cost measures
facility location problem
trees
frequent versions
length
time
false
power P
VLSI
problem
terminals
Many VLSI routing applications, as well as the facility location problem involve computation of Steiner trees with non-linear cost measures. We consider two most frequent versions of this problem. In the power-p Steiner problem the cost is defined as the sum of the edge lengths where each length is raised to the power p > 1. In the bottleneck Steiner problem the objective cost is the maximum of the edge lengths. We show that the power-p Steiner problem is MAX SNP-hard and that one cannot guarantee to find a bottleneck Steiner tree within a factor less than 2, unless P = NP. We prove that in any metric space the minimum spanning tree is at most a constant times worse than the optimal power-p Steiner tree. In particular, for p = 2, we show that the minimum spanning tree is at most 23.3 times worse than the optimum and we construct an instance for which it is 17.2 times worse. We also present a better approximation algorithm for the bottleneck Steiner problem with performance guarantee log2 n, where n is the number of terminals (the minimum spanning tree can be 2 log2 n times worse than the optimum).
SNPs
cost
factors
power
edge length
approximation
117-135
https://doi.org/10.1007/978-1-4757-3171-2_7
instances
bottleneck Steiner tree
number
spanning tree
sum
applications
one
2000-01-01
computation
chapter
NPs
On Approximation of the Power-p and Bottleneck Steiner Trees
edge
location problem
version
2000
algorithm
log2 n
https://scigraph.springernature.com/explorer/license/
minimum spanning tree
maximum
space
objective cost
number of terminals
approximation algorithm
Steiner tree
metric spaces
constant time
Steiner problem
2022-10-01T06:53
chapters
best approximation algorithm
MAX SNP
measures
Department of Computer Science and Engineering, Penn State University, 16802, University Park, PA, USA
Department of Computer Science and Engineering, Penn State University, 16802, University Park, PA, USA
Springer Nature
978-1-4757-3171-2
978-1-4419-4824-3
Advances in Steiner Trees
Zelikovsky
Alexander
Piotr
Berman
Department of Computer Science, Georgia State University, University Plaza, 30303-3083, Atlanta, GA, USA
Department of Computer Science, Georgia State University, University Plaza, 30303-3083, Atlanta, GA, USA
dimensions_id
pub.1035699208
Springer Nature - SN SciGraph project
Smith
J. M.
Applied Mathematics
Du
Ding-Zhu
Rubinstein
J. H.
doi
10.1007/978-1-4757-3171-2_7
Mathematical Sciences