Questions tagged [flow-problems]

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Max Flow Routing

Let G = (V,E,S,I,T) be a directed flow network with nodes V, edges E with unit capacity, source nodes S $\subseteq$ V, intermediate nodes I $\subseteq$ V, and target nodes T $\subseteq$ V. The problem ...
sripurva's user avatar
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1 answer
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Entries of the Inverse Laplacian

Let $L$ be a graph Laplacian. What is the meaning of the entries of its (pseudo)inverse $L^{-1}$? In other words, are there any interpretations which might help with understanding the entries of $L^{-...
Zuza's user avatar
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How to maximize flow through a graph based on edge orientation (in 3D Cartesian Coordinate Space)?

Problem Stmt: Suppose you have a graph $G$ with edges $E$ and nodes $V$. The nodes have ${x,y,z}$ coordinates in 3D Cartesian space. Assuming each node contains an $x$ amount of material, the idea is ...
Vysakh's user avatar
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3 votes
2 answers
348 views

Maximum flow with parity requirement on certain edges

Consider the maximum integral flow problem on a directed graph $G=(V,E)$ with integral capacities $c:E\to \mathbb{N}$. We have an additional constraint that for the set of edges in $F\subseteq E$, the ...
Chao Xu's user avatar
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-3 votes
1 answer
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Finding a path in a graph hitting a particular vertex

Problem: Given three vertices $u, v$ and $w$ from an undirected graph. Find a path (where vertices are not repeated) from $u$ to $w$ that passes through $v$. This problem has been mentioned in ...
William4920's user avatar
3 votes
1 answer
479 views

A stronger Flow Decomposition Theorem?

In the classic Network Flows: Theory, Algorithms, and Applications book (pages 80/81) the flow decomposition theorem is stated as follows: Every nonnegative arc flow x can be represented as a path ...
saper0's user avatar
  • 133
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40 views

Maximum resistor with sublinear number of measurements

Consider a set $X = \{x_1, \dots, x_n\}$ of positive real numbers (or natural numbers, if you like) to be a set of resistors. For any subset $S \subset X$, we can build resistive circuits and measure ...
yadec's user avatar
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2 votes
1 answer
108 views

Computing the existence of a path in a code execution graph

I have a need for an algorithm which I can express as a reachability problem in a graph. Note that I'd appreciate any advices with respect to better wording this question. Also please tell me if this ...
oparisy's user avatar
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1 vote
0 answers
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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 ...
Arty's user avatar
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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 ...
robit's user avatar
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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 ...
Oliver Witt's user avatar
2 votes
0 answers
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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 $\cup$. Question: Is there ...
Oliver Witt's user avatar
1 vote
0 answers
104 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 ...
Oliver Witt's user avatar
14 votes
1 answer
889 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 $s$-...
Oliver Witt's user avatar
2 votes
0 answers
207 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 all $s$-$...
Oliver Witt's user avatar
0 votes
0 answers
93 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 $d_i$ ...
user2150466's user avatar
3 votes
1 answer
277 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 ...
a06e's user avatar
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3 votes
1 answer
966 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 $t_1$ ...
R B's user avatar
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