Odd multiway cut in directed acyclic graphs

Karthekeyan Chandrasekaran, Matthias Mnich, Sahand Mozaffari

Research output: Contribution to journalArticlepeer-review


We investigate the odd multiway node (edge) cut problem where the input is a graph with a specified collection of terminal nodes, and the goal is to find a smallest subset of nonterminal nodes (edges) to delete so that the terminal nodes do not have an odd length path between them. In an earlier work, Lokshtanov and Ramanujan showed that both odd multiway node cut and odd multiway edge cut are fixed-parameter tractable (FPT) when parameterized by the size of the solution in undirected graphs. In this work, we focus on directed acyclic graphs (DAGs) and design a fixed-parameter algorithm. Our main contribution is a broadening of the shadow-removal framework to address parity problems in DAGs. We complement our FPT results with tight approximability as well as polyhedral results for two terminals in DAGs. Additionally, we show inapproximability results for odd multiway edge cut in undirected graphs even for two terminals.

Original languageEnglish (US)
Pages (from-to)1385-1408
Number of pages24
JournalSIAM Journal on Discrete Mathematics
Issue number2
StatePublished - 2020


  • Approximation algorithms
  • Fixed-parameter tractability
  • Odd multiway cut

ASJC Scopus subject areas

  • Mathematics(all)


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