Sensitivity analysis of minimum spanning trees and shortest path trees

1982 ◽  
Vol 14 (1) ◽  
pp. 30-33 ◽  
Author(s):  
Robert Endre Tarjan
Keyword(s):  
Sensitivity Analysis ◽  
Shortest Path ◽  
Spanning Trees ◽  
Minimum Spanning Trees ◽  
Shortest Path Trees

scholarly journals Balancing minimum spanning trees and shortest-path trees

Algorithmica ◽  
1995 ◽  
Vol 14 (4) ◽  
pp. 305-321 ◽  
Author(s):  
S. Khuller ◽  
B. Raghavachari ◽  
N. Young
Keyword(s):  
Shortest Path ◽  
Spanning Trees ◽  
Minimum Spanning Trees ◽  
Shortest Path Trees

CONSTRUCTING MULTIDIMENSIONAL SPANNER GRAPHS

1991 ◽  
Vol 01 (02) ◽  
pp. 99-107 ◽  
Author(s):  
JEFFERY S. SALOWE
Keyword(s):  
Shortest Path ◽  
Complete Graph ◽  
Connected Graph ◽  
Spanning Trees ◽  
Input Parameter ◽  
Minimum Spanning Trees ◽  
Positive Edge ◽  
Spanning Subgraph ◽  
Vertex Set

Given a connected graph G=(V,E) with positive edge weights, define the distance dG(u,v) between vertices u and v to be the length of a shortest path from u to v in G. A spanning subgraph G' of G is said to be a t-spanner for G if, for every pair of vertices u and v, dG'(u,v)≤t·dG(u,v). Consider a complete graph G whose vertex set is a set of n points in [Formula: see text] and whose edge weights are given by the Lp distance between respective points. Given input parameter ∊, 0<∊≤1, we show how to construct a (1+∊)-spanner for G containing [Formula: see text] edges in [Formula: see text] time. We apply this spanner to the construction of approximate minimum spanning trees.

Verification and Sensitivity Analysis of Minimum Spanning Trees in Linear Time

1992 ◽  
Vol 21 (6) ◽  
pp. 1184-1192 ◽  
Author(s):  
Brandon Dixon ◽  
Monika Rauch ◽  
Robert E. Tarjan
Keyword(s):  
Sensitivity Analysis ◽  
Spanning Trees ◽  
Linear Time ◽  
Minimum Spanning Trees
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