论文信息 - On the complexity of scheduling with large communication delays

On the complexity of scheduling with large communication delays

Abstract Given a directed acyclic graph (dag) with unit execution time tasks and constant communication delays c ⩾ 2, we are interested in deciding if there is a schedule for the dag of length at most L. We prove that the problem is polynomial when L is equal to (c + 1), or (c + 2) for the special case of c = 2, and that it is NP-complete for (c + 3) for any value of c, even in the case of a bipartite dag of depth one.

[1] Mihalis Yannakakis,et al. Towards an Architecture-Independent Analysis of Parallel Algorithms , 1990, SIAM J. Comput..

[2] J. Van Leeuwen,et al. Handbook of theoretical computer science - Part A: Algorithms and complexity; Part B: Formal models and semantics , 1990 .

[3] Joseph Y.-T. Leung,et al. On Scheduling Independent Tasks with Restricted Execution Times , 1982, Oper. Res..

[4] E.L. Lawler,et al. Optimization and Approximation in Deterministic Sequencing and Scheduling: a Survey , 1977 .

[5] Victor J. Rayward-Smith,et al. UET scheduling with unit interprocessor communication delays , 1987, Discret. Appl. Math..

[6] Jan Karel Lenstra,et al. Complexity of Scheduling under Precedence Constraints , 1978, Oper. Res..

[7] Jacek Blazewicz,et al. Scheduling in Computer and Manufacturing Systems , 1990 .

[8] B. J. Lageweg,et al. Multiprocessor scheduling with communication delays , 1990, Parallel Comput..

[9] Jan van Leeuwen,et al. Graph Algorithms , 1991, Handbook of Theoretical Computer Science, Volume A: Algorithms and Complexity.

[10] Z Liu,et al. Scheduling Theory and its Applications , 1997 .

[11] David S. Johnson,et al. Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[12] Han Hoogeveen,et al. Three, four, five, six, or the complexity of scheduling with communication delays , 1994, Oper. Res. Lett..

[13] Peter J. Denning,et al. Operating Systems Theory , 1973 .