A Sub-exponential FPT Algorithm and a Polynomial Kernel for Minimum Directed Bisection on Semicomplete Digraphs

Jayakrishnan Madathil, Roohani Sharma, Meirav Zehavi

Research output: Contribution to journalArticlepeer-review

Abstract

Given an n-vertex digraph D and a non-negative integer k, the Minimum Directed Bisection problem asks if the vertices of D can be partitioned into two parts, say L and R, such that | L| and | R| differ by at most 1 and the number of arcs from R to L is at most k. This problem is known to be NP-hard even when k= 0. We investigate the parameterized complexity of this problem on semicomplete digraphs. We show that Minimum Directed Bisection admits a sub-exponential time fixed-parameter tractable algorithm on semicomplete digraphs. We also show that Minimum Directed Bisection admits a polynomial kernel on semicomplete digraphs. To design the kernel, we use (n, k, k2) -splitters, which, to the best of our knowledge, have never been used before in the design of kernels. We also prove that Minimum Directed Bisection is NP-hard on semicomplete digraphs, but polynomial time solvable on tournaments.

Original languageEnglish
Pages (from-to)1861-1884
Number of pages24
JournalAlgorithmica
Volume83
Issue number6
DOIs
StatePublished - 1 Jun 2021

Keywords

  • Bisection
  • Chromatic coding
  • FPT Algorithm
  • Polynomial kernel
  • Semicomplete digraph
  • Splitters
  • Tournament

ASJC Scopus subject areas

  • Computer Science (all)
  • Computer Science Applications
  • Applied Mathematics

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