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Questions tagged [flow-problems]

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Find a max flow in a flow network that passes through a fixed number of nodes

I want to solve a network flow problem with the usual setup of a directed graph with a capacity value for each edge. However, I also have an additional constraint: I want to find the maximum flow ...
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Minimum cost circulation problem with bounded number of edges

Note: the question was taken from https://cs.stackexchange.com/questions/95479/minimum-cost-circulation-problem-with-bounded-number-of-edges Since there was no answer in that forum (even after ...
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Polynomial cases of 0 1 quadratic programm with linear constraints

A pseudo boolean function f:{0,1}^n-> R is defined as f(x)= x^tQx +cx where Q is a symmetric matrix with null elements in the diagonal. Finding the minimum of this function is solvable in polynomial ...
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Reference request on dynamic flows combined with network coding

I have read some papers about network coding and dynamic flows (flows over time). I think I have made comprehensive searches on google, google scholar and IEEE Xplore. IMHO, the reasons for the ...
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0answers
60 views

Multicuts (or multiway cuts) for 3 Terminals of Minimum Capacity

For each fixed $k \geq 3$, the following well-known problem is NP-complete. k-Multicut (aka "Multiway Cut", "k-Way Cut", "Multicut") Input: $(N,l)$ where $N=(V,E,T,c)$ is an undirected $k$-terminal ...
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An Exact Cover Variant encoded in a 4-Terminal Network

During research, I hit the following problem Exact Cover Variant (ECV) Input: Three set systems $S_1, S_2, S_3$ over a universe $U$, each closed with respect to $\cap$ and $\cup$. ...
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98 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 ...
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339 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 $s$-...
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182 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 ...
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76 views

Single source multicommodity flow on a path or tree

Given a graph $G=(V,E)$, a set of terminals $T = \{t_1,\ldots, t_n\}$, and a single source $s$, where $s\in V$ and $T \subseteq V\backslash \{s\}$. Each terminal $i$ is associated with a demand $d_i$ ...
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1answer
191 views

Random flows through fixed network

A flow network is a directed graph in which each edge has a capacity. A flow through this network is an assignment of a value to each edge that is less or equal to the edge capacity, and such that the ...
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1answer
541 views

Can the optimal minimum cost two-commodities flow be fractional on this special case?

Suppose that we have a two commodities flow network $N=<G=(V,E), s_1,s_2,t_1,t_2\in V>$. The problem is to find a minimum cost two-commodity flow in which there a flow $f_1$ from $s_1$ to $t_1$ ...