Work

On Approximating Cutwidth and Pathwidth

Year: 2024

Type: conference-paper

Abstract: We study graph ordering problems with a min-max objective. A classical problem of this type is cutwidth, where given a graph we want to order its vertices such that the number of edges crossing any point is minimized. We give a$\log^{1+o(1)}(n)$approximation for the problem, substantially improving upon the previous poly-logarithmic guarantees based on the standard recursive balanced partitioning approach of Leighton and Rao (FOCS'88). Our key idea is a new metric decomposition procedure that is suitable for handling min-max objectives, which could be of independent interest. We also use this to show other results, including an improved$\log^{1+o(1)}(n)$approximation for computing the pathwidth of a graph.

Source: Annual Symposium on Foundations of Computer Science

DOI: 10.1109/focs61266.2024.00051

Authors: Nikhil Bansal, Dor Katzelnick, Roy Schwartz

Institutions: University of Michigan, Technion – Israel Institute of Technology

Language: English

Topic: Complexity and Algorithms in Graphs

Subfield: Computational Theory and Mathematics

Field: Computer Science

Domain: Physical Sciences

Open Access status: green

Funders: National Science Foundation, European Commission, Nederlandse Organisatie voor Wetenschappelijk Onderzoek, Technion-Israel Institute of Technology

Awards: Collaborative Research: AF: Small: New Directions and Approaches in Discrepancy Theory, G434337789, Continuous Methods in Discrete Optimization