TY - GEN
T1 - (K, n − k)-max-cut
T2 - 12th Latin American Symposium on Theoretical Informatics, LATIN 2016
AU - Saurabh, Saket
AU - Zehavi, Meirav
N1 - Publisher Copyright:
© Springer-Verlag Berlin Heidelberg 2016.
PY - 2016/1/1
Y1 - 2016/1/1
N2 - Max-Cut is a well-known classical NP-hard problem. This problem asks whether the vertex-set of a given graph G = (V,E) can be partitioned into two disjoint subsets, A and B, such that there exist at least p edges with one endpoint in A and the other endpoint in B. It is well known that if p ≤ |E|/2, the answer is necessarily positive. A widelystudied variant of particular interest to parameterized complexity, called (k, n − k)-Max-Cut, restricts the size of the subset A to be exactly k. For the (k, n − k)-Max-Cut problem, we obtain an O∗ (2p)-time algorithm, improving upon the previous best O∗ (4p+o(p))-time algorithm, as well as the first polynomial kernel. Our algorithm relies on a delicate combination of methods and notions, including independent sets, depthsearch trees, bounded search trees, dynamic programming and treewidth, while our kernel relies on examination of the closed neighborhood of the neighborhood of a certain independent set of the graph G.
AB - Max-Cut is a well-known classical NP-hard problem. This problem asks whether the vertex-set of a given graph G = (V,E) can be partitioned into two disjoint subsets, A and B, such that there exist at least p edges with one endpoint in A and the other endpoint in B. It is well known that if p ≤ |E|/2, the answer is necessarily positive. A widelystudied variant of particular interest to parameterized complexity, called (k, n − k)-Max-Cut, restricts the size of the subset A to be exactly k. For the (k, n − k)-Max-Cut problem, we obtain an O∗ (2p)-time algorithm, improving upon the previous best O∗ (4p+o(p))-time algorithm, as well as the first polynomial kernel. Our algorithm relies on a delicate combination of methods and notions, including independent sets, depthsearch trees, bounded search trees, dynamic programming and treewidth, while our kernel relies on examination of the closed neighborhood of the neighborhood of a certain independent set of the graph G.
UR - http://www.scopus.com/inward/record.url?scp=84961695950&partnerID=8YFLogxK
U2 - 10.1007/978-3-662-49529-2_51
DO - 10.1007/978-3-662-49529-2_51
M3 - Conference contribution
AN - SCOPUS:84961695950
SN - 9783662495285
T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
SP - 686
EP - 699
BT - LATIN 2016
A2 - Navarro, Gonzalo
A2 - Kranakis, Evangelos
A2 - Chávez, Edgar
PB - Springer Verlag
Y2 - 11 April 2016 through 15 April 2016
ER -