All Questions
Tagged with exp-time-algorithms graph-algorithms
8 questions
3
votes
1
answer
87
views
What is the fastest algorithm for computing exact network reliability?
In the network reliability problem, we are given an undirected graph $G$ on $n$ vertices and a parameter $p\in (0,1)$, and are tasked with determining the probability that $G$ becomes disconnected (i....
- 696
1
vote
0
answers
40
views
Minimum vertex-separators under edge addition
I am trying to prove the following claim.
Let $T$ be a minimum $st$-separator in an undirected graph $G$, and let $x \in T$.
Let $S\neq T$ be a minimal $st$-separator (i.e., not necessarily minimum), ...
- 103
10
votes
0
answers
162
views
Fastest Known Algorithm to Count Acyclic Orientations in a Graph
Given an undirected graph $G$, an acyclic orientation of $G$ is choice of orientation for each edge of $G$ (turning each edge into an arc) such that the resulting directed graph has no directed cycles....
- 696
4
votes
0
answers
229
views
Fastest Known Algorithm for $k$-Dimensional Matching and $k$-Exact Cover
Given a $k$-uniform hypergraph $G$ (i.e., each edge of $G$ contains precisely $k$ vertices) on $n$ vertices, the $k$-Exact Cover problem is the task of deciding if there exists $n/k$ edges in $G$ ...
- 696
6
votes
1
answer
274
views
What is the fastest known algorithm for computing a 1.99-approximation of Vertex Cover?
It is known that computing $(\sqrt 2 -\epsilon)$-approximation for VC is NP-hard and that UGC implies that even a $(2 -\epsilon)$-approximation is hard.
There is also a parameterized algorithm for ...
- 9,508
10
votes
2
answers
379
views
Subset Numbering
Fix $k\ge5$.
For any big enough $n$, we would like to label all subsets of $\{1..n\}$ of size exactly $n/k$ by positive integers from $\{1...T\}$.
We would like this labelling to satisfy the following ...
- 2,257
46
votes
4
answers
14k
views
Approximation algorithms for Metric TSP
It is known that metric TSP can be approximated within $1.5$ and cannot be approximated better than $123\over 122$ in polynomial time.
Is anything known about finding approximation solutions in ...
- 2,257
3
votes
5
answers
4k
views
Finding cliques in a big graph
I would like to find (all) cliques in a given graph with 8,568 vertices and 12,726,708 edges. The vertex with the lowes degree has 2000, the vertext with the highest degree has 4007.
The cliques ...
- 615