Approximation algorithms for combinatorial problems
D. Johnson. STOC '73: Proceedings of the fifth annual ACM symposium on Theory of computing, page 38--49. New York, NY, USA, ACM, (1973)
DOI: 10.1145/800125.804034
Abstract
Simple, polynomial-time, heuristic algorithms for finding approximate solutions to various polynomial complete optimization problems are analyzed with respect to their worst case behavior, measured by the ratio of the worst solution value that can be chosen by the algorithm to the optimal value. For certain problems, such as a simple form of the knapsack problem and an optimization problem based on satisfiability testing, there are algorithms for which this ratio is bounded by a constant, independent of the problem size. For a number of set covering problems, simple algorithms yield worst case ratios which can grow with the log of the problem size. And for the problem of finding the maximum clique in a graph, no algorithm has been found for which the ratio does not grow at least as fast as 0(n&egr;), where n is the problem size and &egr;> 0 depends on the algorithm.
Description
Approximation algorithms for combinatorial problems
%0 Conference Paper
%1 johnson/stoc/1973
%A Johnson, David S.
%B STOC '73: Proceedings of the fifth annual ACM symposium on Theory of computing
%C New York, NY, USA
%D 1973
%I ACM
%K greedyAlgorithm optimization setCover
%P 38--49
%R 10.1145/800125.804034
%T Approximation algorithms for combinatorial problems
%U http://portal.acm.org/citation.cfm?id=804034
%X Simple, polynomial-time, heuristic algorithms for finding approximate solutions to various polynomial complete optimization problems are analyzed with respect to their worst case behavior, measured by the ratio of the worst solution value that can be chosen by the algorithm to the optimal value. For certain problems, such as a simple form of the knapsack problem and an optimization problem based on satisfiability testing, there are algorithms for which this ratio is bounded by a constant, independent of the problem size. For a number of set covering problems, simple algorithms yield worst case ratios which can grow with the log of the problem size. And for the problem of finding the maximum clique in a graph, no algorithm has been found for which the ratio does not grow at least as fast as 0(n&egr;), where n is the problem size and &egr;> 0 depends on the algorithm.
@inproceedings{johnson/stoc/1973,
abstract = {Simple, polynomial-time, heuristic algorithms for finding approximate solutions to various polynomial complete optimization problems are analyzed with respect to their worst case behavior, measured by the ratio of the worst solution value that can be chosen by the algorithm to the optimal value. For certain problems, such as a simple form of the knapsack problem and an optimization problem based on satisfiability testing, there are algorithms for which this ratio is bounded by a constant, independent of the problem size. For a number of set covering problems, simple algorithms yield worst case ratios which can grow with the log of the problem size. And for the problem of finding the maximum clique in a graph, no algorithm has been found for which the ratio does not grow at least as fast as 0(n&egr;), where n is the problem size and &egr;> 0 depends on the algorithm.},
added-at = {2010-08-04T18:18:55.000+0200},
address = {New York, NY, USA},
author = {Johnson, David S.},
biburl = {https://www.bibsonomy.org/bibtex/2646bf868889af01581ea69944fe24b77/mboley},
booktitle = {STOC '73: Proceedings of the fifth annual ACM symposium on Theory of computing},
description = {Approximation algorithms for combinatorial problems},
doi = {10.1145/800125.804034},
interhash = {bec8a709cc3f8e6c881476aade43d0da},
intrahash = {646bf868889af01581ea69944fe24b77},
keywords = {greedyAlgorithm optimization setCover},
location = {Austin, Texas, United States},
pages = {38--49},
publisher = {ACM},
timestamp = {2010-08-04T18:18:55.000+0200},
title = {Approximation algorithms for combinatorial problems},
url = {http://portal.acm.org/citation.cfm?id=804034},
year = 1973
}