Questions tagged [network-flow]

For questions related to the formulation or solution methodologies of network flow problems. Some of the well-known network flow problems are maximum flow problem, minimum-cost flow problem, and multi-commodity flow problem.

17 questions with no upvoted or accepted answers
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Demonstrating a given solution is basic for a MCFP?

Given a minimum-cost flow problem, how could I go about demonstrating that a specific solution (as sets of basic and non-basic (!) arcs that build a rooted spanning tree for a given graph) is basic ...
5
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0answers
58 views

Complexity of solving a certain commodity flow problem

Does anyone know the complexity of obtaining the optimal solution to the integral multi-commodity network flow problem with unit demands, integral capacities, but the cost of using an arc varies ...
5
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0answers
265 views

Solver for Go Programming Laguage

Has anyone used MIP solvers (open source or commercial) with Go language https://golang.org/? I am looking for a solver for simple linear MIPs for network flows and set cover types of problems.
3
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0answers
87 views

Sources of Min-Cost Flow Models That Utilize Binary Variables for Transportation Networks

I am looking for articles that include min-cost flow models with binary variables for flow transportation like gas networks, traffic systems, heating systems. Is there any specific place(like OR ...
3
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0answers
73 views

Availability of library for solving generalized network flow problems

I need to solve a large-scale generalized network flow problem. For reference, it is a pure network-flow model with the exception that arcs have a positive coefficient applied to flow on them. In my ...
3
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0answers
169 views

Multi-commodity (Integral) flow problem with unit demand; complexity

It seems to me that a multi-commodity flow problem should be treated differently when the commodity demand constraint is an equivalence and not a lower-bound. Consider a unit demand. Apparently, in ...
3
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0answers
69 views

Simplex method on graphs: How do I find a basic solution using the Ford-Fulkerson algorithm?

I'm tasked with solving a minimal cost flow problem. I'm asked to first use the Ford-Fulkerson algorithm on my graph to find a basic solution that will then be used to do the simplex method on that ...
2
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0answers
26 views

Lexicographic flow property and consequences

I am struggling with the understanding of the (quite famous) paper on lexicographical flows: Maximal, Lexicographic, and Dynamic Network Flows - by Edward Minieka ...
2
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0answers
121 views

Solving transportation problem by the Network Simplex

I am trying to solve the following problem using Network Simplex method. But I have questions. My attempt: Basis Matrix$(B)$ Rows: 1, 2, 3, 4, 5 Column: (1,3) (1,4) (1,5) (2,3) (2,4) (2,5) $$ \...
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0answers
22 views

Asserting solution existence via approximation of multi-commodity integral flow

Consider a polynomial $\epsilon$-approximation for MCF with integral flow (like the one based on LP relaxation). Can I (in general) use this algorithm as a predicate, asserting whether a solution ...
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0answers
30 views

Multi-commodity flow problem reduction

Assume to tackle a particular group of instances for the integral multi-commodity flow problem. Particularly, given a digraph $G = (V \cup S \cup T,E)$, such that $S, T, V$ are all disjoint. ...
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0answers
22 views

Solving a max-flow problem through lex-max flow problem

Assume that, for a given network, its multi-sink multi-source max-flow satisfies a lexicographic order. Is this enough to state that I can solve the max-flow problem, by using a lex-max solver (i.e. a ...
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20 views

Complexity of lexicographic integral flow

I read that the lexicographic flow problem is polynomially solvable. However it allows for continuous flow values. Is there any reference about the problem with integral flow (and its complexity)?
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23 views

Is there a difference between "Integral Quickest Transshipment" and "Integral Quickest Multicommodity flow"?

I can't get the difference between this two problems, which seem equal to me. But, for the former, a polynomial solver is known, while, for the latter, it is not. EDIT - References: ...
1
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103 views

Simplex - Network flow problem : Arc from 1 to P with infinite capacity

The Network - Maximum flow problem below aims to find the maximum flow using simplex method : With the LP as follow : LP : \begin{Bmatrix} Z(Max) = \sum_{i=1}^{m} fi \\ Af =0 \end{Bmatrix} ...
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0answers
90 views

struggling to understand why this is a bi-objective function

i am working on a network-design problem. Where Containerflow between 2 Origin-Destination-Port-Pairs has to be fullfilled via some hub-ports. Sure, you want to pick a hub-port based on the distance, ...
0
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0answers
58 views

Different ways to model node switching (Flow on/off) in network flow problem

I would like to model a network flow problem in which there are some pipelines and valves. I would like to model valves in the problem. The valves let flow run or stop just like the on/off switch. One ...