Maximum bounded 3-dimensional matching is MAX SNP-complete
Information Processing Letters
Various notions of approximations: good, better, best, and more
Approximation algorithms for NP-hard problems
A PTAS for the multiple knapsack problem
SODA '00 Proceedings of the eleventh annual ACM-SIAM symposium on Discrete algorithms
A framework for opportunistic scheduling in wireless networks
Computer Networks: The International Journal of Computer and Telecommunications Networking
Faster and Simpler Algorithms for Multicommodity Flow and other Fractional Packing Problems.
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
Maximizing Queueing Network Utility Subject to Stability: Greedy Primal-Dual Algorithm
Queueing Systems: Theory and Applications
Tight approximation algorithms for maximum general assignment problems
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
Scheduling over nonstationary wireless channels with finite rate sets
IEEE/ACM Transactions on Networking (TON)
Scheduling in multi-channel wireless networks: rate function optimality in the small-buffer regime
Proceedings of the eleventh international joint conference on Measurement and modeling of computer systems
Instability of the proportional fair scheduling algorithm for HDR
IEEE Transactions on Wireless Communications
CDMA/HDR: a bandwidth efficient high speed wireless data service for nomadic users
IEEE Communications Magazine
Providing quality of service over a shared wireless link
IEEE Communications Magazine
Opportunistic transmission scheduling with resource-sharing constraints in wireless networks
IEEE Journal on Selected Areas in Communications
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We consider the problem of scheduling multicarrier wireless data in systems such as IEEE 802.16 (WiMAX). Each scheduling decision involves assigning carriers to users for each time slot, subject to the constraint that each carrier is assigned to at most one user, but multiple carriers can potentially be assigned to the same user. One important aspect of our problem is that a scheduler knows the channel rates across all users and all carriers whenever a scheduling decision is made. This "global" information may give a potential for enhancing performance via an optimized allocation of carriers to users. We analyze this problem in a situation where finite queues are fed by a data arrival process. The well-known MaxWeight algorithm for the single-carrier setting maximizes the product of queue size and service rate. We focus on how to adapt MaxWeight to the multicarrier setting. If the same objective is pursued, more service than needed may be assigned to drain a queue, thereby creating wastage. While a simple variant in the objective forbids this wastage, it turns an easy-to-compute old objective into an intractable new objective. We state the hardness of the new optimization problems and propose several extremely simple algorithms with provable performance bounds. We conclude with supporting simulation examples.