Questions tagged [max-flow-min-cut]
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39
questions
5
votes
0answers
61 views
How to find the second smallest cut in a graph?
For an undirected graph, how do we find the second smallest $s,t-$cut(s) for some $s,t\in V$? What's the time complexity of this computation? What if we only cared about finding a cut of size $p+1$, ...
4
votes
0answers
81 views
Complexity of Encoding a Matroid Flow Problem in a Matrix
Context:
Take a directed graph $G$ with a specified subset of source vertices $S$ and target vertices $T$.
We say a subset $I\subseteq T$ of size $r$ is independent if there exist $r$ distinct ...
1
vote
0answers
54 views
polytime approximability of directed multicut
Does anyone know how well directed multicut can be approximated in planar and minor free graphs? Also any survey of approximability of directed multicut and multicut in various graph classes would be ...
3
votes
1answer
105 views
Interval partitioning with restrictions: NP-complete or efficiently solvable?
The interval partitioning problem can be solved efficiently using a greedy algorithm. However, adding restrictions on the interval assignment to the problem results in a problem that appears harder. ...
1
vote
2answers
221 views
Max flow with restriction of individual flows
What is known about the complexity of solving max flow with restrictions on individual flows for some nodes?
More precisely, in addition to wanting the max flow, you have a constraint for some ...
1
vote
0answers
67 views
Space complexity of global minimum cut
Are there any non-trivial bounds on the space complexity of global minimum cut? The problem is known to be in $\mathsf{RNC}$. Is anything known about containment in either $\mathsf{L}$ or $\mathsf{NL}$...
1
vote
1answer
309 views
Minimum graph cut with constraints
Given an undirected acyclic raph $G = \{V,E\}$, with each edge $e$ having weight $c_e$in the range $[-\infty, +\infty] $, I want to compute a partition of the graph into $N$ disjoint sets $G_i, i=1,......
2
votes
0answers
159 views
Maximum weight non-overlapping paths in a DAG
Suppose we have a weighted DAG $G$. A $m$-path-tuple is defined as $(P_1, ..., P_m)$ in which $P_i$ is a path on the graph, and no $P_i$ and $P_j$ share any edges. In other words each edge of the ...
0
votes
0answers
157 views
Minimum cut on a directed graph with negative term
Suppose we are given a directed Graph $G=(V,E)$ and there is a nonnegative weight $w(u,v)$ is defined for the edge from $u$ to $v$. The task is to partition vertices to $A$ and $B$ (partition means $V ...
1
vote
0answers
69 views
Sparse-cut approximation for well connected graphs
Theorem: For any graph $G=(V,E)$, there is a polynomial time algorithm that finds a cut $S \subseteq V$ with conductance at most $\sqrt{2\big(1 − \lambda(G)\big)}$.
If I understand UGC correctly, ...
2
votes
0answers
313 views
expected number of edges for fixed min cut
It is known that a graph $G=(V,E)$ with $n$ nodes and min cut $k$, must have at least $\frac{1}{2}nk$ edges.
Are there any tighter bounds or expectations I can place on $|E|$ if I assume that $G$ ...
2
votes
1answer
267 views
generate a graph with fixed min cut
Is there a constructive way to generate a graph with a fixed min cut equal to $k$?
One approach is to generate a random graph and then try to make edges alterations (additions, deletions, swaps) to ...
6
votes
0answers
900 views
Minimum vertex k-cut
Given an undirected graph $G = (V, E)$ and an integer $k$, the well-known minimum (edge) $k$-cut problem asks to find $E' \subseteq E$ with minimum $|E'|$ that the graph $(V, E \setminus E')$ has at ...
2
votes
2answers
89 views
Name of graph partition that balances edges between sets with edges remaining within sets
Is there a common name for this problem:
Let G=(V, E) be an undirected graph. Partition V into sets $S_1$, $S_2$, ..., $S_k$, such that (the number of edges between sets) + (the number of "non"-...
1
vote
0answers
93 views
Minimum cost flow with Demand and Edge Capacity scaling
Consider a the splittable minimum cost flow problem on network $G(V,E,W,C)$ and a set of commodities $(s_i,t_i)$ with demand $d_i$ for $i=1,2,\dots,k$. Here, $w_e$ and $c_e$ is the weight of edge $e$ ...
0
votes
1answer
185 views
Length bounded minimum cardinality cut in DAGs
Suppose I have a DAG with non-negative edge lengths. The problem is to compute the minimum number of edges which disconnects all paths of length L or less. We call this L-length bounded minimum ...
1
vote
0answers
102 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 ...
14
votes
1answer
556 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 $s$-...
2
votes
1answer
319 views
Maximum flow for all edges in an undirected graph
I was wondering if the following problem has been studied in the past, and what are some of the best ways people can come up with to solve it:
Let $G=(V,E)$ be an undirected graph, which we use as a ...
3
votes
1answer
114 views
Characterizing the set of problems solvable via network flow
What are some ways to prove that a certain problem cannot be solved using Network Flow (NF)?
One way is to prove the problem is NP-hard.
But NF has substantial structure -- is there some symmetry or ...
2
votes
0answers
202 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 $s$-$...
8
votes
0answers
593 views
Efficient Reduction from Min Cut to st-Min Cut
I am aware that many known algorithms for min cut problem is not by reducing the problem to $st$-min cut.
But the question of efficient reduction from min cut to $st$-min cut is still interesting to ...
0
votes
1answer
126 views
Flow networks: Push flow on either edges but not both!
I have a flow network with random capacities on edges, is there some way to add a constraint of the type (push flow on either one of these two edges but not on both)?
I'm not sure if this is correct ...
1
vote
1answer
685 views
Rings and the set of all minimum s-t-cuts
Let $N$ be a flow network with nodes $V$ and edges $E$. For technical reasons, the source side of a minimum $s$-$t$ cut $(A,B)$ with $s \in A$ and $t \in B$ is defined as $A - \{s\}$. Now, let $\...
5
votes
0answers
154 views
Indexing structure for all-pairs min-cuts in a huge DAG
I have a huge DAG - e.g., the dependency graph of all packages in a linux distribution.
Suppose I'd like to make a user-friendly tool that makes it very easy to understand how to break the transitive ...
0
votes
1answer
419 views
karger's algorithm contracting nodes not edges [closed]
Karger's algorithm works by contracting edges, not merging nodes (this is different because nodes need not share an edge).
Is there a reason why this is so?
6
votes
0answers
541 views
Weighted vertex-connectivity; global min vertex-cut
I am interested in the following problem:
Input: a connected undirected graph $G=(V,E)$; a positive weight for each vertex.
Output: a minimum weight subset of $V$ whose removal disconnects $G$.
When ...
8
votes
2answers
12k views
Fastest way to find an s-t min-cut from an s-t max-flow?
Ford-Fulkerson can find sparse s-t flows in time linear in the size of the flow and number of nodes if the edges have unit capacity.
How could I use a sparse s-t flow to find an s-t min-cut in time ...
1
vote
0answers
120 views
Do expander graphs have the property that with high probability an s-t cut is size min{degree(s),degree(t)}?
If we want a specific example, then how about the Erdos-Renyi random graph?
9
votes
1answer
409 views
Increasing the capacity to maximize the min cut
Consider a graph with all edges having unit capacity.
One can find the min cut in polynomial time.
Suppose I am allowed to increase the capacity of any $k$ edges to infinity
(equivalent to merging ...
6
votes
1answer
3k views
Can I get all min-cuts after executing Push-Relabel?
The push-relabel algorithm (here is push-relabel as pseudo-code) assigns a distance-label to each node.
After executing push relabel, you have those distance labels and a max flow in a given network ...
1
vote
0answers
175 views
Edge Cut of interval graphs
On interval graphs, minimal vertex separators are well understood: they are cliques, there are no more than $n$ ones. However, when we turn to the minimal edge cut, my search found no even one single ...
8
votes
1answer
266 views
Request for references on multicommodity flow-cut results
This is a somewhat subjective question. I am interested in studying the literature on multicommodity flow-cut results, especially the 'positive' results which show that flow is a good approximation to ...
3
votes
0answers
288 views
Graph connectivity related game [closed]
I was considering the following game on an undirected unweighted graph $G=(V,E)$ (not necessarily simple). Two players, Police and Runaway, take moves in turn. Police can cut an arbitrary subset of ...
3
votes
1answer
154 views
Primal Dual model in the continuous domain
The continuous max flow problem is posed as follows :
sup $\int_\Omega p_s(x)dx$
subject to :
$|p(x)| \le C(x); \forall x \in \Omega $
$p_s(x) \le C_s(x); \forall x \in \Omega $
$p_t(x) \le ...
15
votes
3answers
896 views
Super Mario Flows in NP?
One classical extension of the max-flow problem is the "max-flow over time" problem: you are given a digraph, two nodes of which are distinguished as the source and the sink, where each arc has two ...
15
votes
2answers
3k views
Number of mincuts of a graph without using Karger's algorithm
We know that Karger's mincut algorithm can be used to prove (in a non-constructive way) that the maximum number of possible mincuts a graph can have is $n \choose 2$.
I was wondering if we could ...
8
votes
3answers
8k views
Minimum cut through vertices/nodes - not edges
we all know and love s-t minimum cut algorithms, but they all cut through the edges in the graph. Are there any variants that cuts through nodes?
6
votes
3answers
748 views
In Strongly connected tournament T.Is it NP-hard to find a minimum number of vertices(V1) which make T\V1 as non strongly connected tournament.
Given strongly connected tournament T.find a minimum number of vertices(V1) which make T\V1 as non strongly connected tournament.
I have doubt whether the problem mentioned can be solved in polynomial ...
