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Erschienen in:
2010 | OriginalPaper | Buchkapitel
On Column-Restricted and Priority Covering Integer Programs
verfasst von : Deeparnab Chakrabarty, Elyot Grant, Jochen Könemann
Erschienen in: Integer Programming and Combinatorial Optimization
Verlag: Springer Berlin Heidelberg
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In a column-restricted covering integer program (CCIP), all the non-zero entries of any column of the constraint matrix are equal. Such programs capture capacitated versions of covering problems. In this paper, we study the approximability of CCIPs, in particular, their relation to the integrality gaps of the underlying 0,1-CIP.
If the underlying 0,1-CIP has an integrality gap
O
(
γ
), and assuming that the integrality gap of the
priority version
of the 0,1-CIP is
O
(
ω
), we give a factor
O
(
γ
+
ω
) approximation algorithm for the CCIP. Priority versions of 0,1-CIPs (PCIPs) naturally capture
quality of service
type constraints in a covering problem.
We investigate priority versions of the line (PLC) and the (rooted) tree cover (PTC) problems. Apart from being natural objects to study, these problems fall in a class of fundamental geometric covering problems. We bound the integrality of certain classes of this PCIP by a constant. Algorithmically, we give a polytime exact algorithm for PLC, show that the PTC problem is APX-hard, and give a factor 2-approximation algorithm for it.