Problem
Research questions and friction points this paper is trying to address.
random contraction
polymatroid
minimum quotient
hypergraph
hedgegraph
A Polymatroidal Perspective on Random Contraction
🤖 AI Summary
研究通过引入商有界多拟阵的概念，提出一种统一的算法框架来理解和推导不同图结构中的随机收缩算法以求解最小商问题。
📝 Abstract
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.
Innovation
Methods, ideas, or system contributions that make the work stand out.
Polymatroid
Random Contraction
Quotient-Bounded Polymatroids
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