TY - JOUR
T1 - Approximation algorithms for partial covering problems
JF - Journal of Algorithms
Y1 - 2004
A1 - Gandhi,Rajiv
A1 - Khuller, Samir
A1 - Srinivasan, Aravind
KW - Approximation algorithms
KW - Partial covering
KW - Primal-dual methods
KW - Randomized rounding
KW - Set cover
KW - Vertex cover
AB - We study a generalization of covering problems called partial covering. Here we wish to cover only a desired number of elements, rather than covering all elements as in standard covering problems. For example, in k-partial set cover, we wish to choose a minimum number of sets to cover at least k elements. For k-partial set cover, if each element occurs in at most f sets, then we derive a primal-dual f-approximation algorithm (thus implying a 2-approximation for k-partial vertex cover) in polynomial time. Without making any assumption about the number of sets an element is in, for instances where each set has cardinality at most three, we obtain an approximation of 4/3. We also present better-than-2-approximation algorithms for k-partial vertex cover on bounded degree graphs, and for vertex cover on expanders of bounded average degree. We obtain a polynomial-time approximation scheme for k-partial vertex cover on planar graphs, and for covering k points in Rd by disks.
VL - 53
SN - 0196-6774
UR - http://www.sciencedirect.com/science/article/pii/S0196677404000689
CP - 1
M3 - 10.1016/j.jalgor.2004.04.002
ER -