scholarly journals SINGLE-SOURCE DILATION-BOUNDED MINIMUM SPANNING TREES

2013 ◽  
Vol 23 (03) ◽  
pp. 159-170
Author(s):  
OTFRIED CHEONG ◽  
CHANGRYEOL LEE
Keyword(s):  
Approximation Algorithm ◽  
Spanning Trees ◽  
Edge Length ◽  
Minimum Spanning Trees ◽  
Np Hard ◽  
Single Source ◽  
Vertex Set ◽  
Dilation Factor

Given a set S of points in the plane, a geometric network for S is a graph G with vertex set S and straight edges. We consider a broadcasting situation, where one point r ∊ S is a designated source. Given a dilation factor δ, we ask for a geometric network G such that for every point v ∊ S there is a path from r to v in G of length at most δ|rv|, and such that the total edge length is minimized. We show that finding such a network of minimum total edge length is NP-hard, and give an approximation algorithm.

scholarly journals BALANCED PARTITION OF MINIMUM SPANNING TREES

2003 ◽  
Vol 13 (04) ◽  
pp. 303-316 ◽  
Author(s):  
MATTIAS ANDERSSON ◽  
JOACHIM GUDMUNDSSON ◽  
CHRISTOS LEVCOPOULOS ◽  
GIRI NARASIMHAN
Keyword(s):  
Approximation Algorithm ◽  
Objective Function ◽  
Manufacturing Industry ◽  
Spanning Trees ◽  
Minimum Spanning Trees ◽  
Np Hard ◽  
Shipbuilding Industry ◽  
Specific Objective ◽  
Fixed Constant ◽  
Balanced Partition

To better handle situations where additional resources are available to carry out a task, many problems from the manufacturing industry involve dividing a task into a number of smaller tasks, while optimizing a specific objective function. In this paper we consider the problem of partitioning a given set [Formula: see text] of n points in the plane into k subsets, [Formula: see text], such that [Formula: see text] is minimized. Variants of this problem arise in applications from the shipbuilding industry. We show that this problem is NP-hard, and we also present an approximation algorithm for the problem, in the case when k is a fixed constant. The approximation algorithm runs in time O(n log n) and produces a partition that is within a factor (4/3+ε) of the optimal if k=2, and a factor (2+ε) otherwise.

On average edge length of minimum spanning trees

1999 ◽  
Vol 70 (5) ◽  
pp. 241-243
Author(s):  
Suman Kumar Nath ◽  
Rezaul Alam Chowdhury ◽  
M. Kaykobad
Keyword(s):  
Spanning Trees ◽  
Edge Length ◽  
Minimum Spanning Trees ◽  
Average Edge Length

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.

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