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A survey on combinatorial optimization

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arxiv 2409.00075 v1 pith:W4PARGGE submitted 2024-08-24 math.OC

classification math.OC
keywords optimizationcombinatorialsurveyalgorithmsproblemsaccuracyadditionallyanalyzes
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This survey revisits classical combinatorial optimization algorithms and extends them to two-stage stochastic models, particularly focusing on client-element problems. We reformulate these problems to optimize element selection under uncertainty and present two key sampling algorithms: SSA and Boost-and-Sample, highlighting their performance guarantees. Additionally, we explore correlation-robust optimization, introducing the concept of the correlation gap, which enables approximations using independent distributions with minimal accuracy loss. This survey analyzes and presents foundational combinatorial optimization methods for researchers at the intersection of this field and reinforcement learning.

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Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Explicit Solution Equation for Every Combinatorial Problem via Tensor Networks: MeLoCoToN

    cs.ET 2025-02 reject novelty 4.0 of 10

    Any finite combinatorial problem with a known logical circuit can be encoded as a tensor network whose contraction defines an explicit, though generally inefficient, solution equation.

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