All Questions
34 questions with no upvoted or accepted answers
12
votes
0
answers
530
views
Finding the diameter of an unknown tree: Is BFS optimal?
I'm interested on the following nice problem that is somewhat standard in CS, but I was surprised on the lack of references on the optimal algorithm to this problem.
Ana and Banana plays the ...
- 63
12
votes
0
answers
349
views
Matroids with prescribed independent sets
Let $A$ be a finite set. Let $B$ be a family of subsets of $A$. We are interested in a matroid with a minimum rank such that every element of $B$ is independent. The answer is obvious - a uniform ...
- 1,791
8
votes
0
answers
152
views
Disjoint Rooted Paths with Specified Patterns
Let $S:=$ { $s_i : i \in [k]$ } and $T:=$ { $t_i : i \in [k]$ } be disjoint subsets of vertices of a graph $G$. Furthermore, let $A$ be a subset of $S_k$ (the symmetric group on $[k]$). A set of ...
- 32.1k
6
votes
0
answers
315
views
Algorithms for computing the Resilience of Graphs
The definition of resilience with a graph $G$ w.r.t to a monotone property $\mathcal{P}$ is well known.
(Global resilience) Let $\mathcal{P}$ be an increasing monotone property. The global ...
- 903
6
votes
0
answers
172
views
Uniformly sampling from the set of all simplicial maps
Let $K$ and $L$ be finite simplicial complexes that remain fixed throughout.
How does one efficiently sample (according to the uniform distribution) elements from the finite set of simplicial maps ...
- 15.5k
4
votes
0
answers
175
views
What is known about the complexity of this covering problem?
Let $G=(V,E)$ be a graph. A vertex set $X\subseteq V$ is called critical if $X\neq\emptyset$ and no vertex in $V\setminus X$ is adjacent to exactly one vertex in $X$. The problem is to find a vertex ...
- 2,966
4
votes
0
answers
220
views
Navigation in a graph
The problem
Let $G=(V,E)$ be a graph. $k = O\left(\log(|V|)\right)$ distinct vertices are picked randomly from $V$. We call the set of chosen $k$ vertices $T$.
Assumptions about the graph: You may ...
- 323
4
votes
0
answers
209
views
Rough structure of the double coset space/Graph bijections up to automorphisms
I am dealing with bijective maps $\pi:\Gamma_1\to \Gamma_2$ between two graphs with the same number of vertices $N=O(10)$.
The graphs have a significant automorphism group (these are disconnected ...
- 679
3
votes
0
answers
370
views
Perfect matching decomposition algorithm for bipartite regular graphs
It is a well-known result that a bipartite graph can be decomposed into edge-disjoint perfect matchings if and only if it is regular. Now here comes the question. Given a bipartite regular graph, is ...
- 51
3
votes
0
answers
280
views
Max flow with minimum number of edges
A max-flow problem may have multiple solutions. Among these max-flows, I seek the one with the minimum number of positive flow edges (by positive flow edges I mean the edges carrying positive flow). ...
- 367
3
votes
0
answers
111
views
Is there a Havel-Hakimi for geometric graphs?
Suppose that we are given $n$ points in the plane, with a degree prescribed for each, and the question is whether we can place a geometric graph on them. Is there an efficient algorithm for this?
...
- 19k
2
votes
0
answers
350
views
NP hard problems on geometric graphs
I have posted this question before but i don't feel i expressed my confusion clearly enough. So i would like to try and explain again. This is a proof of the minimum vertex cover for unit disk graphs ...
- 903
2
votes
0
answers
642
views
Hamiltonian paths in subgraphs of rectangular lattice graphs
Is following decision problem NP-hard / NP-complete:
Having vertex-induced subgraph of rectangular lattice graph determine if any Hamiltonian path exists
Having vertex-induced subgraph of rectangular ...
1
vote
0
answers
76
views
Constructing orientations that increase (directed) distances between vertices in a maximum independent set
An orientation of a simple undirected graph $G=(V,E)$ is a directed graph $G' = (V,E')$ that is constructed by including either $(u,v) \in E'$ or $(v,u) \in E'$, but not both, for all $(u,v) \in E$.
...
- 73
1
vote
0
answers
52
views
How can we hang the weighted trees so that vertices nearer to root (based on distances, not hop count) lie in upper levels?
I have a set of edge weighted trees, each tree rooted at some vertex. Consider these trees are hung from the roots and vertices are arranged in some levels. I wish to design an algorithm (...
1
vote
0
answers
64
views
A variant of node-disjoint path problem
Given a graph $G$, I want to find $2$ (or $k$) node-disjoint paths with minimum total cost (or minimum maximum cost). The problem is a classical problem, but I have the following non-trivial setting. ...
- 367
1
vote
0
answers
185
views
Maximum independent set in dense graphs
Let $0 < A < 1$ and $G$ be connected d-regular graph
with degree $d=[A n]$. The density of $G$ is about $A$.
Q1 Are there constraints on $A$ such that finding maximum
independent set of $G$ is ...
- 25.4k
1
vote
0
answers
168
views
Fastest algorithm to construct a proper edge $(\Delta(G)+1)$-coloring of a simple graph
A proper edge coloring is a coloring of the edges of a graph so that adjacent edges receive distinct colors. Vizing's theorem states that every simple graph $G$ has a proper edge coloring using at ...
- 1,190
1
vote
0
answers
61
views
Algorithm for minimum weight matching with "tree topology"
Given a finite graph $G(V,E)$ with undirected and weighted edges, whose set of vertices $V$ is partitioned into a collection $\mathfrak{P}=\lbrace V_1,\,\dots,\,V_k\rbrace$ of non-empty and pairwise ...
- 13.2k
1
vote
0
answers
74
views
Reduction maximum independent set to MIS in a very dense graph
We got a reduction maximum independent set to MIS in a very dense graph,
or alternatively negative monotone 2-CNF to MAX-ONEs with a formula
with many clauses.
Let $G$ be graph of order $n$ and ...
- 25.4k
1
vote
0
answers
177
views
Reduction graph isomorphism to maximum independent set in very dense graph
We got a reduction graph isomorphism to MIS in a very dense graph,
or alternatively negative monotone 2-CNF to MAX-ONEs with a formula
with many clauses.
Let $G,H$ be graphs of order $n$ and adjacency ...
- 25.4k
1
vote
0
answers
149
views
Minimum delay path in time-dependent graph
Given a time-dependent graph, where each edge $e$ is on for certain time intervals and off otherwise. Traversing $e$ incurs a delay $d_e$ and is possible only when $e$ is on. Given a pair of vertices $...
- 367
1
vote
0
answers
82
views
Treewidth problem equivalence
Say we are solving a tree decomposition problem, e.g.
given a graph $G = (V, E)$ we try to find a chordal graph $H$ such that $V(H) = V(G)$, $E(G) \in E(H)$ and the maximal clique in $H$ is minimal ...
- 71
1
vote
0
answers
78
views
Bipartite clustering is NP-hard?
Let $G = (A\cup B, E)$ be a bipartite graph with edge weights $w: E\to \mathbb{R}$. Find a partition $B_1, B_2$ of $B$ and a nonempty disjoint subsets $A_1, A_2$ of $A$ such that $w(A_1,B_1) + w(A_2, ...
- 221
1
vote
0
answers
54
views
Detecting the Appearance of a Path between a Pair of Vertices
Given
a simple, symmetric graph $G(V,E); \text{card}(V)=n,\ \text{card}(E)=m\le\frac{n(n-1)}{2} $
a set of ordered pairs of vertices $U=\lbrace (u_i,u_j)\rbrace\subset V\times V,\ i\lt j$
a ...
- 13.2k
1
vote
1
answer
298
views
maximal sets of vertices that avoids a clique
I am looking for some known algorithm that finds, for a given graph, all the maximal sets of vertices that avoid a clique of some given size $k$. I'd prefer one written in MATLAB, but other languages ...
- 11
1
vote
0
answers
127
views
Max flow with minimal requirements algo problem
While applying the algorithm to solve the max flow of the network with minimal requirements on edges, I have encountered a problem.
The algorithm states:
For graph G
create an edge from target to ...
- 11
0
votes
0
answers
69
views
What is the complexity of computing isomorphism of two non-regular graphs?
Regular graphs are the graphs in which the degree of each vertex is the same. Much research has gone into investigating isomorphism of regular graphs, and we know that computing isomorphism for ...
- 101
0
votes
2
answers
251
views
Compute the average path weights of paths with the same path length in a directed acyclic graph (DAG)
Given a weighted directed acyclic graph (DAG) $G=(V,E)$ with each edge $e\in E$ has a non-negative weight $w(e)$. For a path $p=(e_1,e_2,\dotsc,e_n)$ in $G$, define the path weight as : $w(p)=\sum_{i=...
- 143
0
votes
0
answers
36
views
Approximabilty of submodular over modular maximization
Given a non-decreasing, normalized, submodular function $f : 2^{[n]}\mapsto \mathbb{R}_+$ and a modular non-decreasing function $g$, I am wondering what is the best approximation ratio I can hope for ...
- 171
0
votes
0
answers
59
views
A variant of travel salesman problem with charging points
Given a graph composed of a set $V$ of nodes, each representing a point to be visited by a salesman, and a set of fixed charging points. The salesman disposes a car that can travel $D$ distance before ...
- 367
0
votes
0
answers
116
views
Procedure to color the edges of a circulant graph
From the first theorem in this paper, it is clear that a cayley graph on abelian group for all generating sets of even order is class $1$, that is can be edge colored in exactly $\Delta$ colors. But, ...
- 2,089
0
votes
0
answers
261
views
Fast removal of weighted edges in a graph in a way such that all shortest paths are preserved
This problem is analogous to fast removal of the minimum number of edges in a weighted graph such that if the graph were to be drawn on paper with edge lengths linear in proportion to their weights, ...
- 1
0
votes
1
answer
431
views
Efficient isomorphic subgraph matching with similarity scores
I'm a computer vision PhD student, and I'm looking for an efficient approximation to the following problem, which could end up helping in image to image matching. Failing that, pointers to relevant ...
- 223