A 3/2-Approximation Algorithm for Generalized Steiner Trees in Complete Graphs with Edge Lengths 1 and 2

2010 ◽  
pp. 15-24
Author(s):  
Piotr Berman ◽  
Marek Karpinski ◽  
Alexander Zelikovsky
Keyword(s):  
Approximation Algorithm ◽  
Steiner Trees ◽  
Complete Graphs

Finding group Steiner trees in graphs with both vertex and edge weights

2021 ◽  
Vol 14 (7) ◽  
pp. 1137-1149
Author(s):  
Yahui Sun ◽  
Xiaokui Xiao ◽  
Bin Cui ◽  
Saman Halgamuge ◽  
Theodoros Lappas ◽  
...  
Keyword(s):  
Approximation Algorithm ◽  
Undirected Graph ◽  
State Of The Art ◽  
Steiner Trees ◽  
Programming Approach ◽  
Weighted Graphs ◽  
Vertex Group ◽  
Dynamic Programming Approach ◽  
Knowledge Graphs ◽  
Approximation Guarantee

Given an undirected graph and a number of vertex groups, the group Steiner trees problem is to find a tree such that (i) this tree contains at least one vertex in each vertex group; and (ii) the sum of vertex and edge weights in this tree is minimized. Solving this problem is useful in various scenarios, ranging from social networks to knowledge graphs. Most existing work focuses on solving this problem in vertex-unweighted graphs, and not enough work has been done to solve this problem in graphs with both vertex and edge weights. Here, we develop several algorithms to address this issue. Initially, we extend two algorithms from vertex-unweighted graphs to vertex- and edge-weighted graphs. The first one has no approximation guarantee, but often produces good solutions in practice. The second one has an approximation guarantee of |Γ| - 1, where |Γ| is the number of vertex groups. Since the extended (|Γ| - 1)-approximation algorithm is too slow when all vertex groups are large, we develop two new (|Γ| - 1)-approximation algorithms that overcome this weakness. Furthermore, by employing a dynamic programming approach, we develop another (|Γ| - h + 1)-approximation algorithm, where h is a parameter between 2 and |Γ|. Experiments show that, while no algorithm is the best in all cases, our algorithms considerably outperform the state of the art in many scenarios.

A Nearly Best-Possible Approximation Algorithm for Node-Weighted Steiner Trees

1995 ◽  
Vol 19 (1) ◽  
pp. 104-115 ◽  
Author(s):  
P. Klein ◽  
R. Ravi
Keyword(s):  
Approximation Algorithm ◽  
Steiner Trees

scholarly journals A super-stabilizinglog(n)-approximation algorithm for dynamic Steiner trees

2013 ◽  
Vol 500 ◽  
pp. 90-112 ◽  
Author(s):  
Lélia Blin ◽  
Maria Potop-Butucaru ◽  
Stephane Rovedakis
Keyword(s):  
Approximation Algorithm ◽  
Steiner Trees

scholarly journals On a Greedy Approach for Genome Scaffolding

2021 ◽  
Author(s):  
Tom Davot ◽  
Annie Chateau ◽  
Rohan Fossé ◽  
Rodolphe Giroudeau ◽  
Mathias Weller
Keyword(s):  
Approximation Algorithm ◽  
Relative Position ◽  
Complete Graphs ◽  
Assembly Process ◽  
Contig Assembly ◽  
Time Approximation ◽  
Genome Scaffolding ◽  
Polynomial Time Approximation Algorithm ◽  
Cover Problem ◽  
Position And Orientation

Abstract Background: Scaffolding is a bioinformatics problem aimed at completing the contig assembly process by determining the relative position and orientation of these contigs. It can be seen as a paths and cycles cover problem of a particular graph called the “scaffold graph”.Results: We provide some NP-hardness and inapproximability results on this problem. We also adapt a greedy approximation algorithm on complete graphs so that it works on a special class aiming to be close to real instances. The described algorithm is the first polynomial-time approximation algorithm designed for this problem on non-complete graphs.Conclusion: Tests on a set of simulated instances show that our algorithm provides better results than the version on complete graphs.

Sign in / Sign up

Export Citation Format

Share Document