A new polynomial-time algorithm for linear programming
Combinatorica
A Strip-Packing Algorithm with Absolute Performance Bound 2
SIAM Journal on Computing
Shelf algorithms for on-line strip packing
Information Processing Letters
An approximation scheme for strip packing of rectangles with bounded dimensions
Discrete Applied Mathematics
Efficient approximation algorithms for scheduling malleable tasks
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)
A Near-Optimal Solution to a Two-Dimensional Cutting Stock Problem
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
OPT Versus LOAD in Dynamic Storage Allocation
SIAM Journal on Computing
Operating Systems for Reconfigurable Embedded Platforms: Online Scheduling of Real-Time Tasks
IEEE Transactions on Computers
Linear time approximation schemes for vehicle scheduling problems
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
Online bin packing with arbitrary release times
Theoretical Computer Science
Maintaining arrays of contiguous objects
FCT'09 Proceedings of the 17th international conference on Fundamentals of computation theory
Scheduling and packing malleable tasks with precedence constraints of bounded width
WAOA'09 Proceedings of the 7th international conference on Approximation and Online Algorithms
On-line bin packing with arbitrary release times
ESCAPE'07 Proceedings of the First international conference on Combinatorics, Algorithms, Probabilistic and Experimental Methodologies
Hi-index | 0.00 |
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 can be used to model scheduling problems in which tasks require a contiguous subset of identical resources that are arranged in a linear topology. The particular variants studied here are motivated by scheduling tasks for dynamically reconfigurable Field-Programmable Gate Arrays (FPGAs) comprised of an array of computing columns. Each column is a computing resource and the array of columns forms the linear topology of resources. We assume that the given FPGA has K columns, where K is a fixed positive integer, and each task occupies a contiguous subset of these columns. For the case in which tasks have precedence constraints, we give an O(log n) approximation, where n is the number of tasks. 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 (1 + ε)- 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], i.e., the rectangles are at least as wide as a column in the FPGA. Our running time is polynomial in n and 1/ε, but exponential in K.