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arXiv · 2610.41560

Polynomially Solvable Cases of the Quadratic Binary Optimization Problem with a Fixed Cardinality Constraint

Thi Thanh Tu Le·Thorsten Koch
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Abstract

Quadratic Unconstrained Binary Optimization (QUBO) problems and their variant with a fixed cardinality constraint are both well-known NP-hard problems. While certain structural properties of the cost matrix can make some QUBO instances solvable in polynomial time, this advantage typically disappears once a cardinality constraint is added. In this work, we investigate specific structural conditions on the cost matrix under which the constrained version-quadratic binary optimization with a fixed cardinality-remains tractable.

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Thi Thanh Tu Le, Thorsten Koch. 2026-10-30. Polynomially Solvable Cases of the Quadratic Binary Optimization Problem with a Fixed Cardinality Constraint. https://arxiv.org/abs/2610.41560

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