Skip to main content
Share Your Experience: Take the 2024 Developer Survey

Questions tagged [max-cut]

Questions on the maximum cut problem, where one is given a graph and wants to find a subset of the vertex set such that number of edges between it and the complementary subset is as large as possible.

Filter by
Sorted by
Tagged with
2 votes
2 answers
84 views

Max cut 2-approximation algorithm

Given an undirected unweighted graph $G$, we'll define $f(G)$ as the maximum number of edges crossing a cut in $G$. Find a (polynomial) 2-approximation for $f$. I know about the probabilistic method, ...
sadcat_1's user avatar
  • 241
2 votes
1 answer
42 views

Finding a Maximum Cut With Force Labeled Vertices for Planar Graphs

The maximum cut problem is a combinatorial optimization problem that seeks to partition the vertices of a graph into two sets, $S$ and $T$, in a way that maximizes the number of edges that cross ...
Daniel García's user avatar
1 vote
1 answer
127 views

Reduction from MAX-3-CUT to MAX-CUT

Both MAX-CUT and MAX-3-CUT are known to be NP-complete. This post shows a reduction from MAX-CUT to MAX-3-CUT. I am curious if there is a way to reduce MAX-3-CUT to MAX-CUT? MAX-CUT: Given an ...
Phasivio's user avatar
  • 113
2 votes
1 answer
232 views

Min-cut with maximal number of edges

I’ve searched for a solution for this problem for some time now, it is out of an algorithm question sheet. We know that in order to find the minimal amount of edges in a flow graph’s min-cut we need ...
Aishgadol's user avatar
  • 355
3 votes
1 answer
120 views

Efficiently determine which nodes should leave a graph while maintaining connectedness

Suppose I have a graph with node weights, where a weight is either -1 or a positive integer. For example: If a node has weight -1, it is "happy", and cannot be kicked out of the graph. If a ...
416E64726577's user avatar
0 votes
0 answers
200 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. ...
Prboetic's user avatar
1 vote
1 answer
65 views

Split a graph before actually creating it

Consider a weighted graph $G=(V,E)$ of vertex set $V = \{v_1, ..., v_n\}$ and weighted edge set $E = \{\langle v_i, v_j, w(i,j)\rangle \mid i, j \in 1, ..., n\}$, where $w$ is the function that assign ...
incud's user avatar
  • 551
0 votes
1 answer
28 views

Maxcut problem of spatial embedding graphs

Given a graph $(V,E)$, I'm interested in embedding it into a Euclidean space $\mathbb{R}^n$ such that each vertex $v\in V$ becomes a point $x_v\in\mathbb{R}^n$ and $d(x_v,x_u) \leq 1$ (Euclidean ...
user113988's user avatar
9 votes
1 answer
688 views

Spatial embedding of graph

Given a graph $(V,E)$, I'm interested in embedding it into a Euclidean space $\mathbb{R}^n$ such that each vertex $v\in V$ becomes a point $x_v\in\mathbb{R}^n$ and $d(x_v,x_u) \leq 1$ (Euclidean ...
user113988's user avatar
0 votes
0 answers
69 views

Score and bound in Goemans-Williamson algorithm

I am trying to have a deeper understanding of the following implementation of the Goemans-Williamson algorithm for solving the maxcut problem. ...
Omar Shehab's user avatar
1 vote
0 answers
41 views

Finding a cut maximizing average weight of cut edges

Just checking if this version of Max Cut is still NP-hard: Given a fully connected graph $G(V,E)$, where every vertex is connected to every other vertex, and where every edge has a weight associated ...
DBrons's user avatar
  • 13
1 vote
1 answer
98 views

How to find a cut in a graph with additional constraints?

I have a complete undirected graph $G=(V,E)$ with positive non-null rational weights $c:E \to \mathbb{Q}^+_{*}$ on the edges, such that $c(v,v) = 0$ for all $v$, and a subset $C \subset V$. I would ...
Matheus Diógenes Andrade's user avatar
3 votes
1 answer
1k views

Using a greedy algorithm to find a cut S which at least half of the edges cut

Let $G$ be an undirected graph. Find a greedy algorithm that finds a cut $S$ which at least half of the edges cut. I tried to think about something like choosing the vertex with the highest degree, ...
EL_9's user avatar
  • 133
2 votes
1 answer
31 views

Separation guarantee in Goemans Williamson algorithm

In the original paper in Goemans-Williamson paper for max-cut, we need to sample a random vector r and we output $$ S = \{i : r^{T}x_{i} \geq 0\} $$ where $x_{i}$ are column vector of a feasible ...
exteral's user avatar
  • 135
2 votes
0 answers
38 views

planar max cut graph with constrains

Given a planar graph $G=(V, E)$ I am looking for a max cut algorithm with the following conditions : some vertices are in one of the partition sets? Is the algo is still polynomial ? I mean a ...
wildelkhadra's user avatar
9 votes
2 answers
992 views

Prove that the 2-approximation of a modified local search algorithm for max-cut is tight

Consider the following local search approximation algorithm for the unweighted max cut problem: start with an arbitrary partition of the vertices of the given graph $G = (V,E) $, and as long as you ...
Tav's user avatar
  • 113
1 vote
1 answer
1k views

How can i prove that MAX-CUT is in NP?

How can i show/explain/prove that Max-Cut is in NP? "For a graph, a maximum cut is a cut whose size is at least the size of any other cut. The problem of finding a maximum cut in a graph is known as ...
user108220's user avatar
1 vote
1 answer
179 views

Derandomize MAX-CUT problem using $\log n$ bits

Consider the MAX-CUT problem. We can flip $n$ coins to generate a random cut, and by linearity of expectation we get that with "good probability" our cut we'll be bigger then $\frac{n}{2}$. Using ...
galah92's user avatar
  • 327
2 votes
2 answers
526 views

Complexity of finding Exact Size Cut-Sets in Bipartite Graphs

I am interested in the problem of deciding if a cut-set of a given size $k$ (i.e. the number of edges crossing the partitions is $k$) exists in a given bipartite graph (both the graph and $k$ are part ...
allrtaken's user avatar
0 votes
1 answer
901 views

Reducing INDSET and MAXCUT to 3SAT

Given a graph and an integer $k$ is there an independent set larger than $k$ is INDSET problem and is there a cut larger that $k$ is the MAXCUT problem. Is there standard way to convert to 3SAT from ...
Turbo's user avatar
  • 2,891
1 vote
2 answers
2k views

Does graph G with all vertices of degree 3 have a cut vertex?

I'm asked to draw a simple connected graph, if possible, in which every vertex has degree 3 and has a cut vertex. I tried drawing a cycle graph, in which all the degrees are 2, and it seems there is ...
Mohanad Osman's user avatar
1 vote
0 answers
522 views

solving max cut problem on a huge graph (500 x 500) using Semidefinite Programming with CVXOPT

So I am learning to do SDP relaxation on graph problems, and for this max cut problem I am given a 500*500 graph, and I am using the straightforward relaxation. $W$ is the weight matrix, $X = u u^T$ ...
Donnie's user avatar
  • 11
3 votes
1 answer
299 views

Why the Goemans-Williamson's MAX-CUT algorithm relax the variables to vectors of $n-$dimension on unit sphere?

Why not to some constant like 3 or 4 dimension? I suspect that it is because Cholesky Decompostion will work only for $n \times n$ matrix $B$ where $B^TB = P$ where $P$ is a semidefinite matrix. Is it ...
Vimal Raj Sharma's user avatar
3 votes
0 answers
754 views

Greedy max k-cut approximation algorithm

I'm trying to formulate a greedy algorithm for the Max k-cut problem: Let's have an not oriented graph $G(V,E)$, each edge $e \in E$ has its weight $w_e$. The goal of the algorithm is to divide all ...
jenda's user avatar
  • 151
0 votes
2 answers
466 views

NP hardness of partitioning a graph into two subgraphs

Given a planner graph which it's vertexes have weights and an integer, W, this graph should be partitioned into two subgraphs which sum of weights for each subgraph becomes at least W. I wanted to ...
NedaHn's user avatar
  • 135
4 votes
1 answer
6k views

Maximum cut using a 1/2 approximation greedy algorithm

I have the following greedy algorithm for max cut problem: Initialization: $A \leftarrow \{v_1\}$ , $B \leftarrow \{v_2\}$ For $v \in V − \{v_1, v_2\}$ do: if $d(v,A) \geq d(v,B)$ then $B \...
NedaHn's user avatar
  • 135
2 votes
1 answer
1k views

Maximum flow with edge demands: can't understand the example of transition to transformed graph in the lecture notes

TL;DR: There're lecture notes about a very simple reduction from "maximum flow with edge demands problem to the maximum flow problem. But I can't get the new capacities at the picture: E.g., look at ...
Alex's user avatar
  • 21
1 vote
1 answer
77 views

Maximum One Third Cut

I want to solve the following problem (This is a homework problem. Not looking for definite or complete answers): Maximum One Third Cut: Input: An undirected graph G=(V,E) where V={1,2,...,n}, such ...
Idra's user avatar
  • 167
1 vote
1 answer
607 views

Degree Reduction in Max Cut and Vertex Cover

I have been reading Alimonti and Kann's paper "Some APX-Completeness results for cubic graphs" and I don't understand why the degree-reduction gadgets for Max Cut and Min Vertex Cover have to be ...
SamTheTomato's user avatar
2 votes
1 answer
659 views

Relation between MAX CUT and MIN CUT

I'd like to ask a question about MAX CUT and MIN CUT on graphs with unit edge-weight. I know that MAX CUT is NP-Hard, but MIN CUT is in P (i think)? Barahona, in 1982, showed (Lemma 1) finding a cut ...
SamTheTomato's user avatar
5 votes
1 answer
3k views

Reduction from PARTITION to MAX-CUT

I am trying to prove the NP-Hardness of the MAX-CUT problem. Other sources seem to reduce from the NAE-3SAT problem, however I have been trying to reduce from PARTITION because PARTITION and MAX-CUT ...
Dave White's user avatar
5 votes
1 answer
238 views

What is the significance of the vector dimension in semidefinite programming relaxations?

Let's say that we want to design a semi-definite programming approximation for an optimization problem such as MAX-CUT or MAX-SAT or what have you. So, we first write down an integer quadratic ...
Zur Luria's user avatar
  • 349
5 votes
3 answers
1k 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 ...
TestUser5's user avatar