抬起的多切口的多面体研究

IF 0.9 4区 数学 Q3 MATHEMATICS, APPLIED
Bjoern Andres , Silvia Di Gregorio , Jannik Irmai , Jan-Hendrik Lange
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引用次数: 2

摘要

数据分析中许多应用的基础是图的分解,即将节点集划分为组件诱导子集。编码分解的一种方法是通过多元集,即跨越不同组件的边的子集。最近,在图像分析领域中,已经提出了将多集从图G=(V,E)提升到增广图G=。在这项工作中,我们详细研究了RE-F中的多面体,其顶点正是从G提升的G的多集的特征向量,特别是将其与先前关于团划分和多线性多面体的大量工作联系起来。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
A polyhedral study of lifted multicuts

Fundamental to many applications in data analysis are the decompositions of a graph, i.e. partitions of the node set into component-inducing subsets. One way of encoding decompositions is by multicuts, the subsets of those edges that straddle distinct components. Recently, a lifting of multicuts from a graph G=(V,E) to an augmented graph Ĝ=(V,EF) has been proposed in the field of image analysis, with the goal of obtaining a more expressive characterization of graph decompositions in which it is made explicit also for pairs FV2E of non-neighboring nodes whether these are in the same or distinct components. In this work, we study in detail the polytope in REF whose vertices are precisely the characteristic vectors of multicuts of Ĝ lifted from G, connecting it, in particular, to the rich body of prior work on the clique partitioning and multilinear polytope.

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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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