The tag has no wiki summary.

learn more… | top users | synonyms

-1
votes
1answer
28 views

Max-Flow Min-Cut Theorem Intuition

What is the intuition behind the Max-Flow Min-Cut Theorem? I know that the Min-Cut is the dual of Max-Flow when formulated as a linear program, but the result seems artificial to me.
1
vote
0answers
40 views

Network clearance algorithms

In the network clearance problem, we are given a simple undirected graph with a capacity assigned to each edge (and/or to each vertex). Each edge can transport up to its capacity each time step (i.e., ...
1
vote
2answers
32 views

Litterature on network-flow (optimization) approximation algorithms

I've been searching on litterature about approximation algorithms in the context of network-flow problems (optimization) to finish my bachelor degree. However, been looking in several well-known ...
3
votes
1answer
103 views

Linear programming formulation of cheapest k-edge path between two nodes

Given a directed graph $G = (V,E)$ with positive edge weights, find the minimum cost path between $s$ and $t$ that traverses exactly $k$ edges. Here is my attempt using a flow network: \begin{align} ...
2
votes
1answer
85 views

“Minimum” maximum flow with extra capacities

Problem: Suppose there is a graph, a source and a sink. Each edge has a capacity and an extra capacity that it can hold. If sink needs a defined amount of flow F, ...
0
votes
0answers
19 views

Algorithm: “Minimum” maximum flow with extra capacities [duplicate]

Problem: Suppose there is a graph, a source and a sink. Each edge has a capacity and an extra capacity that it can hold. If sink needs a defined amount of flow F, ...
1
vote
0answers
43 views

Does Edmonds Karp take back-edges into account?

I amb doubting with the implementation of the Edmonds-Karp implementation of the Ford-Fulkerson algorithm. This is a problem with flow networks. As I understand the algorithm, it consists on taking ...
3
votes
1answer
58 views

Unsplittable flow in capacitated networks

I have an undirected network with capacitated links/edges. Between some nodes unsplittable traffic has to be routed. All demands and capacities are known, but it is uncertain if all flows can be ...
1
vote
0answers
17 views

MaxSNP flow problems

Currently, I'm trying to understand the definition and notion of MaxSNP and MaxSNP-hardness. I see that several combinatorical problems such as Max-3SAT are in MaxSNP since one can easily express them ...
1
vote
0answers
78 views

Getting ALL negative weight cycles of a graph using Bellman-Ford

I'm doing a min cost assignation problem to assign doctors to their working days for a hospital. After correctly getting the max flow with Ford-Fulkerson algorithm, I would like to use the cycle ...
-1
votes
1answer
36 views

How to find a minimum cut of a network flow?

I am currently reading the lecture slides from Princeton regarding network flows but I cannot understand how they manage to find out minimum cuts from a directed graph. Could someone explain how ...
7
votes
0answers
88 views

Compute a max-flow from a min-cut

We know that computing a maximum flow resp. a minimum cut of a network with capacities is equivalent; cf. the max-flow min-cut theorem. We have (more or less efficient) algorithms for computing ...
1
vote
1answer
75 views

Formulate the Marriage Problem into a Maximum-flow problem (Graph theory)

Suppose I have $M=\{1,\ldots, n\}$ men and $W = \{1, \ldots, n\}$ women and $B =\{1, \ldots, m\}$ brokers, such that each broker knows a subset of $M \times W$ and for each pair in this subset a ...
0
votes
0answers
21 views

Maximum Flow - Proof of Total flow is equal to flow from source is equal to flow to the sink

In Maximum Flow of CLRS Book Chapter-26,in the section Lemma 26.1, the proof of total flow in the network is given as below. $|f| = f(s,V) $ [by definition] $= f(V,V) - f(V-s,V)$ [by Lemma 26.1 part ...
2
votes
1answer
23 views

Are there FPTASs for the min cost flow problem?

In literature, one can find many approximation algorithms for the multicommodity min cost flow problem or other variants of the standard single-commodity min cost flow problem. But are there FPTASs ...
1
vote
1answer
51 views

Ford-Fulkerson algorithm clarification

In the second edition of the book of Cormen "Introduction to Algorithms" appears the following example (in the left part is the residual network while in the right part shows the flow results): I ...
2
votes
0answers
22 views

Distributed push relabel with changing graph topology

There is at least one (1) distributed version propsosed for the push-relabel maximum-flow algorithm. I wonder if and how this algorithm can cope with nodes leaving or enterig the graph during runtime. ...
-1
votes
1answer
34 views

Determine whether there is a valid rounding in a table of numbers

I was told this question would be better suited here: Suppose you have a table such as: $\begin{array}{ccc} 11.998 & 9.083 & 2.919 &|& 24\\ 12.983 & 10.872 & 3.145 ...
0
votes
0answers
35 views

sum of max flow in residual graph and value of flow

My teacher today explained us this . Consider a network and suppose that at any stage during the application of the Edmonds Karp algorithm to find the max flow, let ...
3
votes
1answer
105 views

Finding a subset in bipartite graph violating Hall's condition

We are given a bipartite graph of $n \leq 200$ vertices in both the first and the second partite set. Let $U$ be some set of vertices in the first set, and $V$ those vertices from the second that are ...
3
votes
0answers
66 views

Efficient update to rational flow network?

Once we've computed the max flow in a flow network with integral capacities, we can change one of its edges' capacity by a unit and recompute a maxflow in linear time using BFS. Is there something ...
2
votes
0answers
45 views

Max Flow on low depth DAGs

I have a family of acyclic networks in which every path from the source of a given network to its target has length exactly $3$. I'm aware of a publication that in general, finding a max flow in a DAG ...
4
votes
1answer
137 views

Complexity of the decision version of determining a min-cut

I was wondering what the complexity of the following problem is: Given: A flow network $N$ with a source $s$, sink $t$ and a number $k$. Question: Is there an $s$-$t$ cut of capacity at most ...
0
votes
1answer
70 views

For a flow network, is it possible to show that there always exists a maximum flow which would assign integer values to all the edges? [closed]

Is it possible to prove that for a flow network, there always exists a maximum flow which assigns an integer value to every edge?
1
vote
3answers
128 views

Can not follow the example for max-flow-min-cut on Wikipedia

This Wikipedia example is very confusing. Its saying the max flow = min cut. But I see the max flow = 9 and the min cut = 7. If not, how does the capacity =min cut here? Which is the max flow min cut ...
2
votes
2answers
162 views

Don't understand this graph definition

I'm studying for my finals in algorithms and reading the part about flow networks. There's a certain section that has me completely stumped and it is as follows: Given a graph $G= \langle V_G, E_G ...
2
votes
1answer
59 views

Determining the minimum vertex cover in a bipartite graph from a maximum flow/matching using the residual network rather than alternating paths

Wikipedia shows how one can determine the minimum vertex cover in a bipartite graph ($G(X \cup Y, E)$) in polytime from a maximum flow using alternating paths. However, I read that the (S,T) cut ...
2
votes
2answers
177 views

What is the difference between maximal flow and maximum flow?

What is the difference between maximal flow and maximum flow. I am reading these terms while working on Ford Fulkerson algorithms and they are quite confusing. I tried on internet, but couldn't get a ...
1
vote
1answer
44 views

Minimum cut versus sparsest cut? [closed]

My question is that I'm trying to find the sparsest cut in a connected, undirected graph (all weights are = 1). Basically, I am looking trying to find the smallest cut (i.e., number of edges cut since ...
1
vote
1answer
132 views

maximum bipartite matching

I am working out with the rooks problem. If there are m rooks on an nxn chessboard,i have to give describe a polynomial (in m and n) time algorithm that finds a maximum-sized subset of the rooks such ...
0
votes
0answers
45 views

Picking an optimal initial congestion window size (high bw, high latency and short bursts)?

What is a known strategy to approach a situation where short bursts of data are being sent very often over a high bandwidth, high latency cable? I am aware of cubic but even that does not utilize a ...
5
votes
3answers
242 views

Maximum number of matched vertexes in a one-to-many bipartite graph

I have a variant of bidding problem at hand. There are N bidders(~20) who bid for items from a pool of many items(~10K). Each bidder can bid many items. I want to maximize the number of bidders who ...
0
votes
1answer
51 views

Network Flow with multiple connected subsets

Given a set of buyers, houses, agents with the following constraints: Agents only know a subset of buyers Agents only know a subset of houses Agents can only do some amount of transactions ...
6
votes
1answer
77 views

Why can't you write the 2-paths problem as a max-flow problem?

This is a follow-up question to this. Consider the 2-paths problem: Given a directed graph $D=(V,A)$ and pairs of vertices $(s_1,t_1)$ and $(s_2,t_2)$, are there paths $P_1 = (s_1,\dots, t_1)$ and ...
2
votes
0answers
284 views

Potential values of minimum cost maximum flow algorithm

I have a simple directed graph $G(V,E)$ that has a source $s$ and sink $t$. Each edge $e$ of $G$ has positive integer capacity $c(e)$ and positive integer cost $a(e)$. I am trying to find the minimum ...
1
vote
1answer
85 views

Prove that every maximal flow yields the same minimal cut

Hi I'm trying to prove the following proposition: Given a network $G,s,t,\omega$ where $\omega$ is the capacity, create a minimal cut cut ${S=\left\{ (s,v)\in E_{G_{r\_max}}\right\} }$ where ...
1
vote
0answers
40 views

residual network for a network with lower and upper bounds?

How does one construct the residual network in such a case? The formula is for edge $(u, v)$ is $$rf(u,v) = (c_{\mathrm{upper}}(u,v) - f(u,v)) + (f(v,u) - c_{\mathrm{lower}}(v, u))\,,$$ where ...
5
votes
0answers
204 views

Understanding Dinic's algorithm using dynamic trees

I have here a directed graph that I used to perform Dinic's algorithm to find maximum flow. I need to adjust this graph and this algorithm to work with dynamic trees (i.e. the Sleator-Tarjan ...
1
vote
1answer
113 views

Finding paths from the result of max flow [closed]

Suppose that I have run maxflow algorithm on a graph G and, as a result, I have a set of edges with flow on them. I would like to enumerate all possible sets of paths that comprise the maxflow. That ...
2
votes
2answers
125 views

State machine with knowledge of prior states?

I'm attepting to model a process flow where the transition to the next state is occasionally based on not only the input to the current state, but a prior state as well. Below is an example graph ...
2
votes
1answer
77 views

Multicommodity circulation formulation

On the circulation problem page on wikipedia, the multicommodity circulation problem formulation seems to be insufficient, since we can just set all but one flow to $0$, and reduce it to a circulation ...
2
votes
0answers
490 views

Effect of increasing the capacity of an edge in a flow network with known max flow

I need your help with an exercise on Ford-Fulkerson. Suppose you are given a flow network with capacities $(G,s,t)$ and you are also given the max flow $|f|$ in advance. Now suppose you are ...
0
votes
3answers
343 views

In flow networks, may source/sink have incoming/outgoing edges?

I was wondering. May the source and sink have in-out going edges in a flow-network, and if so - does Ford-Fulkerson and the max-flow min-cut theorem apply ? Flow-networks are always pictures with no ...
2
votes
1answer
458 views

Maximum number of augmenting paths in a network flow

Let's say we a have flow network with $m$ edges and integer capacities. Prove that there exists a sequence of at most $m$ augmenting paths that yield the maximum flow. A good way to start thinking ...
13
votes
2answers
394 views

Are link-cut trees ever used in practice, for max flow computation or other applications?

Many max flow algorithms that I commonly see implemented, Dinic's algorithm, push relabel, and others, can have their asymptotic time cost improved through the use of dynamic trees (also known as ...
0
votes
1answer
114 views

Push relabel algorithms in flow networks

In the CLRS book (http://en.wikipedia.org/wiki/Introduction_to_Algorithms) Chapter 26 (Maximum Flow) page 744 (third edition), there is the following equation - $$ \sum_{u \in U}e(u) \;=\; \sum_{u ...
6
votes
4answers
296 views

XOR-like behavior in flow networks

XOR is not the correct name, but I am looking for some kind of exclusive behavior. I am currently solving a set of different (assignment) problems by modeling flow networks and running a ...
4
votes
1answer
1k views

Remove minimum number of vertices to disconnect the graph

Consider an undirected graph with a source and a sink vertex. We would like to remove minimum number of vertices in that graph to disconnect any path between source and sink. Can we do this using say ...
2
votes
1answer
802 views

2OPT Approximation Algorithm for Multiway Cut Problem

In the multiway cut problem, the input is an undirected graph $G= (V, E)$ and set of terminal nodes $s_1, s_2,\ldots s_k$ are in $V$. The goal is to find a minimum set of edges in $E$ whose removal ...
7
votes
2answers
2k views

Finding negative cycles for cycle-canceling algorithm

I am implementing the cycle-canceling algorithm to find an optimal solution for the min-cost flow problem. By finding and removing negative cost cycles in the residual network, the total cost is ...