2026-07-24T03:16:10Z https://drops.dagstuhl.de/oai

oai:drops-oai.dagstuhl.de:18746 2024-03-06T11:02:37Z ddc:004 open_access

Approximating Connected Maximum Cuts via Local Search Schieber, Baruch Vahidi, Soroush approximation algorithms graph theory max-cut local search 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]. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Baruch Schieber and Soroush Vahidi 2023 Is Part Of LIPIcs, Volume 274, 31st Annual European Symposium on Algorithms (ESA 2023) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.ESA.2023.93 urn:nbn:de:0030-drops-187466 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2023.93 eng https://creativecommons.org/licenses/by/4.0/legalcode