scholarly journals A Superstabilizing log(n)-Approximation Algorithm for Dynamic Steiner Trees

2009 ◽  
pp. 133-148 ◽  
Author(s):  
Lélia Blin ◽  
Maria Gradinariu Potop-Butucaru ◽  
Stephane Rovedakis
Keyword(s):  
Approximation Algorithm ◽  
Steiner Trees

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

An Improved Sequential Polygonal Approximation Algorithm on Skeleton Curves

2009 ◽  
Vol 34 (12) ◽  
pp. 1467-1474
Author(s):  
Zhe LV ◽  
Fu-Li WANG ◽  
Yu-Qing CHANG ◽  
Yang LIU
Keyword(s):  
Approximation Algorithm ◽  
Polygonal Approximation

The minimum zone fitting and error evaluation for the logarithmic curve based on geometry optimization approximation algorithm

2019 ◽  
Vol 41 (15) ◽  
pp. 4380-4386
Author(s):  
Tu Xianping ◽  
Lei Xianqing ◽  
Ma Wensuo ◽  
Wang Xiaoyi ◽  
Hu Luqing ◽  
...  
Keyword(s):  
Approximation Algorithm ◽  
Evaluation Method ◽  
Geometry Optimization ◽  
Reference Points ◽  
Approximation Technique ◽  
Error Evaluation ◽  
Iterative Approximation ◽  
Logarithmic Curve ◽  
Normal Distance ◽  
Minimum Zone

The minimum zone fitting and error evaluation for the logarithmic curve has important applications. Based on geometry optimization approximation algorithm whilst considering geometric characteristics of logarithmic curves, a new fitting and error evaluation method for the logarithmic curve is presented. To this end, two feature points, to serve as reference, are chosen either from those located on the least squares logarithmic curve or from amongst measurement points. Four auxiliary points surrounding each of the two reference points are then arranged to resemble vertices of a square. Subsequently, based on these auxiliary points, a series of auxiliary logarithmic curves (16 curves) are constructed, and the normal distance and corresponding range of values between each measurement point and all auxiliary logarithmic curves are calculated. Finally, by means of an iterative approximation technique consisting of comparing, evaluating, and changing reference points; determining new auxiliary points; and constructing corresponding auxiliary logarithmic curves, minimum zone fitting and evaluation of logarithmic curve profile errors are implemented. The example results show that the logarithmic curve can be fitted, and its profile error can be evaluated effectively and precisely using the presented method.

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