Questions tagged [max-flow-min-cut]

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8
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0answers
630 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 ...
6
votes
0answers
941 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 ...
6
votes
0answers
557 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 ...
5
votes
0answers
169 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 $p+1$, ...
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 ...
4
votes
0answers
84 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 ...
2
votes
1answer
152 views

Minimum cut with size bounds $k\leq |S| \leq |V|-k$

It is known by the max flow min cut theorem that the minimum cut problem is in $P$. I am interested in knowing what is known on the complexity of the minimum cut with size $k\leq |S| \leq , |V|- k$. ...
2
votes
0answers
184 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 ...
2
votes
0answers
317 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
0answers
203 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 $s$-$...
1
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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 ...
1
vote
0answers
69 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
0answers
158 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
71 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, ...
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 $e$ ...
1
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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 ...
1
vote
0answers
126 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?
1
vote
0answers
190 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 ...