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Questions tagged [minimum-cut]

A problem in computer science related to graph theory

The minimum cut (min-cut) problem is a etic problem in computer science, studied in the theory of s. It is closely related to the problem for flow networks.

The problem is: given a weighted graph, find the cut that crosses edges with the smallest possible total weight.

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Max-Flow - Detect If A Given Edge Is Found In Some Min Cut

Given a network G=(V,E) , a max flow f and an edge e in E , I need to find an efficeint algorithm in order to detect whether there is some min cut which contains e. Another question is if I found out the e is contained in some min-cut, is it…
user975343
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Finding the minimum cut in graph with Kruskal's algorithm?

We have already seen that spanning trees and cuts are intimately related. Here is another connection. Let’s remove the last edge that Kruskal’s algorithm adds to the spanning tree; this breaks the tree into two components, thus defining a cut (S,S)…
fdh
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Randomized Min-Cut, Karger's Algorithm

I am implementing Karger's algorithm. From what I understand, the number of edges between the final two nodes is not always the Min Cut. What I am having trouble understanding is how do I actually get the min cut from this algorithm. I keep…
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s-t cut for undirected weighted graph

I recently got interested in graph theory. I came across the s-t cut for a directed graph. I learned online that the min-cut is equal to the max flow and there are standard algorithms out there that can solve the s-t min cut for a directed graph.…
Oliver Chang
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minimum cut between two arbitrary vertices given as input for an undirected unweighted graph

I have an undirected weighted graph and I need to find the minimum cut that separates two sets of vertices. I can modify my setup so as to reduce the problem to finding the minimum cut that separates two given vertices. I want to add that the…
user2844647
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Minimal cuts vs Edge connectivity

Here is a question asking the connection between the edge connectivity of a graph and its minimal cuts. As we know, the edge connectivity of an undirected graph is the minimum number k of edges that must be removed to disconnect the graph. For…
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Find the minimum set of vertices in a DAG that disconnects a certain fraction of paths

The problem is given as follows: Given a DAG and a number 0 < p ≤ 1, return the minimum-cardinality set of vertices that disconnects at least a p-fraction of paths from a source (i.e., no incoming arcs) to a sink (i.e., no outgoing arcs). For p = 1,…
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Finding the minimum cost set of nodes so that once removed, the graph is disconnected

It would be great if someone could help me. I have an undirected graph where every vertex has a weight and where no edges have weights. I want to find a set of nodes with minimum total weight for which their removal makes the graph disconnected. …
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Finding minimal cut of a flow network

I am trying to find a minimum cut of the following network I am using the following algorithm: Run Ford-Fulkerson algorithm and consider the final residual graph. Find the set of vertices that are reachable from source in the residual graph. All…
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independent times to ensure minimum cut of graph at least one trial succeeds

I just finished with the first module in the algo specialization course in coursera. There was an exam question that i could not quite understand. I have passed that exam, so there's no point for me to retake it. Out of curiosity, I want to learn…
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Looking for algorithms: Minimum cut to produce bipartite graph

Given an undirected weighted graph (or a single connected component of a larger disjoint graph) which typically will contain numerous odd and even cycles, I am searching for algorithms to remove the smallest possible number of edges necessary in…
Robert Hairgrove
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Divide a graph into same size disjoint sets with minimum cut

Is there any algorithm or code that divide graph nodes into two or more disjoint sets that satisfy following conditions: first, only edges allowed to remove. second, edges are weighted and those that would be removed must has minimum weight(minimum…
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Max Flow Min Cut

So I have worked out that there is a Max Flow of 10, which therefore means there is a minimum cut also of 10 however how do I draw a minimum cut of 10 on this image?
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Is there any difference between graph cut and graph search?

Graph based methods have been used for medical image segmentation problems. Each pixel (voxel in 3D) in the image is represented by a node in the graph while edges connect neighboring nodes. In addition, two nodes namely source and sink are added. A…
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Graph cuts and removal of edges

I am trying to understand some code from Vladimir Kolmogorov's excellent Graph cut library and I have a question regarding graph construction. Say I have a system of binary variables and I need to represent the following cut costs E(0, 0) E(0,…
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