Abstract

We show how to round any half-integral solution to the subtour-elimination relaxation for the TSP, while losing a less-than \(-\)  1.5 factor. Such a rounding algorithm was recently given by Karlin, Klein, and Oveis Gharan based on sampling from max-entropy distributions. We build on an approach of Haddadan and Newman to show how sampling from the matroid intersection polytope, combined with a novel use of max-entropy sampling, can give better guarantees.

中文翻译：

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基于Matroid的半积分解的TSP舍入

摘要

我们展示了如何将任何半积分解舍入到 TSP 的子巡回消除松弛，同时损失小于\(-\)  1.5 的因子。最近，Karlin、Klein 和 Oveis Gharan 基于最大熵分布采样给出了这种舍入算法。我们以 Haddadan 和 Newman 的方法为基础，展示了如何从拟阵交叉多胞体中进行采样，并结合最大熵采样的新颖用法来提供更好的保证。