# Primal-dual approximation algorithms for a packing-covering pair of problems

Sofia Kovaleva; Frits C.R. Spieksma

RAIRO - Operations Research (2010)

- Volume: 36, Issue: 1, page 53-71
- ISSN: 0399-0559

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topKovaleva, Sofia, and Spieksma, Frits C.R.. "Primal-dual approximation algorithms for a packing-covering pair of problems." RAIRO - Operations Research 36.1 (2010): 53-71. <http://eudml.org/doc/105261>.

@article{Kovaleva2010,

abstract = {
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.
},

author = {Kovaleva, Sofia, Spieksma, Frits C.R.},

journal = {RAIRO - Operations Research},

keywords = {Primal-dual; approximation algorithms; packing-covering; intervals.; primal-dual; intervals},

language = {eng},

month = {3},

number = {1},

pages = {53-71},

publisher = {EDP Sciences},

title = {Primal-dual approximation algorithms for a packing-covering pair of problems},

url = {http://eudml.org/doc/105261},

volume = {36},

year = {2010},

}

TY - JOUR

AU - Kovaleva, Sofia

AU - Spieksma, Frits C.R.

TI - Primal-dual approximation algorithms for a packing-covering pair of problems

JO - RAIRO - Operations Research

DA - 2010/3//

PB - EDP Sciences

VL - 36

IS - 1

SP - 53

EP - 71

AB -
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.

LA - eng

KW - Primal-dual; approximation algorithms; packing-covering; intervals.; primal-dual; intervals

UR - http://eudml.org/doc/105261

ER -

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