Packing under Convex Quadratic Constraints

Max Klimm; Marc E. Pfetsch; Rico Raber; Martin Skutella

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arXiv · 1912.00468

Packing under Convex Quadratic Constraints

Max Klimm·Marc E. Pfetsch·Rico Raber·Martin Skutella

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Abstract

We consider a general class of binary packing problems with a convex quadratic knapsack constraint. We prove that these problems are APX-hard to approximate and present constant-factor approximation algorithms based upon three different algorithmic techniques: (1) a rounding technique tailored to a convex relaxation in conjunction with a non-convex relaxation whose approximation ratio equals the golden ratio; (2) a greedy strategy; (3) a randomized rounding leading to an approximation algorithm for the more general case with multiple convex quadratic constraints. We further show that a combination of the first two strategies can be used to yield a monotone algorithm leading to a strategyproof mechanism for a game-theoretic variant of the problem. Finally, we present a computational study of the empirical approximation of the three algorithms for problem instances arising in the context of real-world gas transport networks.

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BibTeX RIS

Max Klimm, Marc E. Pfetsch, Rico Raber, Martin Skutella. 2019-12-01. Packing under Convex Quadratic Constraints. https://arxiv.org/abs/1912.00468

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