eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2018-02-12
40:1
40:15
10.4230/LIPIcs.FSTTCS.2017.40
article
Balanced Judicious Bipartition is Fixed-Parameter Tractable
Lokshtanov, Daniel
Saurabh, Saket
Sharma, Roohani
Zehavi, Meirav
The family of judicious partitioning problems, introduced by Bollob\'as and Scott to the field of extremal combinatorics, has been extensively studied from a structural point of view for over two decades. This rich realm of problems aims to counterbalance the objectives of classical partitioning problems such as Min Cut, Min Bisection and Max Cut. While these classical problems focus solely on the minimization/maximization of the number of edges crossing the cut, judicious (bi)partitioning problems ask the natural question of the minimization/maximization of the number of edges lying in the (two) sides of the cut. In particular, Judicious Bipartition (JB) seeks a bipartition that is "judicious" in the sense that neither side is burdened by too many edges, and Balanced JB also requires that the sizes of the sides themselves are "balanced" in the sense that neither of them is too large. Both of these problems were defined in the work by Bollob\'as and Scott, and have received notable scientific attention since then. In this paper, we shed light on the study of judicious partitioning problems from the viewpoint of algorithm design. Specifically, we prove that BJB is FPT (which also proves that JB is FPT).
https://drops.dagstuhl.de/storage/00lipics/lipics-vol093-fsttcs2017/LIPIcs.FSTTCS.2017.40/LIPIcs.FSTTCS.2017.40.pdf
Judicious Partition
Tree Decomposition
Parameterized Complexity
Odd Cycle Transversal
Minimum Bisection