Odd multiway cut in directed acyclic graphs

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 non-terminal 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 2 terminals in DAGs. Additionally, we show inapproximability results for odd multiway edge cut in undirected graphs even for 2 terminals.

Name thesis:degree_name

M.S.

Level thesis:degree_level

Thesis

Discipline thesis:degree_discipline

Computer Science

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2022

Author dc:creator

• Mozaffari, Sahand

Contributors dc:contributor

• Chandrasekaran, Karthekeyan

• Fixed-parameter Tractability
• Graphs
• Algorithm Design

Statement dc:rights

• Copyright 2021 Sahand Mozaffari

Language dc:language

en

Handle dc:identifier

http://hdl.handle.net/2142/113081

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/113081