Paradigms for parallel dynamic programming

We extend the sequential model for dynamic programming to a parallel model. We propose three general parallel dynamic programming algorithms for pipeline and ring networks for multistage automatons. The study of the optimality lead us to the introduction of two new classes of multistage automatons: nondecreasing automatons and strongly increasing automatons. As an example, this parallel dynamic programming approach is applied to the single resource allocation problem. Results both for transputer networks and for local area networks using PVM are reported. The experience proves that the proposed algorithms can be easily and efficiently implemented. Furthermore, these procedures constitute a suitable kernel to build general parallel tools for dynamic programming.

[1]  Paul Helman,et al.  A common schema for dynamic programming and branch and bound algorithms , 1989, JACM.

[2]  M. Held,et al.  Finite-State Processes and Dynamic Programming , 1967 .

[3]  Alan George,et al.  Dynamic Programming on a Shared-Memory Multiprocessor , 1993, Parallel Comput..

[4]  Bryan L. Deuermeyer,et al.  On a language for discrete dynamic programming and a microcomputer implementation , 1989, Comput. Oper. Res..

[5]  茨木 俊秀,et al.  Enumerative approaches to combinatorial optimization , 1987 .

[6]  Harry W. J. M. Trienekens,et al.  Experiments with Parallel Algorithms for Combinatorial Problems , 1985 .

[7]  Francisco Almeida,et al.  The single resource allocation problem: parallel algorithms on distributed systems , 1996 .

[8]  Francisco Almeida,et al.  A Parallel Algorithm for the Integer Knapsack Problem for Pipeline Networks , 1995, Parallel Algorithms Appl..

[9]  Wojciech Rytter,et al.  Efficient parallel algorithms , 1988 .

[10]  Sartaj Sahni,et al.  A Hypercube Algorithm for the 0/1 Knapsack Problem , 1988, J. Parallel Distributed Comput..

[11]  Benjamin W. Wah,et al.  Multiprocessing of Combinatorial Search Problems , 1985, Computer.

[12]  Jeffrey D. Ullman,et al.  Introduction to Automata Theory, Languages and Computation , 1979 .

[13]  Shang-Hua Teng,et al.  Adaptive Parallel Algorithms for Integral Knapsack Problems , 1990, J. Parallel Distributed Comput..

[14]  Gen-Huey Chen,et al.  An improved parallel algorithm for 0/1 knapsack problem , 1992, Parallel Comput..

[15]  T. Ibaraki.  Enumerative approaches to combinatorial optimization - part I , 1988 .

[16]  Thomas L. Morin,et al.  Branch-and-Bound Strategies for Dynamic Programming , 2015, Oper. Res..

[17]  Pearl Y. Wang,et al.  Solving a Two-Dimensional Knapsack Problem on SIMD Computers , 1992, ICPP.

[18]  Dan I. Moldovan,et al.  Partitioning and Mapping Algorithms into Fixed Size Systolic Arrays , 1986, IEEE Transactions on Computers.

[19]  Zvi Galil,et al.  Parallel Algorithms for Dynamic Programming Recurrences with More than O(1) Dependency , 1994, J. Parallel Distributed Comput..

[20]  守屋 悦朗,et al.  J.E.Hopcroft, J.D. Ullman 著, "Introduction to Automata Theory, Languages, and Computation", Addison-Wesley, A5変形版, X+418, \6,670, 1979 , 1980 .

[21]  José Luis Roda García,et al.  Integral knapsack problems: parallel algorithms and their implementations on distributed systems , 1995, ICS '95.

[22]  Patrice Quinton,et al.  Dynamic programming parallel implementations for the knapsack problem , 1993 .