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e-approximations with minimum packing constraint violation (extended abstract)

Jyh-Han Lin, Jeffrey Scott Vitter

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Abstract

We present efficient new randomized and deterministic methods for transforming optimal solutions for a type of relaxed integer linear program into provably good solutions for the corresponding NP-hard discrete optimization problem. Without any constraint violation, the ε-approximation problem for many problems of this type is itself NP-hard. Our methods provide polynomial-time ε-approximations while attempting to minimize the packing constraint violation.

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What this paper is about

We present efficient new randomized and deterministic methods for transforming optimal solutions for a type of relaxed integer linear program into provably good solutions for the corresponding NP-hard discrete optimization problem. Without any constraint violation, the ε-approximation problem for many problems of this type is itself NP-hard. Our methods provide polynomial-time ε-approximations while attempting to minimize the packing constraint violation.

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OpenAlex reports 216 citations for this work. Citation counts describe recorded attention and do not establish research quality.

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Available abstract

We present efficient new randomized and deterministic methods for transforming optimal solutions for a type of relaxed integer linear program into provably good solutions for the corresponding NP-hard discrete optimization problem. Without any constraint violation, the ε-approximation problem for many problems of this type is itself NP-hard. Our methods provide polynomial-time ε-approximations while attempting to minimize the packing constraint violation.

Key concepts: Constraint (computer-aided design), Computer science, Mathematical optimization, Mathematics, Geometry

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