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0answers
21 views

Minimum cost flow with Demand and Edge Capacity scaling

Consider a the splittable minimum cost flow problem on network $G(V,E,W,C)$ and a set of commodities $(s_i,t_i)$ with demand $d_i$ for $i=1,2,\dots,k$. Here, $w_e$ and $c_e$ is the weight of edge $e$ ...
0
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1answer
58 views

Length bounded minimum cardinality cut in DAGs

Suppose I have a DAG with non-negative edge lengths. The problem is to compute the minimum number of edges which disconnects all paths of length L or less. We call this L-length bounded minimum ...
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0answers
77 views

Multicuts composed of Min-Cuts

Multicuts or multiway cuts are (edge) cuts of minimum capacity that separate each pair of a set of terminals (a subset of the entire node set). For two terminals, this is the classical $s$-$t$ mincut ...
13
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1answer
208 views

Second Smallest $s$-$t$-Cut in a Network

Is anything known about the second smallest $s$-$t$-cut in a flow network? Or, more general, about this problem: Input: A network $N$ and a number $k$, all in binary. Output: A $k$th smallest ...
2
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1answer
99 views

Maximum flow for all edges in an undirected graph

I was wondering if the following problem has been studied in the past, and what are some of the best ways people can come up with to solve it: Let $G=(V,E)$ be an undirected graph, which we use as a ...
3
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1answer
72 views

Characterizing the set of problems solvable via network flow

What are some ways to prove that a certain problem cannot be solved using Network Flow (NF)? One way is to prove the problem is NP-hard. But NF has substantial structure -- is there some symmetry or ...
2
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0answers
145 views

Characterization of the Set of all s-t-Min-Cut Edge Sets

I would like to know how to answer the following problem: Input: A family of sets $S$ over a universe $U$. Question: Is there a directed flow network $N$ with edges $U$ such that the set of ...
8
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1answer
176 views

Efficient Reduction from Min Cut to st-Min Cut

I am aware that many known algorithms for min cut problem is not by reducing the problem to $st$-min cut. But the question of efficient reduction from min cut to $st$-min cut is still interesting to ...
0
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1answer
61 views

Flow networks: Push flow on either edges but not both!

I have a flow network with random capacities on edges, is there some way to add a constraint of the type (push flow on either one of these two edges but not on both)? I'm not sure if this is correct ...
1
vote
1answer
255 views

Rings and the set of all minimum s-t-cuts

Let $N$ be a flow network with nodes $V$ and edges $E$. For technical reasons, the source side of a minimum $s$-$t$ cut $(A,B)$ with $s \in A$ and $t \in B$ is defined as $A - \{s\}$. Now, let ...
4
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0answers
97 views

Indexing structure for all-pairs min-cuts in a huge DAG

I have a huge DAG - e.g., the dependency graph of all packages in a linux distribution. Suppose I'd like to make a user-friendly tool that makes it very easy to understand how to break the transitive ...
0
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1answer
210 views

karger's algorithm contracting nodes not edges [closed]

Karger's algorithm works by contracting edges, not merging nodes (this is different because nodes need not share an edge). Is there a reason why this is so?
5
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0answers
261 views

Weighted vertex-connectivity; global min vertex-cut

I am interested in the following problem: Input: a connected undirected graph $G=(V,E)$; a positive weight for each vertex. Output: a minimum weight subset of $V$ whose removal disconnects ...
5
votes
2answers
3k views

Fastest way to find an s-t min-cut from an s-t max-flow?

Ford-Fulkerson can find sparse s-t flows in time linear in the size of the flow and number of nodes if the edges have unit capacity. How could I use a sparse s-t flow to find an s-t min-cut in time ...
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0answers
104 views

Do expander graphs have the property that with high probability an s-t cut is size min{degree(s),degree(t)}?

If we want a specific example, then how about the Erdos-Renyi random graph?
6
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0answers
173 views

Increasing the capacity to maximize the min cut

Consider a graph with all edges having unit capacity. One can find the min cut in polynomial time. Suppose I am allowed to increase the capacity of any $k$ edges to infinity (equivalent to merging ...
5
votes
1answer
607 views

Can I get all min-cuts after executing Push-Relabel?

The push-relabel algorithm (here is push-relabel as pseudo-code) assigns a distance-label to each node. After executing push relabel, you have those distance labels and a max flow in a given network ...
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0answers
110 views

Edge Cut of interval graphs

On interval graphs, minimal vertex separators are well understood: they are cliques, there are no more than $n$ ones. However, when we turn to the minimal edge cut, my search found no even one single ...
8
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1answer
220 views

Request for references on multicommodity flow-cut results

This is a somewhat subjective question. I am interested in studying the literature on multicommodity flow-cut results, especially the 'positive' results which show that flow is a good approximation to ...
3
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0answers
243 views

Graph connectivity related game [closed]

I was considering the following game on an undirected unweighted graph $G=(V,E)$ (not necessarily simple). Two players, Police and Runaway, take moves in turn. Police can cut an arbitrary subset of ...
3
votes
1answer
143 views

Primal Dual model in the continuous domain

The continuous max flow problem is posed as follows : sup $\int_\Omega p_s(x)dx$ subject to : $|p(x)| \le C(x); \forall x \in \Omega $ $p_s(x) \le C_s(x); \forall x \in \Omega $ $p_t(x) \le ...
14
votes
3answers
791 views

Super Mario Flows in NP?

One classical extension of the max-flow problem is the "max-flow over time" problem: you are given a digraph, two nodes of which are distinguished as the source and the sink, where each arc has two ...
8
votes
1answer
920 views

Number of mincuts of a graph without using Karger's algorithm

We know that Karger's mincut algorithm can be used to prove (in a non-constructive way) that the maximum number of possible mincuts a graph can have is $n \choose 2$. I was wondering if we could ...
5
votes
2answers
2k views

Minimum cut through vertices/nodes - not edges

we all know and love s-t minimum cut algorithms, but they all cut through the edges in the graph. Are there any variants that cuts through nodes?
6
votes
3answers
438 views

In Strongly connected tournament T.Is it NP-hard to find a minimum number of vertices(V1) which make T\V1 as non strongly connected tournament.

Given strongly connected tournament T.find a minimum number of vertices(V1) which make T\V1 as non strongly connected tournament. I have doubt whether the problem mentioned can be solved in polynomial ...