This chapter is devoted to the Minmax Regret Minimum Cut problem. Let G =( V , E ) be a given undirected graph with two distinguished nodes s and t called respectively a source and a sink . Consider a partition of set V into two disjoined subsets V 1 and V 2 such that s ∈ V ...
Given an s-t cut S 0, the minimax inverse minimum-cut problem (MIMC) is to find a modified upper bound utildeisin RA such that S 0 is a minimum cut for utilde and max {|u ij-utilde ij par(i,j)isinA} is minimum. This paper shows that the MIMC is closely related to the ...
1 Minimum Cost Flow and Minimum Cut Lecture 7: Jan 31 2 Flows An s-t flow is a function f on the edges which satisfies: (ca..
Each coalition selects economic activities from private activities available to its members and public activities available to all coalitions. For each coalition, a minimum-cut problem finds an optimal selection and the value of the characteristic function. The game is a convex game. Applying the ...
HDU-6214 Smallest Minimum Cut(最少边最小割) 题目链接:http://acm.hdu.edu.cn/showproblem.php?pid=6214 Problem Description Consider a networkG=(V,E)with sourcesand sinkt. An s-t cut is a partition of nodes setVinto two parts such thatsandtbelong to different parts. The cut set is ...
problem is easy to determine. considering the second scenario flow \(f^2\) first, the only option to send two flow units from source s to sink t is along paths \(sv_1t\) and \(sv_2t\) due to the capacity constraints. as the second scenario flow \(f^2\) uses both fixed arcs,...
Here $d(s,t)$ is the distance from $s$ to $t$ in $H$ and $n(s,t)$ is the number of edges of $G$ between the sets in $Π$ that contains $s$ and $t$. When the graph $H$ is complete, $(*)$ turns into the minimum multiway cut problem, which is known to be NP-...
首先是当年stoer和wagner两位大佬发表的关于这个算法的论文:A Simple Min-Cut Algorithm 直接上算法部分: 分割线begin 在这整篇论文中,我们假设一个普通无向图G=(V,E),其中每条边e都有一个正实数权值w(e)。 如果我们知道:怎样找到两个节点s,t,以及怎样得到对于s-t的最小割,我们就几乎解决了整个问题: ...
Given a connected undirected multigraph G=(V, E) with positive edge capacities and a positive integer k with k≥2, the minimum k-cut problem is to find a set SE of minimum capacity whose removal leaves k connected components. It is known that this problem is NP-hard. In this paper we...
The vast literature on the minimum cut problem can be classified into three main approaches: The maximum-flow approach The minimum cut problem was originally solved by computing the maximum st-flow [6] for all pairs of vertices s and t. In 1961, Gomory and Hu [14] showed that only O(n...