Abstract
A number of scheduling and assignment problems are presented involving the execution of periodic operations in a multiprocessor environment. We consider the computational complexity of these problems and propose approximation algorithms for operations with identical periods as well as for operations with arbitrary integer periods.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Bibliography
Bartholdi, J.J. [ 1981 ], A guaranteed-accuracy round-off algorithm for cyclic scheduling and set covering, Operations Research 29, 501 - 510.
Bartholdi, J.J., J.B. Orlin, and H.D. Ratliff [ 1980 ], Cyclic scheduling via integer programs with circular ones, Operations Research 28, 1074 - 1085.
Bertossi, A.A. and M.A. Bonuccelli [ 1983 ], Preemptive scheduling of periodic jobs in uniform multiprocessor systems, Information Processing Letters 16, 3 - 6.
Bertossi, A.A. and M.A. Bonuccelli [ 1985 ], A polynomial feasibility test for preemptive periodic scheduling of unrelated processors, Discrete Applied Mathematics 12, 195 - 201.
Burkard, R.E. [ 1986 ], Optimal schedules for periodically recurring events, Discrete Applied Mathematics 15, 167 - 180.
Chetto, H. and M. Chetto [ 1989 ], Scheduling periodic and sporadic tasks in a real-time system, Information Processing Letters 30, 177 - 184.
Coffmann, E.G., Jr., M.R. Garey, and D.S. Johnson [ 1984 ], Approximation algorithms for bin packing - an updated survey, in: G. Ausiello, M. Lucertini, and P. Serafini (Eds.), Algorithms Design and Computer System Design, CISM Courses and Lectures 284, Springer, Vienna, 49 - 106.
Dhall, S.K. and C.L. Liu [ 1978 ], On a real-time scheduling problem, Operations Research 26, 127 - 140.
Edmonds, J. [ 1965 ], Paths, trees and flowers, Canadian Journal of Mathematics 17, 449 - 467.
Garey, M.R. and D.S. Johnson [ 1979 ], Computers and Intractability: A Guide to the Theory of NP-Completeness, W.H. Freeman and Co., San Francisco.
Garey, M.R., D.S. Johnson, G.L. Miller, and C.H. Papadimitriou [ 1980 ], The complexity of coloring circular arcs and chords, SIAM Journal on Algebraic and Discrete Methods 1, 216 - 227.
Gonzalez, M.J. and J.W. Soh [ 1975 ], Periodic job scheduling in a distributed processor system, IEEE Transactions on Aerospace and Electronic Systems 12, 530 - 536.
Gupta, U.I., D.T. Lee, and J.Y.-T. Leung [ 1979 ], An optimal solution for the channel-assignment problem, IEEE Transaction on Computers 28, 807 - 810.
Hashimoto, A. and J. Stevens [ 1971 ], Wire routing by optimizing channel assignment with large apertures, Proceedings of the 8th Design Automation Conference, 155 - 169.
Hoperoft, J.E. and R.M. Karp [ 1973 ], An n 5/2 algorithm for maximum matchings in bipartite graphs, SIAM Journal on Computing 2, 225 - 231.
Korst, J.H.M., E.H.L. Aarts, J.K. Lenstra, and J. Wessels [ 1991 ], Periodic Assignment and Graph Colouring, Philips Research Manuscript.
Labetoulle, J. [ 1974 ], Some theorems on real time scheduling, in: E. Gelenbe and R. Mahl (Eds.), Computer Architecture and Networks, North-Holland, Amsterdam, 285 - 293.
Lawler, E.L. and C.U. Martel [ 1981 ], Scheduling periodically occurring tasks on multiple processors, Information Processing Letters 12, 9 - 12.
Leung, J.Y.-T. and M.L. Merrill [ 1980 ], A note on preemptive scheduling of periodic, real-time tasks, Information Processing Letters 11, 115 - 118.
Leung, J.Y.-T. and J. Whitehead [ 1982 ], On the complexity of fixed-priority scheduling of periodic, real-time tasks, Performance Evaluation 2, 237 - 250.
Liu, C.L. and J.W. Layland [ 1973 ], Scheduling algorithms for multiprogramming in a hard real-time environment, Journal of the Association for Computing Machinery 20, 46 - 61.
Orlin, J.B. [ 1982 ], Minimizing the number of vehicles to meet a fixed periodic schedule: an application of periodic posets, Operations Research 30, 760 - 776.
Orlin, J.B., M.A. Bonuccelli, and D.P. Bovet [ 1981 ], An 0(n 2 ) algorithm for coloring proper circular arc graphs, SIAM Journal on Algebraic and Discrete Methods 2, 88 - 93.
Park, K.S. and D.K. Yun [ 1985 ], Optimal scheduling of periodic activities, Operations Research 33, 690 - 695.
Serafini, P. and W. Ukovich [ 1989 ], A mathematical model for periodic scheduling problems, SIAM Journal on Discrete Mathematics 2, 550 - 581.
Shih, W.-K. and W.-L. Hsu [ 1989 ], An 0(n 1 . 5 ) algorithm to color proper circular arcs, Discrete Applied Mathematics 25, 321 - 323.
Tucker, A [ 1975 ], Coloring a family of circular arcs, SIAM Journal on Applied Mathematics 29, 493 - 552.
Vince, J. [ 1989 ], Scheduling periodic events, Discrete Applied Mathematics 25, 299 - 310.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1991 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Korst, J., Aarts, E., Lenstra, J.K., Wessels, J. (1991). Periodic Multiprocessor Scheduling. In: Aarts, E.H.L., van Leeuwen, J., Rem, M. (eds) Parle ’91 Parallel Architectures and Languages Europe. Lecture Notes in Computer Science, vol 505. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-25209-3_12
Download citation
DOI: https://doi.org/10.1007/978-3-662-25209-3_12
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-662-23206-4
Online ISBN: 978-3-662-25209-3
eBook Packages: Springer Book Archive