CDMA: principles of spread spectrum communication
CDMA: principles of spread spectrum communication
Randomized algorithms
On the asymptotic worst case behavior of harmonic fit
Journal of Algorithms
Approximation algorithms for bin packing: a survey
Approximation algorithms for NP-hard problems
New Algorithms for Bin Packing
Journal of the ACM (JACM)
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Worst-case analysis of memory allocation algorithms
STOC '72 Proceedings of the fourth annual ACM symposium on Theory of computing
An efficient approximation scheme for the one-dimensional bin-packing problem
SFCS '82 Proceedings of the 23rd Annual Symposium on Foundations of Computer Science
The Average-Case Analysis of Some On-Line Algorithms for Bin Packing
SFCS '84 Proceedings of the 25th Annual Symposium onFoundations of Computer Science, 1984
Power control and capacity of spread spectrum wireless networks
Automatica (Journal of IFAC)
The capacity of wireless networks
IEEE Transactions on Information Theory
A framework for uplink power control in cellular radio systems
IEEE Journal on Selected Areas in Communications
Lower and upper bounds for the Bin Packing Problem with Fragile Objects
Discrete Applied Mathematics
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We consider two related optimization problems: bin-packing with fragile objects and frequency allocation in cellular networks. The former is a generalization of the classical bin-packing problem and is motivated by the latter. The problem is as follows: each object has two attributes, weight and fragility. The goal is to pack objects into bins such that, for every bin, the sum of weights of objects in that bin is no more than the fragility of any object in that bin. We consider approximation algorithms for this problem. We provide a 2-approximation to the problem of minimizing the number of bins. We also show a lower bound of 3/2 on the approximation ratio. Unlike for the classical bin-packing problem, this lower bound holds in the asymptotic case. We then consider the approximation with respect to fragility and provide a 2-approximation algorithm (i.e., our algorithm uses the same number of bins as the optimum, but the weight of objects in a bin can exceed the fragility by a factor of 2). We then consider the frequency allocation problem (which is a special case of bin-packing with fragile objects) and give improved approximation algorithms for it. Finally, we consider a probabilistic setting and show that our algorithm for frequency allocation approaches optimality as the number of users increases.