All Questions
Tagged with graph-theory approximation-algorithms
24 questions with no upvoted or accepted answers
6
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0
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472
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Any approximation algorithms for self-avoiding walks?
I've a graph whose edges are weighted by probabilities, perhaps all equal. I would like to compute the overall probability of traveling between vertices x and y in the graph after I delete each edge ...
- 565
5
votes
0
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115
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Approximating a max-cut's intersection with other cuts
(This is a cross-post from the Theoretical Computer Science Stack Exchange.)
For the purposes of this question, a cut in a graph $G$ is the edge-set $\delta (S)\subseteq E(G)$ between some vertex-set ...
- 631
4
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0
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207
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Disjoint paths in temporal graphs
Given a graph $G=(V,E)$ and a pair of source-destination nodes $s$ and $t$. Time is divided in periods with the total number of periods denoted by $T$. Each edge $e$ is either operational or broken at ...
- 367
4
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0
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73
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Is the $d$-dimensional Arrangement of Trees still $NP$-hard?
The $d$-dimensional Arrangement Problem for general graphs is known to be $NP$-hard since the special case $d=1$ (OLA) already is (Garey et al, [1976]). For Trees however, the one dimensional case can ...
- 41
3
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0
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588
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Group Travel Salesman Problem
For the following Group Traveling Salesman problem, I'd like to know if there exists some poly-time approximation algorithm with constant approximation factor.
Group TSP is defined as follows: Take a ...
- 367
3
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0
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243
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Polynomial-time algorithm solving approximately a generalization of the travelling salesman problem
Take a graph $G$ and a number of sets of nodes of $G$. The problem is to find the shortest path passing through at least one node in each node set. If each node set consists of only one node, the ...
- 367
2
votes
1
answer
112
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Finding survivable paths with a set of vulnerable edges
Consider a graph $G=(V,E)$ and a source-destination pair $(s,t)$. A set of edges $E'\subseteq E$ are vulnerable in the sense that at most $k$ of them may fail. My problem is to find a set of $(s,t)$ ...
- 367
2
votes
0
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63
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Maximize connectivity probability with a number of edges
We are given a graph $G$, whose edges are either open or closed. Initially all the edges are closed. For each edge $e$, if we choose to activate it, then after the activation, it becomes open with ...
- 367
2
votes
0
answers
99
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Relationship between weight of spanning tree in a tree metric approximation and the original metric
So suppose we have a tree metric which approximates the Euclidean distance between a finite set of points. The leaves correspond to points in the original space. It may be an ultra metric, and ...
- 161
1
vote
0
answers
65
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Find a cut of a graph that minimizes the ratio between the edge weights of the cut and the edge weights inside one subgraph
Given an edge-weighted undirected graph $G=(V,E)$ (can assume the weights are non-negative) and a source node $v_s\in V$, a cut is a partition of $G$'s vertices into two complementary sets $S$ and $T$....
- 143
1
vote
0
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124
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Steiner tree subject to non-trivial constraint
Given a edge-weighted transportation network modeled as a graph. A source node $s$ needs to send an object to a set of $k$ destination nodes $t_i$, $1\le i\le k$. For the transportation, $s$ needs to ...
- 367
1
vote
0
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75
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Why does Y. Moshe Vardi use this specific matrix when estimating source-destination traffic intensities with EM algorithm?
Sorry for the verbose title, but the question is super specific. If you happen to know a site better suited for these types of question, feel free to direct me.
The article to which I am referring to ...
- 151
1
vote
0
answers
149
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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
104
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Meaning of L-reduction from Dominating set problem
We are working in a variation of Locating dominating sets. Recently, we realized that the reduction from dominating set to our problem in proving its NP-completeness turns out to be also an L-...
- 11
1
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0
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119
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Heuristics for this "subset" traveling salesman problem
Are there any known heuristics for the following variation of the traveling salesman problem: given $n$ sets of points $S_1,\dots,S_n$, and $n$ integers $k_i$ such that $k_i \leq |S_i|$, find the ...
- 4,049
1
vote
0
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258
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3-Approximation Algorithm for Weighted 3-Hitting Set (Weighted Set Cover)
I need to find a 3-Approximation Algorithm for a weighted 3-Hitting Set.
I have an 2-Approximation Algorithm for a weighted 2-Hitting Set and in its explanation the Hitting-Set-Problem is formulated ...
- 133
1
vote
0
answers
79
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An MST-like problem with vertex selection
Consider a planar pointset in a rectangle, where every point has a color (an integer label).
We need to select one point of every color, so as to minimize the cost of a planar MST of selected points (...
- 341
0
votes
0
answers
24
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Minimizing intersections between spanning trees of graph embeddings in polynomial time
Assume I have $N$ complete graphs $G_1, G_2,...,G_N$, and consider their embeddings $E_1, E_2,...,E_N$ in $\mathbb{R}^2$. Is there a (potentially stochastic) polynomial time algorithm to construct ...
- 1
0
votes
0
answers
123
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A variant of Steiner tree
Consider a directed Steiner tree problem with a source node $s$ a set $T$ of terminals with the following constraint. For each node $v$ on the tree, we assign a branching value $b_v$ as follows. (1) $...
- 367
0
votes
2
answers
251
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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
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0
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50
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Can we talk about approximation when the decision problem for solution existence is NP-Hard
I am wishing to design an approximation algorithm for an optimization problem where the existence of solution for corresponding decision problem is not guaranteed. Is it wise to find an approximation ...
0
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0
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36
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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
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0
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59
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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
1
answer
431
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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