Theory of linear and integer programming
Theory of linear and integer programming
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
Approximation algorithms
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 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
Journal of Algorithms - Special issue: Twelfth annual ACM-SIAM symposium on discrete algorithms
Improved approximation algorithms for geometric set cover
SCG '05 Proceedings of the twenty-first annual symposium on Computational geometry
Covering Problems with Hard Capacities
SIAM Journal on Computing
Approximation algorithms for capacitated rectangle stabbing
CIAC'06 Proceedings of the 6th Italian conference on Algorithms and Complexity
WAOA'06 Proceedings of the 4th international conference on Approximation and Online Algorithms
Variable-Size Rectangle Covering
COCOA '09 Proceedings of the 3rd International Conference on Combinatorial Optimization and Applications
Brief announcement: pan and scan
Proceedings of the 29th ACM SIGACT-SIGOPS symposium on Principles of distributed computing
Exact and approximation algorithms for geometric and capacitated set cover problems
COCOON'10 Proceedings of the 16th annual international conference on Computing and combinatorics
Brief announcement: configuration of actuated camera networks for multi-target coverage
SSS'10 Proceedings of the 12th international conference on Stabilization, safety, and security of distributed systems
Pervasive and Mobile Computing
Bandwidth provisioning in infrastructure-based wireless networks employing directional antennas
ICDCN'10 Proceedings of the 11th international conference on Distributed computing and networking
Journal of Discrete Algorithms
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Motivated by the widespread proliferation of wireless networks employing directional antennas, we study some capacitated covering problems arising in these networks. Geometrically, the area covered by a directional antenna with parameters α,ρ,r is a set of points with polar coordinates (r,θ) such that r ≤ r and α ≤ θ ≤ α + ρ. Given a set of customers, their positions on the plane and their bandwidth demands, the capacitated covering problem considered here is to cover all the customers with the minimum number of directional antennas such that the demands of customers assigned to an antenna stays within a bound. We consider two settings of this capacitated cover problem arising in wireless networks. In the first setting where the antennas have variable angular range, we present an approximation algorithm with ratio 3. In the setting where the angular range of antennas is fixed, we improve this approximation ratio to 1.5. These results also apply for a related problem of bin packing with deadlines. In this problem we are are given a set of items, each with a weight, arrival time and deadline, and we want to pack each item into a bin after it arrives but before its deadline. The objective is to minimize the number of bins used. We present a 3-approximation algorithm for this problem, and 1.5-approximation algorithm for the special case when each difference between a deadline and the corresponding arrival time is the same.