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Combinatorica
A Strip-Packing Algorithm with Absolute Performance Bound 2
SIAM Journal on Computing
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Information Processing Letters
An approximation scheme for strip packing of rectangles with bounded dimensions
Discrete Applied Mathematics
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Proceedings of the eleventh annual ACM symposium on Parallel algorithms and architectures
Preemptive Scheduling with Release Times, Deadlines, and Due Times
Journal of the ACM (JACM)
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Mathematics of Operations Research
Reverse-Fit: A 2-Optimal Algorithm for Packing Rectangles
ESA '94 Proceedings of the Second Annual European Symposium on Algorithms
An Exact Approach to the Strip-Packing Problem
INFORMS Journal on Computing
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SIAM Journal on Computing
Operating Systems for Reconfigurable Embedded Platforms: Online Scheduling of Real-Time Tasks
IEEE Transactions on Computers
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Theoretical Computer Science - Special issue: Online algorithms in memoriam, Steve Seiden
On strip packing With rotations
Proceedings of the thirty-seventh annual ACM symposium on Theory of computing
Proceedings of the 42nd annual Design Automation Conference
Scheduling malleable tasks with precedence constraints
Proceedings of the seventeenth annual ACM symposium on Parallelism in algorithms and architectures
An efficient approximation scheme for the one-dimensional bin-packing problem
SFCS '82 Proceedings of the 23rd Annual Symposium on Foundations of Computer Science
Heuristics for the strip packing problem with unloading constraints
Computers and Operations Research
The Bin Packing Problem with Precedence Constraints
Operations Research
The Bin Packing Problem with Precedence Constraints
Operations Research
Scheduling and packing malleable and parallel tasks with precedence constraints of bounded width
Journal of Combinatorial Optimization
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The strip packing problem seeks to tightly pack a set of n rectangles into a strip of fixed width and arbitrary height. The rectangles model tasks and the height models time. This paper examines two variants of strip packing: when the rectangles to be placed have precedence constraints and when the rectangles have release times. Strip packing is used to model scheduling problems in which tasks require a contiguous subset of identical resources that are arranged in a linear topology. The variants studied here are motivated by scheduling tasks for dynamically reconfigurable Field-Programmable Gate Arrays (FPGAs) comprised of a linear arrangement of K homogeneous computing resources, where K is a fixed positive integer, and each task occupies a contiguous subset of these resources. For the case in which tasks have precedence constraints, we give an O(logn) approximation algorithm. We then consider the special case in which all the rectangles have uniform height, and reduce it to the resource constrained scheduling studied by Garey, Graham, Johnson and Yao, thereby extending their asymptotic results to our special case problem. We also give an absolute 3-approximation for this special case problem. For strip packing with release times, we provide an asymptotic polynomial time approximation scheme. We make the standard assumption that the rectangles have height at most 1. In addition, we also require widths to be in [1K,1]. For the FPGA application, this would imply that the rectangles are at least as wide as a column. Our running time is polynomial in n and 1/@e, but exponential in K.