eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2023-08-30
93:1
93:17
10.4230/LIPIcs.ESA.2023.93
article
Approximating Connected Maximum Cuts via Local Search
Schieber, Baruch
1
Vahidi, Soroush
1
Department of Computer Science, New Jersey Institute of Technology, Newark, NJ, USA
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].
https://drops.dagstuhl.de/storage/00lipics/lipics-vol274-esa2023/LIPIcs.ESA.2023.93/LIPIcs.ESA.2023.93.pdf
approximation algorithms
graph theory
max-cut
local search