Approximation schemes for covering and packing problems in image processing and VLSI
Journal of the ACM (JACM)
Transmission scheduling in ad hoc networks with directional antennas
Proceedings of the 8th annual international conference on Mobile computing and networking
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
On the online bin packing problem
Journal of the ACM (JACM)
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
Incremental Clustering and Dynamic Information Retrieval
SIAM Journal on Computing
Proceedings of the nineteenth annual ACM symposium on Parallel algorithms and architectures
An efficient approximation scheme for the one-dimensional bin-packing problem
SFCS '82 Proceedings of the 23rd Annual Symposium on Foundations of Computer Science
A randomized algorithm for online unit clustering
WAOA'06 Proceedings of the 4th international conference on Approximation and Online Algorithms
An improved algorithm for online unit clustering
COCOON'07 Proceedings of the 13th annual international conference on Computing and Combinatorics
Online clustering with variable sized clusters
MFCS'10 Proceedings of the 35th international conference on Mathematical foundations of computer science
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In wireless communication networks, optimal use of the directional antenna is very important. The directional antenna coverage (DAC) problem is to cover all clients with the smallest number of directional antennas. In this paper, we consider the variable-size rectangle covering (VSRC) problem , which is a transformation of the DAC problem. There are n points above the base line y = 0 of the two-dimensional plane. The target is to cover all these points by minimum number of rectangles, such that the dimension of each rectangle is not fixed but the area is at most 1, and the bottom edge of each rectangle is on the base line y = 0. In some applications, the number of rectangles covering any position in the two-dimensional plane is bounded, so we also consider the variation when each position in the plane is covered by no more than two rectangles. We give two polynomial time algorithms for finding the optimal covering. Further, we propose two 2-approximation algorithms that use less running time (O (n logn ) and O (n )).