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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
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0answers
27 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
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1answer
23 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
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0answers
47 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
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1answer
54 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
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0answers
15 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
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1answer
19 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
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1answer
35 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
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0answers
20 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
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1answer
32 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
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0answers
23 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
80 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
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0answers
55 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
42 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
132 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
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1answer
59 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
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3answers
115 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
156 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
52 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
153 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
33 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
92 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
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0answers
39 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
210 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
47 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 ...
5
votes
1answer
74 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
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0answers
221 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
81 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
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0answers
36 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
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0answers
178 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
107 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
117 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
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1answer
76 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
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0answers
382 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
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3answers
300 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
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1answer
386 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
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2answers
345 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
113 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 ...
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4answers
269 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 ...
3
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
475 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
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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 ...
-2
votes
1answer
507 views

Dijskstra's algorithm, maximum flow

For directed graph $(G=(V, E),s,t,{Ce})$ in which we want to maximize max flow. All edge capacities are at least one. Define the capacity of an $s \to t$ path to be the smallest capacities of ...
5
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0answers
539 views

A variation in Ford-Fulkerson algorithm

Suppose that we redefine the residual network to disallow edges into $s$. Argue that the procedure FORD-FULKERSON still correctly computes a maximum flow. I was thinking that when we augment a ...
10
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2answers
3k views

Maximum Independent Set of a Bipartite Graph

I'm trying to find the Maximum Independent Set of a Biparite Graph. I found this in some notes "May 13, 1998 - University of Washington - CSE 521 - Applications of network flow": Problem: ...
2
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1answer
284 views

Reason for global update steps in the push-relabel algorithm

I know why and how the push relabel algorithm works for solving the max-flow problem. But why is a global update step required?
8
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1answer
344 views

CLRS - Maxflow Augmented Flow Lemma 26.1 - don't understand use of def. in proof

In Cormen et. al., Introduction to Algorithms (3rd ed.), I don't get a line in the proof of Lemma 26.1 which states that the augmented flow $f\uparrow f'$ is a flow in $G$ and is s.t. $|f\uparrow f'| ...
6
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1answer
379 views

Why is the complexity of negative-cycle-cancelling $O(V²AUW)$?

We want to solve a minimal-cost-flow problem with a generic negative-cycle cancelling algorithm. That is, we start with a random valid flow, and then we do not pick any "good" negative cycles such as ...
7
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2answers
3k views

Reducing minimum vertex cover in a bipartite graph to maximum flow

Is it possible to show that the minimum vertex cover in a bipartite graph can be reduced to a maximum flow problem? Or to the minimum cut problem (then follow max-flow min-cut theorem, the claim ...
3
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2answers
581 views

Finding the maximum bandwidth along a single path in a network

I am trying to search for an algorithm that can tell me which node has the highest download (or upload) capacity given a weighted directed graph, where weights correspond to individual link ...