partnerID=8YFLogxK
U2 - 10.1007/978-3-319-90530-3_21
DO - 10.1007/978-3-319-90530-3_21
M3 - Conference contribution
SN - 9783319905297
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 244
EP - 256
BT - Computer Science - Theory and Applications - 13th International Computer Science Symposium in Russia, CSR 2018, Proceedings
A2 - Podolskii, Vladimir V.
A2 - Fomin, Fedor V.
PB - Springer Verlag
T2 - 13th International Computer Science Symposium in Russia, CSR 2018
Y2 - 6 June 2018 through 10 June 2018
ER -