Processor Allocation in Hypercube Multiprocessors

The processor allocation problem requires recognizing and locating a free subcube that can accommodate a request for a subcube of a specified size for an incoming task. Methods reported in the literature fall into two strategies: bottom-up or bit mapped technique (BMT) and top-downer available cube technique (ACT). Our algorithm that solves the allocation problem in faulty hypercubes falls into the category of ACT's which offer the advantage over BMT's of quickly recognizing whether or not a requested subcube is available in the list of fault-free subcubes. We introduce new algebraic functions and the concept of separation factor to select a subcube for allocation. The notion of overlap-syndrome, defined in the text, quantifies the overlap among free subcubes. Our technique has full subcube recognition ability and thus recognizes more subcubes as compared to bit mapped techniques: Buddy, Gray code and its variants. The advantages of our approach over some of the existing ACT's in terms of fragmentation and overall completion time are described in the text and in simulation results. >

[1]  Suresh Rai,et al.  CAREL: Computer Aided Reliability Evaluator for Distributed Computing Networks , 1991, IEEE Trans. Parallel Distributed Syst..

[2]  Abdol-Hossein Esfahanian,et al.  Generalized Measures of Fault Tolerance with Application to N-Cube Networks , 1989, IEEE Trans. Computers.

[3]  Trevor Mudge,et al.  Hypercube supercomputers , 1989, Proc. IEEE.

[4]  Dhiraj K. Pradhan,et al.  Fast and Efficient Strategies for Cubic and Non-Cubic Allocation in Hypercube Multiprocessors , 1993, 1993 International Conference on Parallel Processing - ICPP'93.

[5]  Qing Yang,et al.  Prime Cube Graph Approach for Processor Allocation in Hypercube Multiprocessors , 1991, ICPP.

[6]  Jerry L. Trahan,et al.  A Reconfiguration Technique for Fault Tolerance in a Hypercube , 1992, Parallel Process. Lett..

[7]  Nian-Feng Tzeng,et al.  A Fast Recognition-Complete Processor Allocation Strategy for Hypercube Computers , 1992, IEEE Trans. Computers.

[8]  John P. Hayes,et al.  Subcube Allocation in Hypercube Computers , 1991, IEEE Trans. Computers.

[9]  B. Bose,et al.  A new strategy for processors allocation in an N-cube multiprocessor , 1989, Eighth Annual International Phoenix Conference on Computers and Communications. 1989 Conference Proceedings.

[10]  Nripendra N. Biswas,et al.  Logic design theory , 1992 .

[11]  Laxmi N. Bhuyan,et al.  Fault Tolerant Subcube Allocation in Hypercubes , 1993, 1993 International Conference on Parallel Processing - ICPP'93.

[12]  J. Kim,et al.  A Top-Down Processor Allocation Scheme for Hypercube Computers , 1991, IEEE Trans. Parallel Distributed Syst..

[13]  Ming-Syan Chen,et al.  Processor Allocation in an N-Cube Multiprocessor Using Gray Codes , 1987, IEEE Transactions on Computers.

[14]  Seung Ryoul Maeng,et al.  A heuristic processor allocation strategy in hypercube systems , 1991, Proceedings of the Third IEEE Symposium on Parallel and Distributed Processing.

[15]  M. H. Schultz,et al.  Topological properties of hypercubes , 1988, IEEE Trans. Computers.

[16]  Dharma P. Agrawal,et al.  Advances in distributed system reliability , 1990, IEEE Computer Society Press Tutorial.

[17]  James R. Armstrong,et al.  Fault Diagnosis in a Boolean n Cube Array of Microprocessors , 1981, IEEE Transactions on Computers.

[18]  F. Harary,et al.  A survey of the theory of hypercube graphs , 1988 .

[19]  Hyunsoo Yoon,et al.  A processor allocation strategy using cube coalescing in hypercube multicomputers , 1993, Proceedings of 1993 5th IEEE Symposium on Parallel and Distributed Processing.