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Questions tagged [minimum-cuts]

A cut is a partition of a graph's nodes into two classes. Each cut is associated with a cut-set, the set of edges straddling the cut. For more, see: https://en.wikipedia.org/wiki/Minimum_cut https://en.wikipedia.org/wiki/Stoer%E2%80%93Wagner_algorithm https://en.wikipedia.org/wiki/Karger%27s_algorithm

65 questions
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Minimum-cut with minimum number of edges

I am sure many folks here know the famous min-cut max-flow theorem - the capacity of the minimum cut is equal to the maximum flow from a given source, s, to a given sink, t, in a graph. Firstly, let's state (for completeness) that an s-t cut is the…
Donald
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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 the min cut for these graphs? If we still use the…
Federer
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Finding a minimum cut with an upper bound on the set sizes

In the (unweighted) minimum k-cut problem, the goal is to partition the nodes in a given graph to at least $k$ subsets, such that the number of edges between different subsets is as small as possible. I am interested in a variant in which the number…
Erel Segal-Halevi
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Does there exist an algorithm / software that finds optimal graph partition while enforcing contiguity on a subgraph?

I am interested in the traditional graph partitioning problem, which roughly speaking seeks to obtain a partition of a graph into a number of components, in which each component has about the same size (either in terms of number of nodes or sum…
Ike348
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find the union of all min cuts of a flow network

I'm trying to solve the following question : Given a flow network $N = (G=(V,E),c,s,t)$. Let $\mathcal F$ be the set of all minimum cuts. Prove that $\mathcal F$ is closed under intersections and unions, i.e. for every $ S_1,S_2\in\mathcal F , S_1…
giorgioh
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Karger's min-cut (contraction): Combinatorial argument for success probability?

The contraction algorithm for min-cut is: pick an edge $(u,v)$ uniformly at random, and "contract" it by merging $u$ and $v$ into a single vertex, deleting self-loops. Continue until two vertices remain; return this cut. The probability of finding…
usul
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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 "if you manage to make this object unreachable,…
jkff
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Will the Ford-Fulkerson Algorithm always return the same min-cut for any source-sink from one side of the min-cut to the other?

I was playing around with https://visualgo.net/en/maxflow when I realized a pattern: Take this graph, for example. We notice that the min-cut divides the graph into two sets of nodes: {0, 2, 3, 6} and {1, 4, 5, 7}. I noticed that choosing any node…
Green Ideology
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The Cut Lemma for graphs with non-distinct edges

In my introductory algorithms class I recently learned about the Cut Lemma and how it can be used to prove correctness for many Minimum Spanning Tree algorithms like Kruskal's and Prim's. In class, to simplify these proofs-of-correctness, we assumed…
Andrew Bell
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Karger's min cut and tips on bounding nonlinear recurrences

I was recently working on an old qualifying exam problem asking us to generalize Karger's randomized global min cut algorithm to that of a global min $k$-cut. I recalled the strategy of running a recursive version of the randomized edge contraction…
spektr
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Smallest $s$-component in mincut

Suppose there is a directed graph $G=(V,E)$, with source $s$ and sink $t$, and I compute the max flow on it. Then I know that I can find a min-cut $(A,B)$, by letting $A$ be the set of vertices that are reachable from the source $s$. My question is…
eatfood
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is it possible to find the maximal min cut in polynomial time?

A maximal minimum cut is a minimum capacity cut with the largest number of edges.
42069walrus
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Forcing an edge to be in S-T min-cut

Given a flow-network $N=(G,c,s,t)$ and an edge $e=(u,v)$, I am trying to build an algorithm that finds a minimum $(S,T)$ cut in the given network, that includes e. So, I tried couple of steps, first, I know I must saturate $e$ so it could be in any…
Yoav Ben Haim
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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 not, how close to "exactly one" can we get?
Larry Moss
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Algorithm for finding cut vertex and bridge in directed graph

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.
Dumb Scientist
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