# Multicriteria approximation through decomposition

## Abstract

The authors propose a general technique called solution decomposition to devise approximation algorithms with provable performance guarantees. The technique is applicable to a large class of combinatorial optimization problems that can be formulated as integer linear programs. Two key ingredients of the technique involve finding a decomposition of a fractional solution into a convex combination of feasible integral solutions and devising generic approximation algorithms based on calls to such decompositions as oracles. The technique is closely related to randomized rounding. The method yields as corollaries unified solutions to a number of well studied problems and it provides the first approximation algorithms with provable guarantees for a number of new problems. The particular results obtained in this paper include the following: (1) The authors demonstrate how the technique can be used to provide more understanding of previous results and new algorithms for classical problems such as Multicriteria Spanning Trees, and Suitcase Packing. (2) They show how the ideas can be extended to apply to multicriteria optimization problems, in which they wish to minimize a certain objective function subject to one or more budget constraints. As corollaries they obtain first non-trivial multicriteria approximation algorithms for problems including the k-Hurdle and the Networkmore »

- Authors:

- Carnegie Mellon Univ., Pittsburgh, PA (United States). School of Computer Sciences|[Sandia National Labs., Albuquerque, NM (United States)
- Univ. of Wuerzburg (Germany). Dept. of Computer Science
- Los Alamos National Lab., NM (United States)
- Sandia National Labs., Albuquerque, NM (United States). Applied Mathematics Dept.
- Rutgers Univ., NJ (United States). Dept. of Computer Science|[Sandia National Labs., Albuquerque, NM (United States)

- Publication Date:

- Research Org.:
- Sandia National Labs., Albuquerque, NM (United States); Los Alamos National Lab., NM (United States)

- Sponsoring Org.:
- USDOE, Washington, DC (United States)

- OSTI Identifier:
- 642754

- Report Number(s):
- SAND-97-3087C; CONF-980633-

ON: DE98001686; TRN: AHC2DT02%%80

- DOE Contract Number:
- AC04-94AL85000; W-7405-ENG-36

- Resource Type:
- Conference

- Resource Relation:
- Conference: 6. conference on integer programming and combinatorial optimization, Houston, TX (United States), 22-24 Jun 1998; Other Information: PBD: Dec 1997

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 99 MATHEMATICS, COMPUTERS, INFORMATION SCIENCE, MANAGEMENT, LAW, MISCELLANEOUS; LINEAR PROGRAMMING; ALGORITHMS; OPTIMIZATION; CALCULATION METHODS; DIAGRAMS

### Citation Formats

```
Burch, C., Krumke, S., Marathe, M., Phillips, C., and Sundberg, E.
```*Multicriteria approximation through decomposition*. United States: N. p., 1997.
Web.

```
Burch, C., Krumke, S., Marathe, M., Phillips, C., & Sundberg, E.
```*Multicriteria approximation through decomposition*. United States.

```
Burch, C., Krumke, S., Marathe, M., Phillips, C., and Sundberg, E. Mon .
"Multicriteria approximation through decomposition". United States. https://www.osti.gov/servlets/purl/642754.
```

```
@article{osti_642754,
```

title = {Multicriteria approximation through decomposition},

author = {Burch, C. and Krumke, S. and Marathe, M. and Phillips, C. and Sundberg, E.},

abstractNote = {The authors propose a general technique called solution decomposition to devise approximation algorithms with provable performance guarantees. The technique is applicable to a large class of combinatorial optimization problems that can be formulated as integer linear programs. Two key ingredients of the technique involve finding a decomposition of a fractional solution into a convex combination of feasible integral solutions and devising generic approximation algorithms based on calls to such decompositions as oracles. The technique is closely related to randomized rounding. The method yields as corollaries unified solutions to a number of well studied problems and it provides the first approximation algorithms with provable guarantees for a number of new problems. The particular results obtained in this paper include the following: (1) The authors demonstrate how the technique can be used to provide more understanding of previous results and new algorithms for classical problems such as Multicriteria Spanning Trees, and Suitcase Packing. (2) They show how the ideas can be extended to apply to multicriteria optimization problems, in which they wish to minimize a certain objective function subject to one or more budget constraints. As corollaries they obtain first non-trivial multicriteria approximation algorithms for problems including the k-Hurdle and the Network Inhibition problems.},

doi = {},

journal = {},

number = ,

volume = ,

place = {United States},

year = {1997},

month = {12}

}