A linear-time algorithm for triangulating simple polygons
STOC '86 Proceedings of the eighteenth annual ACM symposium on Theory of computing
Optimal shortest path queries in a simple polygon
SCG '87 Proceedings of the third annual symposium on Computational geometry
Energy-efficient packet transmission over a wireless link
IEEE/ACM Transactions on Networking (TON)
A scheduling model for reduced CPU energy
FOCS '95 Proceedings of the 36th Annual Symposium on Foundations of Computer Science
On Energy-Constrained Real-Time Scheduling
ECRTS '04 Proceedings of the 16th Euromicro Conference on Real-Time Systems
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We consider a class of k-server optimal task scheduling problems 驴 partitioning and scheduling N tasks with various reql-time constrains and work loads on k servers with convex task processing cost function so as to minimize the total task processing cost while still guarantee satisfaction of all time constrains. This class has broad expressing power for practical scheduling problems in several areas such as real-time multi-media wireless transmission [2, 7, 4], CPU energy conservation [10, 1, 8], and warehouse order processing management, et. al.. Our formulation is quite general such that most previous works can be readily reduced to a special case of the presented k-server optimal task scheduling problem. We show that, when k=1, optimal solution can be obtained in computational complexity of 0(N) and the corresponding optimal scheduling problem is equivalent to finding the shortest 2DEuclidean distance between two vertices inside a well-defined 2D polygon. However, when k 驴 2, the optimal scheduling problem can be demonstrated to be NP-hard by reducing it to a well-known NP-complete bin-packing problem. Therefore, we conclude no polynomial time algorithm exists for a general k-server optimal task scheduling problem. We then construct approximation algorithmsto solve the presented k-server problem in a practical way and illustrate its performance by simulation results and analysis.