# Bicriteria network design problems

## Abstract

We study several bicriteria network design problems phrased as follows: given an undirected graph and two minimization objectives with a budget specified on one objective, find a subgraph satisfying certain connectivity requirements that minimizes the second objective subject to the budget on the first. Define an ({alpha}, {beta})-approximation algorithm as a polynomial-time algorithm that produces a solution in which the first objective value is at most {alpha} times the budget, and the second objective value is at most {alpha} times the minimum cost of a network obeying the budget oil the first objective. We, present the first approximation algorithms for bicriteria problems obtained by combining classical minimization objectives such as the total edge cost of the network, the diameter of the network and a weighted generalization of the maximum degree of any node in the network. We first develop some formalism related to bicriteria problems that leads to a clean way to state bicriteria approximation results. Secondly, when the two objectives are similar but only differ based on the cost function under which they are computed we present a general parametric search technique that yields approximation algorithms by reducing the problem to one of minimizing a single objective of themore »

- Authors:

- Publication Date:

- Research Org.:
- Los Alamos National Lab., NM (United States)

- Sponsoring Org.:
- USDOE, Washington, DC (United States); Department of Defense, Washington, DC (United States); National Science Foundation, Washington, DC (United States)

- OSTI Identifier:
- 39638

- Report Number(s):
- LA-UR-94-4088; CONF-950644-1

ON: DE95005261; CNN: DARPA Contract N0014-92-J-1799;NSF Grant CCR 92-12184;NSF Grant CCR 89-03319;NSF Grant CCR 90-06396

- DOE Contract Number:
- W-7405-ENG-36

- Resource Type:
- Conference

- Resource Relation:
- Conference: Conference on functional programming languages and computer architectures, La Jolla, CA (United States), 26-28 Jun 1995; Other Information: PBD: [1994]

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 99 MATHEMATICS, COMPUTERS, INFORMATION SCIENCE, MANAGEMENT, LAW, MISCELLANEOUS; COMPUTER NETWORKS; ALGORITHMS; DATA TRANSMISSION; DESIGN

### Citation Formats

```
Marathe, M V, Ravi, R, Sundaram, R, Ravi, S S, Rosenkrantz, D J, and Hunt, III, H B.
```*Bicriteria network design problems*. United States: N. p., 1994.
Web.

```
Marathe, M V, Ravi, R, Sundaram, R, Ravi, S S, Rosenkrantz, D J, & Hunt, III, H B.
```*Bicriteria network design problems*. United States.

```
Marathe, M V, Ravi, R, Sundaram, R, Ravi, S S, Rosenkrantz, D J, and Hunt, III, H B. Sat .
"Bicriteria network design problems". United States. https://www.osti.gov/servlets/purl/39638.
```

```
@article{osti_39638,
```

title = {Bicriteria network design problems},

author = {Marathe, M V and Ravi, R and Sundaram, R and Ravi, S S and Rosenkrantz, D J and Hunt, III, H B},

abstractNote = {We study several bicriteria network design problems phrased as follows: given an undirected graph and two minimization objectives with a budget specified on one objective, find a subgraph satisfying certain connectivity requirements that minimizes the second objective subject to the budget on the first. Define an ({alpha}, {beta})-approximation algorithm as a polynomial-time algorithm that produces a solution in which the first objective value is at most {alpha} times the budget, and the second objective value is at most {alpha} times the minimum cost of a network obeying the budget oil the first objective. We, present the first approximation algorithms for bicriteria problems obtained by combining classical minimization objectives such as the total edge cost of the network, the diameter of the network and a weighted generalization of the maximum degree of any node in the network. We first develop some formalism related to bicriteria problems that leads to a clean way to state bicriteria approximation results. Secondly, when the two objectives are similar but only differ based on the cost function under which they are computed we present a general parametric search technique that yields approximation algorithms by reducing the problem to one of minimizing a single objective of the same type. Thirdly, we present an O(log n, log n)-approximation algorithm for finding a diameter-constrained minimum cost spanning tree of an undirected graph on n nodes generalizing the notion of shallow, light trees and light approximate shortest-path trees that have been studied before. Finally, for the class of treewidth-bounded graphs, we provide pseudopolynomial-time algorithms for a number of bicriteria problems using dynamic programming. These pseudopolynomial-time algorithms can be converted to fully polynomial-time approximation schemes using a scaling technique.},

doi = {},

url = {https://www.osti.gov/biblio/39638},
journal = {},

number = ,

volume = ,

place = {United States},

year = {1994},

month = {12}

}