An Approximation Algorithm for the Minimum Latency Set Cover Problem
The input to the minimum latency set cover problem consists of a set of jobs and a set of tools. Each job j needs a specific subset S j of the tools in order to be processed. It is possible to install a single tool in every time unit. Once the entire subset S j has been installed, job j can be processed instantly. The problem is to determine an order of job installations which minimizes the weighted sum of job completion times. We show that this problem is NP-hard in the strong sense and provide an e-approximation algorithm. Our approximation algorithm uses a framework of approximation algorithms which were developed for the minimum latency problem.
KeywordsMinimum sum set cover minimum latency approximation algorithm
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- 1.Archer, A., Levin, A., Williamson, D.P.: Faster approximation algorithm for the minimum latency problem, Cornell OR&IE Technical report 1362 (2003)Google Scholar
- 3.Blum, A., Chalasani, P., Coppersmith, D., Pulleyblank, W., Raghavan, P., Sudan, M.: The minimum latency problem. In: Proceeding of the 26th ACM Symposium on the Theory of Computing, pp. 163–171 (1994)Google Scholar
- 9.Hochbaum, D.S.: Economically preferred facilities locations with networking effect (2004) (manuscript)Google Scholar
- 15.Witzgall, D.D., Saunders, R.E.: Electronic mail and the locator’s dilemma. In: Ringeisen, R.D., Roberts, F.S. (eds.) Applications of Discrete Mathematics, pp. 65–84. SIAM, Philadelphia (1988)Google Scholar