Primal-dual approximation algorithms for a packing-covering pair of problems
RAIRO - Operations Research - Recherche Opérationnelle, Tome 36 (2002) no. 1, pp. 53-71.

We consider a special packing-covering pair of problems. The packing problem is a natural generalization of finding a (weighted) maximum independent set in an interval graph, the covering problem generalizes the problem of finding a (weighted) minimum clique cover in an interval graph. The problem pair involves weights and capacities; we consider the case of unit weights and the case of unit capacities. In each case we describe a simple algorithm that outputs a solution to the packing problem and to the covering problem that are within a factor of 2 of each other. Each of these results implies an approximative min-max result. For the general case of arbitrary weights and capacities we describe an LP-based (2+ϵ)-approximation algorithm for the covering problem. Finally, we show that, unless 𝒫=𝒩𝒫, the covering problem cannot be approximated in polynomial time within arbitrarily good precision.

DOI : https://doi.org/10.1051/ro:2002005
Classification : 05A05
Mots clés : primal-dual, approximation algorithms, packing-covering, intervals
@article{RO_2002__36_1_53_0,
     author = {Kovaleva, Sofia and Spieksma, Frits C. R.},
     title = {Primal-dual approximation algorithms for a packing-covering pair of problems},
     journal = {RAIRO - Operations Research - Recherche Op\'erationnelle},
     pages = {53--71},
     publisher = {EDP-Sciences},
     volume = {36},
     number = {1},
     year = {2002},
     doi = {10.1051/ro:2002005},
     zbl = {1027.90107},
     mrnumber = {1920379},
     language = {en},
     url = {http://www.numdam.org/articles/10.1051/ro:2002005/}
}
Kovaleva, Sofia; Spieksma, Frits C. R. Primal-dual approximation algorithms for a packing-covering pair of problems. RAIRO - Operations Research - Recherche Opérationnelle, Tome 36 (2002) no. 1, pp. 53-71. doi : 10.1051/ro:2002005. http://www.numdam.org/articles/10.1051/ro:2002005/

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