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Approximating Connected Maximum Cuts via Local Search

Authors Baruch Schieber, Soroush Vahidi

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Author Details

Baruch Schieber
  • Department of Computer Science, New Jersey Institute of Technology, Newark, NJ, USA
Soroush Vahidi
  • Department of Computer Science, New Jersey Institute of Technology, Newark, NJ, USA

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Baruch Schieber and Soroush Vahidi. Approximating Connected Maximum Cuts via Local Search. In 31st Annual European Symposium on Algorithms (ESA 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 274, pp. 93:1-93:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023) https://doi.org/10.4230/LIPIcs.ESA.2023.93

Abstract

The Connected Max Cut (CMC) problem takes in an undirected graph G(V,E) and finds a subset S ⊆ V such that the induced subgraph G[S] is connected and the number of edges connecting vertices in S to vertices in V⧵S is maximized. This problem is closely related to the Max Leaf Degree (MLD) problem. The input to the MLD problem is an undirected graph G(V,E) and the goal is to find a subtree of G that maximizes the degree (in G) of its leaves. [Gandhi et al. 2018] observed that an α-approximation for the MLD problem induces an 𝒪(α)-approximation for the CMC problem.
We present an 𝒪(log log |V|)-approximation algorithm for the MLD problem via local search. This implies an 𝒪(log log |V|)-approximation algorithm for the CMC problem. Thus, improving (exponentially) the best known 𝒪(log |V|) approximation of the Connected Max Cut problem [Hajiaghayi et al. 2015].

Subject Classification

ACM Subject Classification
  • Theory of computation → Graph algorithms analysis
  • Theory of computation → Routing and network design problems
  • Theory of computation → Approximation algorithms analysis
Keywords
  • approximation algorithms
  • graph theory
  • max-cut
  • local search

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