Treffer: An improved approximation algorithm for Hypergraph Max [formula omitted]-Section.

In this paper, we address the design of an approximation algorithm for the well-known Hypergraph Max p -Section problem. The objective is to maximize the total weight of hyperedges crossing different partitions while ensuring that the number of vertices in each subset is equal. To tackle this challenge, we propose a novel semidefinite programming randomized approximation algorithm that integrates porcupine rounding with a perturbation technique. Our approach extends previous results in the literature and provides improved approximation ratio for maximizing the p -section of hypergraphs. Specifically, for the case where p = 2 and the hypergraph does not include hyperedges containing exactly two vertices, our algorithm achieves a significantly enhanced approximation ratio of 0.7546, better than the previous best approximation ratio of 0.7042. [ABSTRACT FROM AUTHOR]