Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Wireless Networks
On rectangle packing: maximizing benefits
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
Packing weighted rectangles into a square
MFCS'05 Proceedings of the 30th international conference on Mathematical Foundations of Computer Science
LMDS systems and their application
IEEE Communications Magazine
An approximation algorithm for sequential rectangle placement
Information Processing Letters
On the complexity of sequential rectangle placement in IEEE 802.16/WiMAX systems
Information and Computation
Computational analysis and efficient algorithms for micro and macro OFDMA downlink scheduling
IEEE/ACM Transactions on Networking (TON)
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We study the problem of scheduling transmissions on the Downlink of IEEE 802.16/WiMAX systems that use the OFDMA technology. These transmissions are scheduled using a matrix whose dimensions are frequency and time, where every matrix cell is a time slot on some carrier channel. The IEEE 802.16 standard mandates that (i) every transmission occupies a rectangular set of cells, and (ii) transmissions must be scheduled according to a given order. We show that if the number of cells required by a transmission is not limited (up to the matrix size), the problem of maximizing matrix utilization is very hard to approximate. On the positive side we show that if the number of cells of every transmission is limited to some constant fraction of the matrix area, the problem can be approximated to within a constant factor. As far as we know this is the first paper that considers this sequential rectangle placement problem.