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Title: On optimal strategies for upgrading networks

Abstract

We study {ital budget constrained optimal network upgrading problems}. Such problems aim at finding optimal strategies for improving a network under some cost measure subject to certain budget constraints. Given an edge weighted graph {ital G(V,E)}, in the {ital edge based upgrading model}, it is assumed that each edge {ital e} of the given network has an associated function {ital c(e)} that specifies for each edge {ital e} the amount by which the length {ital l(e)} is to be reduced. In the {ital node based upgrading model} a node {ital v} can be upgraded at an expense of cost {ital (v)}. Such an upgrade reduces the cost of each edge incident on {ital v} by a fixed factor {rho}, where 0 < {rho} < 1. For a given budget, {ital B}, the goal is to find an improvement strategy such that the total cost of reduction is a most the given budget {ital B} and the cost of a subgraph (e.g. minimum spanning tree) under the modified edge lengths is the best over all possible strategies which obey the budget constraint. Define an ({alpha},{beta})-approximation algorithm as a polynomial-time algorithm that produces a solution within {alpha} times the optimal function value,more » violating the budget constraint by a factor of at most {Beta}. The results obtained in this paper include the following 1. We show that in general the problem of computing optimal reduction strategy for modifying the network as above is {bold NP}-hard. 2. In the node based model, we show how to devise a near optimal strategy for improving the bottleneck spanning tree. The algorithms have a performance guarantee of (2 ln {ital n}, 1). 3. for the edge based improvement problems we present improved (in terms of performance and time) approximation algorithms. 4. We also present pseudo-polynomial time algorithms (extendible to polynomial time approximation schemes) for a number of edge/node based improvement problems when restricted to the class of treewidth-bounded graphs.« less

Authors:
;  [1];  [2];  [3];  [4];  [5]
  1. Wuerzburg Univ. (Germany). Dept. of Computer Science
  2. Los Alamos National Lab., NM (United States)
  3. State Univ. of New York, Albany, NY (United States). Dept. of Computer Science
  4. Carnegie-Mellon Univ., Pittsburgh, PA (United States). Graduate School of Industrial Administration
  5. Massachusetts Inst. of Tech., Cambridge, MA (United States)
Publication Date:
Research Org.:
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Sponsoring Org.:
USDOE Assistant Secretary for Human Resources and Administration, Washington, DC (United States)
OSTI Identifier:
435321
Report Number(s):
LA-UR-96-2719; CONF-970142-1
ON: DE96014461
DOE Contract Number:  
W-7405-ENG-36
Resource Type:
Conference
Resource Relation:
Conference: 8. annual Association for Computing Machinery (ACM)-Society for Industrial and Applied Mathematics (SIAM) symposium on discrete algorithms, New Orleans, LA (United States), 5-7 Jan 1997; Other Information: PBD: 2 Jul 1996
Country of Publication:
United States
Language:
English
Subject:
99 MATHEMATICS, COMPUTERS, INFORMATION SCIENCE, MANAGEMENT, LAW, MISCELLANEOUS; OPTIMIZATION; STATISTICAL MODELS; COMPUTER CALCULATIONS; LIMITING VALUES; ALGORITHMS; POLYNOMIALS; PARAMETRIC ANALYSIS; NODAL EXPANSION METHOD

Citation Formats

Krumke, S O, Noltemeier, H, Marathe, M V, Ravi, S S, Ravi, R, and Sundaram, R. On optimal strategies for upgrading networks. United States: N. p., 1996. Web.
Krumke, S O, Noltemeier, H, Marathe, M V, Ravi, S S, Ravi, R, & Sundaram, R. On optimal strategies for upgrading networks. United States.
Krumke, S O, Noltemeier, H, Marathe, M V, Ravi, S S, Ravi, R, and Sundaram, R. 1996. "On optimal strategies for upgrading networks". United States. https://www.osti.gov/servlets/purl/435321.
@article{osti_435321,
title = {On optimal strategies for upgrading networks},
author = {Krumke, S O and Noltemeier, H and Marathe, M V and Ravi, S S and Ravi, R and Sundaram, R},
abstractNote = {We study {ital budget constrained optimal network upgrading problems}. Such problems aim at finding optimal strategies for improving a network under some cost measure subject to certain budget constraints. Given an edge weighted graph {ital G(V,E)}, in the {ital edge based upgrading model}, it is assumed that each edge {ital e} of the given network has an associated function {ital c(e)} that specifies for each edge {ital e} the amount by which the length {ital l(e)} is to be reduced. In the {ital node based upgrading model} a node {ital v} can be upgraded at an expense of cost {ital (v)}. Such an upgrade reduces the cost of each edge incident on {ital v} by a fixed factor {rho}, where 0 < {rho} < 1. For a given budget, {ital B}, the goal is to find an improvement strategy such that the total cost of reduction is a most the given budget {ital B} and the cost of a subgraph (e.g. minimum spanning tree) under the modified edge lengths is the best over all possible strategies which obey the budget constraint. Define an ({alpha},{beta})-approximation algorithm as a polynomial-time algorithm that produces a solution within {alpha} times the optimal function value, violating the budget constraint by a factor of at most {Beta}. The results obtained in this paper include the following 1. We show that in general the problem of computing optimal reduction strategy for modifying the network as above is {bold NP}-hard. 2. In the node based model, we show how to devise a near optimal strategy for improving the bottleneck spanning tree. The algorithms have a performance guarantee of (2 ln {ital n}, 1). 3. for the edge based improvement problems we present improved (in terms of performance and time) approximation algorithms. 4. We also present pseudo-polynomial time algorithms (extendible to polynomial time approximation schemes) for a number of edge/node based improvement problems when restricted to the class of treewidth-bounded graphs.},
doi = {},
url = {https://www.osti.gov/biblio/435321}, journal = {},
number = ,
volume = ,
place = {United States},
year = {Tue Jul 02 00:00:00 EDT 1996},
month = {Tue Jul 02 00:00:00 EDT 1996}
}

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