Proceedings Article10.1145/800009.808055
Polynomial complete scheduling problems
Jeffrey D. Ullman
- 01 Jan 1973
- Vol. 7, Iss: 4, pp 96-101
105
TL;DR: It is shown that the problem of finding an optimal schedule for a set of jobs is polynomial complete even in the following two restricted cases, tantamount to showing that the scheduling problems mentioned are intractable.
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Abstract: We show that the problem of finding an optimal schedule for a set of jobs is polynomial complete even in the following two restricted cases.(1) All jobs require one time unit.(2) All jobs require one or two time units, and there are only two processors.As a consequence, the general preemptive scheduling problem is also polynomial complete.These results are tantamount to showing that the scheduling problems mentioned are intractable.
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Citations
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References
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Richard M. Karp
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TL;DR: Throughout the 1960s I worked on combinatorial optimization problems including logic circuit design with Paul Roth and assembly line balancing and the traveling salesman problem with Mike Held, which made me aware of the importance of distinction between polynomial-time and superpolynomial-time solvability.
13.6K
•Book
The Design and Analysis of Computer Algorithms
Alfred V. Aho,John E. Hopcroft +1 more
- 01 Jan 1974
TL;DR: This text introduces the basic data structures and programming techniques often used in efficient algorithms, and covers use of lists, push-down stacks, queues, trees, and graphs.
10.6K
The complexity of theorem-proving procedures
Stephen A. Cook
- 03 May 1971
TL;DR: It is shown that any recognition problem solved by a polynomial time-bounded nondeterministic Turing machine can be “reduced” to the problem of determining whether a given propositional formula is a tautology.
7.4K
Optimal scheduling for two-processor systems
Edward G. Coffman,Ron Graham +1 more
TL;DR: It is proved that the algorithm gives optimal solutions and its application to preemptive scheduling disciplines is discussed.
623
Optimal Sequencing of Two Equivalent Processors
M. Fujii,T. Kasami,K. Ninomiya +2 more
TL;DR: This paper presents an efficient algorithm for a class of sequencing problems in which n tasks with an arbitrary precedence relation have to be processed by two processors of equal ability, and each task requires one unit of time.
192