Packing under convex quadratic constraints

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 two different algorithmic techniques: a rounding technique tailored to a conve...

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Bibliographic Details
Published in:Mathematical programming Vol. 192; no. 1-2; pp. 361 - 386
Main Authors: Klimm, Max, Pfetsch, Marc E., Raber, Rico, Skutella, Martin
Format: Journal Article
Language:English
Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.03.2022
Springer
Springer Nature B.V
Subjects:
Algorithms
Approximation
Calculus of Variations and Optimal Control; Optimization
Combinatorics
Full Length Paper
Game theory
Mathematical analysis
Mathematical and Computational Physics
Mathematical Methods in Physics
Mathematics
Mathematics and Statistics
Mathematics of Computing
Numerical Analysis
Rounding
Theoretical
90C35
68Q25
90C27
ISSN:0025-5610, 1436-4646
Online Access:Get full text
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Summary: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 two different algorithmic techniques: a rounding technique tailored to a convex relaxation in conjunction with a non-convex relaxation, and a greedy strategy. We further show that a combination of these techniques 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 these algorithms for problem instances arising in the context of real-world gas transport networks.
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ISSN:0025-5610
1436-4646
DOI:10.1007/s10107-021-01675-6