# Questions tagged [minimum-cuts]

A cut is a partition of a graph's nodes into two classes. Each cut is associated with a cut-set, the set of edges straddling the cut. For more, see: https://en.wikipedia.org/wiki/Minimum_cut https://en.wikipedia.org/wiki/Stoer%E2%80%93Wagner_algorithm https://en.wikipedia.org/wiki/Karger%27s_algorithm

54 questions
Filter by
Sorted by
Tagged with
44 views

### Prove minimum vertex bisection problem is reducible from bisection width, thereby proving NP-Completeness

The bisection width problem gives you a yes or a no -> if there exists a bisection of size at most $K$ for $G=V,E$. Minimum Vertex Bisection problem gives you a bisection of the smallest size. ...
1 vote
11 views

### What are the locally optimal points in an LP formulation of the max flow problem?

I'm taking a grad level algorithms course and we just ended the course talking about linear programming, and we had previously talked about the max flow/min cut problem. Our professor said that the ...
1 vote
108 views

62 views

### Karger's min cut and tips on bounding nonlinear recurrences

I was recently working on an old qualifying exam problem asking us to generalize Karger's randomized global min cut algorithm to that of a global min $k$-cut. I recalled the strategy of running a ...
1 vote
279 views

### Finding s-t min-cut of undirected graph

Given an undirected graph with non-negative edge weights, and two vertices $s,t$ in the graph. I would like to find the minimal cut such that $s$ and $t$ are on different sides of the cut. For example ...
61 views

### Properties of Gomory-Hu trees

Given an undirected graph $G=(V,E)$ a Gomory-Hu tree $T$ for $G$ has the following properties: $T$ has a node for each vertex in the graph G and each edge in the tree corresponds to a minimum cut ...
1 vote
62 views

### Minimum cost of wood for woodworking project problem

This is a fun one, I really can't wrap my head around it. It's like an n-sum problem combined w/ a knapsack problem and I cant seem to find a solution. I'm currently building a cabinet, and had just ...
36 views

1 vote
392 views

### Minimum number of cuts to divide a rectangle

We're given a big rectangle, and a list of small rectangles contained inside it, with their vertex coordinates. We want a list of the minimum number of lines defined by a pair of points (x,y) that ...
1 vote
97 views

### Minimum number of words to define any other

I'm interested in finding the minimum number of words needed to define some fraction (perhaps 95%) of the words occurring in an English dictionary (while ignoring the challenges of disambiguating ...
1 vote
535 views

### a cut containing exactly one edge in each path

Given a digraph with a source $s$ and target $t$, must there be an edge cut which contains exactly one edge in every path from $s$ to $t$? I'm not interested in a minimum cut; any cut would do. If ...
1k views

### Is there a procedural way to find minimum s-t cut without guessing cuts?

I was reading about max flow theorem and there I saw scenario where the min s-t cut is found. But wherever I searched they did it after knowing the max flow or by guessing the cuts by iterating ...
231 views

### How to uniquely determine a min-cut? [duplicate]

There are possibly several min-cuts for the source and target nodes of a graph. I think I can determine the same min-cut for the same graph by putting the following restriction "if there are ...