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Questions tagged [minimum-cuts]

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Min Cut Algorithm using Randomly inserted directions

I had a question about a different randomized min cut algorithm (I don't think it is as efficient as Karger's algorithm for larger sizes of min cuts but it is more efficient for smaller ones). My ...
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1answer
24 views

Set of DAG vertices disconnecting a vertex from forbidden vertices

Let $v$ be a vertex with in-degree 0 in an (acyclic) DAG $G$, and let $F$ be a subset of $G$'s vertices (the "forbidden") vertices. Now suppose $U$ is a set of vertices such that every path from $v$ ...
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2answers
24 views

Maximum Changes that don't Break the Build

Let's say I have a set of changes, e.g. replacing foo with bar in a codebase, how do I programmatically discover the largest set ...
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1answer
19 views

Is there an FPRAS for the number of min st cuts in general graphs?

Provan and Ball [1] showed that the problem of counting the number of minimum st cuts is #P-Complete. What is known about the problem of approximating the number of min st cuts? Is it possible to get ...
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1answer
41 views

Why 2 different edge min-cuts in an undirected multigraph must be completely disjoint?

For the proof of a maximum of (n 2) min-cuts in any n-vertex undirected multigraph using the random contraction algorithm, we need to know that no min-cut shares an edge with another different one. ...
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1answer
37 views

Increasing the weights of all edges in an undirected graph makes a minimum cut still minimum

We have an undirected graph, with a weight function and a minimum cut. If you raise the weights of all the edges by one, the minimum cut remains minimal even with the new weights. I know this is ...
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1answer
393 views

Please indicate whether each of the following statements is TRUE or FALSE and provide a brief justification

I provided my answers in the "answer your own question" bit. I have applied the same logic for my answers to a&b and c&c which seem to be essentially the same questions. Am I right though? a)...
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1answer
382 views

Given max-flow determine if edge is in a min-cut

We were given an exam question of: Given a flow network G=(V,E) with integer edge capacities, a max-flow f in G, and a specific edge e in E, design a linear time algorithm that determines whether or ...
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1answer
31 views

If value of LP relaxation of s-t minimum cuts is P ,then wen can find a s-t cut at most P edges?

My problem is mainly from this lecture notes on convex optimization here page4 Consider a s-t Minimum problem, on unweighted undirected graph $G=(V,E)$,we can formalize in following linear integer ...
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0answers
42 views

For a minimum cut $(S, T)$, why do edges entering $S$ have a flow value of $0$?

I'm studying for an exam and I'm having trouble with a specific question: Let there be a flow network $G = (V, E)$ with a maximum flow $f$ and capacity $c$, a source $s \in V$ and a sink $t \in V$, ...
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171 views

Separating a Graph into Two Components

I have an unweighted and undirected graph, and I want to divide this graph into two connected components by removing some vertices. The main objective is to minimize the number of vertices which must ...
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151 views

LP realaxation for multicut problem with polynomial number of constraints

The integer linear programming formulation for the multicut problem for the given graph $G = (V,E)$ and distinguished source-sink pairs of vertices $(s_1,t_1),...,(s_k,t_k)$ is: \begin{alignat}{3} \...
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1answer
433 views

Hackerearth practice problem not able to understand

I am not able to understand below problem, mainly the example. I have tried to ask explanation in their website but not received help yet. how they are calculating 36 and 43? and why 36+43 = 30$ is ...
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1answer
75 views

Minimum number of cuts to divide a rectangle

We're given a big rectangle, and a list of small rectangles contained inside it, with their vertex coordinates. We want a list of the minimum number of lines defined by a pair of points (x,y) that ...
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0answers
47 views

Minimum number of words to define any other

I'm interested in finding the minimum number of words needed to define some fraction (perhaps 95%) of the words occurring in an English dictionary (while ignoring the challenges of disambiguating ...
1
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1answer
187 views

a cut containing exactly one edge in each path

Given a digraph with a source $s$ and target $t$, must there be an edge cut which contains exactly one edge in every path from $s$ to $t$? I'm not interested in a minimum cut; any cut would do. If ...
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0answers
413 views

Is there a procedural way to find minimum s-t cut without guessing cuts?

I was reading about max flow theorem and there I saw scenario where the min s-t cut is found. But wherever I searched they did it after knowing the max flow or by guessing the cuts by iterating ...
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0answers
61 views

How to uniquely determine a min-cut? [duplicate]

There are possibly several min-cuts for the source and target nodes of a graph. I think I can determine the same min-cut for the same graph by putting the following restriction "if there are ...
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0answers
345 views

Algorithm for finding cut vertex and bridge in directed graph [closed]

In un-directed graph it is easy to find cut vertex and bridge but in directed graph removing cut vertex/bridge must increase number of strongly connected componenets.
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1answer
158 views

Max flow not min cut?

I understand the relation between max flow and min cut, however I made this (simplified) graph, and I cant figure out why max flow seems to be different from my min cut. Im probably overlooking ...
5
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1answer
288 views

Min-cut in graph with demands/lower bounds

This week I read something about network flow from Algorithm Design. But I am confused about some concepts. We say, if a graph G contains some nodes with demands, positive or negative, how to define ...
2
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1answer
310 views

Karger's algorithm: why does every vertex have degree at least the number of edges crossing a min cut?

I'm currently watching a video on the analysis of Krager's Algorithm, and I am confused about something. The analysis goes as follows: Fix a min cut $(A,B)$. Let $k$ = # of edges crossing $(A,B)$ , ...
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162 views

Small LP for directed min cut?

Undirected min cut has a well known poly sized LP formulation by expressing the problem as one of finding a certain metric on the vertices minimizing the sum of distances on edges. Can this be ...
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0answers
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Dominator tree with edges annotated by min-cut size

Consider the dominator tree of, say, the graph of objects in memory, computed by a memory profiler - one of the most powerful memory leak debugging features, I believe. The dominator tree tells you "...