Approximation Algorithms for the $b$-Matching and List-Restricted Variants of MaxQAP

Jiratchaphat Nanta; Vorapong Suppakitpaisarn; Piyashat Sripratak

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arXiv · 2512.07618

Approximation Algorithms for the $b$-Matching and List-Restricted Variants of MaxQAP

Jiratchaphat Nanta·Vorapong Suppakitpaisarn·Piyashat Sripratak

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Abstract

We study approximation algorithms for two natural generalizations of the Maximum Quadratic Assignment Problem (MaxQAP). In the Maximum List-Restricted Quadratic Assignment Problem, each node in one partite set may only be matched to nodes from a prescribed list. For instances on $n$ nodes where every list has size at least $n - k$, we design a randomized $O(\sqrt{n}+k)$-approximation algorithm based on the linear-programming relaxation and randomized rounding framework of Makarychev, Manokaran, and Sviridenko. In the Maximum Quadratic $b$-Matching Assignment Problem, we seek a $b$-matching that maximizes the MaxQAP objective. We refine the standard MaxQAP relaxation and combine randomized rounding over $b$ independent iterations with a polynomial-time algorithm for maximum-weight $b$-matching problem to obtain an $O(\sqrt{bn})$-approximation. When $b$ is constant and all lists have size $n - O(\sqrt{n})$, our guarantees asymptotically match the best known approximation factor for MaxQAP, yielding the first approximation algorithms for these two variants.

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Jiratchaphat Nanta, Vorapong Suppakitpaisarn, Piyashat Sripratak. 2025-12-08. Approximation Algorithms for the $b$-Matching and List-Restricted Variants of MaxQAP. https://arxiv.org/abs/2512.07618

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