Using dual approximation algorithms for scheduling problems theoretical and practical results
Journal of the ACM (JACM)
Introduction to algorithms
Approximation schemes for covering and packing problems in image processing and VLSI
Journal of the ACM (JACM)
Approximation algorithms for bin packing: a survey
Approximation algorithms for NP-hard problems
Transmission scheduling in ad hoc networks with directional antennas
Proceedings of the 8th annual international conference on Mobile computing and networking
On the maximum stable throughput problem in random networks with directional antennas
Proceedings of the 4th ACM international symposium on Mobile ad hoc networking & computing
On the capacity improvement of ad hoc wireless networks using directional antennas
Proceedings of the 4th ACM international symposium on Mobile ad hoc networking & computing
An efficient fully polynomial approximation scheme for the Subset-Sum problem
Journal of Computer and System Sciences
Improved approximation algorithms for geometric set cover
SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
Polynomial-Time Approximation Schemes for Geometric Intersection Graphs
SIAM Journal on Computing
Proceedings of the nineteenth annual ACM symposium on Parallel algorithms and architectures
Small-size ε-nets for axis-parallel rectangles and boxes
Proceedings of the forty-first annual ACM symposium on Theory of computing
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First, we study geometric variants of the standard set cover motivated by assignment of directional antenna and shipping with deadlines, providing the first known polynomial-time exact solutions. Next, we consider the following general (non-necessarily geometric) capacitated set cover problem. There is given a set of elements with real weights and a family of sets of the elements. One can use a set if it is a subset of one of the sets in the family and the sum of the weights of its elements is at most one. The goal is to cover all the elements with the allowed sets. We show that any polynomial-time algorithm that approximates the uncapacitated version of the set cover problem with ratio r can be converted to an approximation algorithm for the capacitated version with ratio r +1.357. The composition of these two results yields a polynomial-time approximation algorithm for the problem of covering a set of customers represented by a weighted n-point set with a minimum number of antennas of variable angular range and fixed capacity with ratio 2.357.