发表机构
Grainger College of Engineering. Univ. of Illinois, Urbana-Champaign（伊利诺伊大学厄巴纳-香槟分校格雷格工程学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文从拟阵多面体视角，研究随机收缩算法，引入商有界拟阵概念，将图、超图等的多种最小割算法纳入统一框架。
AI 中文摘要
Karger用于求解图全局最小割的优雅随机收缩算法具有极高影响力，近年已有多种不同的非均匀随机收缩算法被提出，用于求解超图和 hedgegraph 的最小割。为实现以统一方式理解这些算法的概念目标，我们研究用于求解拟阵多面体最小商的随机收缩算法，引入商有界拟阵的概念，并证明若干现有结果可在商有界拟阵的通用算法框架下推导和理解。
英文摘要
Karger's elegant random contraction algorithm for finding a global mincut in a graph has been highly influential. More recent work has obtained several different (nonuniform) random contraction algorithms for mincut in hypergraphs and hedgegraphs. Motivated by the conceptual goal of understanding these algorithms in a unified fashion, we study random contraction algorithms for finding a minimum quotient of a polymatroid. We introduce the notion of quotient-bounded polymatroids and show that several existing results can be derived and understood under a common algorithmic framework for quotient-bounded polymatroids.
