Approximation Algorithms and Hardness Results for Packing Element-Disjoint Steiner Trees in Planar Graphs

2009 ◽  
pp. 1-14 ◽  
Author(s):  
Ashkan Aazami ◽  
Joseph Cheriyan ◽  
Krishnam Raju Jampani
Keyword(s):  
Approximation Algorithms ◽  
Planar Graphs ◽  
Steiner Trees ◽  
Packing Element

Approximation Algorithms and Hardness Results for Packing Element-Disjoint Steiner Trees in Planar Graphs

Algorithmica ◽  
2011 ◽  
Vol 63 (1-2) ◽  
pp. 425-456 ◽  
Author(s):  
A. Aazami ◽  
J. Cheriyan ◽  
K. R. Jampani
Keyword(s):  
Approximation Algorithms ◽  
Planar Graphs ◽  
Steiner Trees ◽  
Packing Element

scholarly journals On the k-restricted structure ratio in planar and outerplanar graphs

2008 ◽  
Vol Vol. 10 no. 3 (Graph and Algorithms) ◽  
Author(s):  
Gruia Călinescu ◽  
Cristina G. Fernandes
Keyword(s):  
Approximation Algorithms ◽  
Planar Graphs ◽  
Rates Of Convergence ◽  
Simple Graph ◽  
Maximum Weight ◽  
Outerplanar Graphs ◽  
Weighted Version ◽  
International Audience ◽  
Unweighted Case

Graphs and Algorithms International audience A planar k-restricted structure is a simple graph whose blocks are planar and each has at most k vertices. Planar k-restricted structures are used by approximation algorithms for Maximum Weight Planar Subgraph, which motivates this work. The planar k-restricted ratio is the infimum, over simple planar graphs H, of the ratio of the number of edges in a maximum k-restricted structure subgraph of H to the number edges of H. We prove that, as k tends to infinity, the planar k-restricted ratio tends to 1 = 2. The same result holds for the weighted version. Our results are based on analyzing the analogous ratios for outerplanar and weighted outerplanar graphs. Here both ratios tend to 1 as k goes to infinity, and we provide good estimates of the rates of convergence, showing that they differ in the weighted from the unweighted case.

Sign in / Sign up

Export Citation Format

Share Document