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Title: An Improved Approximation Algorithm for the Max-3-Section Problem
We consider the Max-3-Section problem, where we are given an undirected graph G = (V, E) equipped with non-negative edge weights w : E → R+ and the goal is to find a partition of V into three equisized parts while maximizing the total weight of edges crossing between different parts. Max-3-Section is closely related to other well-studied graph partitioning problems, e.g., Max-Cut, Max-3-Cut, and Max-Bisection. We present a polynomial time algorithm achieving an approximation of 0.795, that improves upon the previous best known approximation of 0.673. The requirement of multiple parts that have equal sizes renders Max-3-Section much harder to cope with compared to, e.g., Max-Bisection. We show a new algorithm that combines the existing approach of Lassere hierarchy along with a random cut strategy that suffices to give our result.  more » « less
Award ID(s):
2106444 1910423
Author(s) / Creator(s):
; ; ;
Publisher / Repository:
Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik
Date Published:
Journal Name:
31st Annual European Symposium on Algorithms (ESA 2023)
Medium: X
Sponsoring Org:
National Science Foundation
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