基本类上2边连通子图凸组合的有效构造

IF 0.9 4区 数学 Q3 MATHEMATICS, APPLIED
Arash Haddadan , Alantha Newman
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引用次数: 6

摘要

我们提出了基于着色的树增强算法,并使用它们来构造2边连通子图的凸组合。这个经典工具以前已经应用于这个问题,但是我们的算法展示了它的灵活性,它-与生成树的选择协调-可以用来获得在我们的应用程序中有用的各种属性(例如,2顶点连接)。我们使用这些着色算法设计了两种已被充分研究的LP解类型上的2边连通多图问题(2ECM)和2边连通生成子图问题(2ECS)的近似算法。第一类点是半整数平方点,属于一类基本极值点,它们与一般情况具有相同的完整性间隙。对于半整数平方点,已知2ECM的完整性间隙在65到43之间。我们把上界变成97。我们研究的第二类点是一致点,其支持是一个3边连通图,每个入口为23。虽然最著名的2ECS对这些点的完整性间隙的上界小于43,但以前的结果并没有产生一个有效的算法。对于这类点,我们给出了比小于43的2ECS的第一个近似算法。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Efficient constructions of convex combinations for 2-edge-connected subgraphs on fundamental classes

We present coloring-based algorithms for tree augmentation and use them to construct convex combinations of 2-edge-connected subgraphs. This classic tool has been applied previously to the problem, but our algorithms illustrate its flexibility, which – in coordination with the choice of spanning tree – can be used to obtain various properties (e.g., 2-vertex connectivity) that are useful in our applications.

We use these coloring algorithms to design approximation algorithms for the 2-edge-connected multigraph problem (2ECM) and the 2-edge-connected spanning subgraph problem (2ECS) on two well-studied types of LP solutions. The first type of points, half-integer square points, belong to a class of fundamental extreme points, which exhibit the same integrality gap as the general case. For half-integer square points, the integrality gap for 2ECM is known to be between 65 and 43. We improve the upper bound to 97. The second type of points we study are uniform points whose support is a 3-edge-connected graph and each entry is 23. Although the best-known upper bound on the integrality gap of 2ECS for these points is less than 43, previous results do not yield an efficient algorithm. We give the first approximation algorithm for 2ECS with ratio below 43 for this class of points.

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来源期刊
Discrete Optimization
Discrete Optimization 管理科学-应用数学
CiteScore
2.10
自引率
9.10%
发文量
30
审稿时长
>12 weeks
期刊介绍: Discrete Optimization publishes research papers on the mathematical, computational and applied aspects of all areas of integer programming and combinatorial optimization. In addition to reports on mathematical results pertinent to discrete optimization, the journal welcomes submissions on algorithmic developments, computational experiments, and novel applications (in particular, large-scale and real-time applications). The journal also publishes clearly labelled surveys, reviews, short notes, and open problems. Manuscripts submitted for possible publication to Discrete Optimization should report on original research, should not have been previously published, and should not be under consideration for publication by any other journal.
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