This Article 
   
 Share 
   
 Bibliographic References 
   
 Add to: 
 
Digg
Furl
Spurl
Blink
Simpy
Google
Del.icio.us
Y!MyWeb
 
 Search 
   
Scaling Simulation of the Fusing-Restricted Reconfigurable Mesh
September 1998 (vol. 9 no. 9)
pp. 861-871

Abstract—This paper deals with the ability of a model to adapt algorithm instances of different sizes to run on a given model size without significant loss of efficiency. The overhead in simulating a step of a large instance of the model on a smaller instance can quantify this ability. A reconfigurable mesh (R-Mesh) can use its bus structure as a computational resource, presenting an obstacle to efficiently scaling down algorithms to run on a smaller R-Mesh. We construct a scaling simulation of a Fusing-Restricted Reconfigurable Mesh (FR-Mesh), a version of the R-Mesh. The overhead of this simulation depends only on the simulating machine size and not on the simulated machine size. Previously, the R-Mesh was not known to admit such a simulation overhead without significantly reducing its computational power. The small overhead holds importance for flexibility in algorithm design and for running algorithms with various input sizes on an available model of given size. The results of this paper extend to a variety of concurrent write rules and also translate to an improved scaling simulation of an unrestricted R-Mesh.

[1] H.M. Alnuweiri, "Parallel Constant-Time Connectivity Algorithms on a Reconfigurable Network of Processors," IEEE Trans. Parallel and Distributed Systems, vol. 6, no. 1, pp. 105-110, Jan. 1995.
[2] Y. Ben-Asher, D. Gordon, and A. Schuster, “Efficient Self-Simulation Algorithms for Reconfigurable Arrays,” J. Parallel Distributed Computing, vol. 30, no. 1, pp. 1–22, 1995.
[3] Y. Ben-Asher, K.J. Lange, D. Peleg, and A. Schuster, “The Complexity of Reconfiguring Network Models,” Information and Computation, vol. 121, pp. 41–58, 1995.
[4] Y. Ben-Asher,D. Peleg,R. Ramaswami,, and A. Schuster,“The power of reconfiguration,” J. of Parallel and Distributed Computing, vol. 13, no. 2, pp. 139-153, Oct. 1991.
[5] J. Bruck, L. De Coster, N. Dewulf, C.-T. Ho, and R. Lauwereins, "On the Design and Implementation of Broadcast and Global Combine Operations Using the Postal Model," IEEE Trans. Parallel and Distributed Systems, vol. 7, no. 3, pp. 256-265, Mar. 1996.
[6] J.A. Fernández-Zepeda, J.L. Trahan, and R. Vaidyanathan, "Scaling the FR-Mesh under Different Concurrent Write Rules," Proc. World Multiconference Systemics, Cybernetics, and Informatics, pp. 437-444, 1997.
[7] J. Gunnels, C. Lin, G. Morrow, and R. van de Geijn, "A Flexible Class of Parallel Matrix Multiplication Algorithms," Proc. 12th Int'l Parallel Processing Symp. and Ninth Symp. Parallel and Distributed Processing, pp. 110-116, 1998.
[8] J. J'aJ'a, An Introduction to Parallel Algorithms.New York: Addison-Wesley, 1992.
[9] J. Jang, M. Nigam, V.K. Prasanna, and S. Sahni, “Constant Time Algorithms for Computational Geometry on the Reconfigurable Mesh,” IEEE Trans. Parallel and Distributed Systems, vol. 8, no. 1, pp. 1–12, Jan. 1997.
[10] R.M. Karp and V. Ramachandran, "Parallel Algorithms for Shared-Memory Machines," Handbook of Theoretical Computer Science, J. van Leeuwen, ed., vol. A, pp. 869-941.Amsterdam: NorthHolland, 1990.
[11] T.H. Lai and M.-J. Sheng, "Constructing Euclidean Minimum Spanning Trees and All Nearest Neighbors on Reconfigurable Meshes," IEEE Trans. Parallel and Distributed Systems, vol. 7, no. 8, pp. 806-817, Aug. 1996.
[12] H. Li and Q.F. Stout, "Reconfigurable SIMD Massively Parallel Computers," IEEE Proc., vol. 79, no. 4, pp. 429-443, Apr. 1991.
[13] R. Lin and S. Olariu, "Reconfigurable Buses with Shift Switching: Concepts and Applications," IEEE Trans. Parallel and Distributed Systems, vol. 6, no. 1, pp. 93-102, Jan. 1995.
[14] M. Maresca, "Polymorphic Processor Arrays," IEEE Trans. Parallel and Distributed Systems, vol. 4, pp. 490-506, 1993.
[15] Y. Matias and A. Schuster, "Fast, Efficient Mutual and Self Simulations for Shared Memory and Reconfigurable Mesh," Proc. Seventh Symp. Parallel and Distributed Processing, pp. 238-246, 1995.
[16] R. Miller,V.K. Prasanna Kumar,D.I. Reisis, and Q.F. Stout,“Parallel computations on reconfigurable meshes,” IEEE Trans. on Computers, pp. 678-692, June 1993.
[17] M.M. Murshed and R.P. Brent, "Algorithms for Optimal Self-Simulation of Some Restricted Reconfigurable Meshes," Proc. Second Int'l Conf. Computational Intelligence and Multimedia Applications, pp. 734-744, 1998.
[18] K. Nakano, "A Bibliography of Published Papers on Dynamically Reconfigurable Architectures," Parallel Processing Letters, vol. 5, no. 1, pp. 111-124, Mar. 1995.
[19] N. Nisan and A. Ta-Shma, "Symmetric Logspace Is Closed Under Complement," Proc. 27th ACM Symp Theory of Computing, pp. 140-146, 1995.
[20] S. Sahni, "Computing Reconfigurable Bus Architectures," Computer Systems and Education, Balakrishnan et al., eds., pp. 386-398.New Delhi, India: Tata McGraw-Hill, 1994.
[21] J.L. Trahan, A.G. Bourgeois, and R. Vaidyanathan, "Tighter and Broader Complexity Results for Reconfigurable Models," Parallel Processing Letters, to appear.
[22] J.L. Trahan, Y. Pan, R. Vaidyanathan, and A.G. Bourgeois, "Scalable Basic Algorithms on a Linear Array with a Reconfigurable Pipelined Bus System," Proc. 10th ISCA Int'l Conf. Parallel and Distributed Computer Systems, pp. 564-569, 1997.
[23] J.L. Trahan, R. Vaidyanathan, and R.K. Thiruchelvan, "On the Power of Segmenting and Fusing Buses," J. Parallel and Distributed Computing, vol. 34, no. 1, pp. 82-94, Apr. 1996.
[24] J.L. Trahan and R. Vaidyanathan, "Relative Scalability of the Reconfigurable Multiple Bus Machine," Proc. Workshop Reconfigurable Architecture and Algorithms, 1996.
[25] U. Vishkin, "Structural Parallel Algorithmics," Proc. Int'l Colloquium Automata, Languages, and Programming, pp. 363-380, 1991.
[26] B. F. Wang and G. H. Chen,“Constant time algorithms for the transitive closure problem and some related graph problems on processor arrays with reconfigurable bus systems,” IEEE Trans. on Parallel and Distributed Systems, vol. 1, no. 4, pp. 500-507, 1991.

Index Terms:
Reconfigurable mesh, scaling simulation, simulation overhead, concurrent write rules, model simulation, parallel algorithms.
Citation:
José Alberto Fernández-Zepeda, Ramachandran Vaidyanathan, Jerry L. Trahan, "Scaling Simulation of the Fusing-Restricted Reconfigurable Mesh," IEEE Transactions on Parallel and Distributed Systems, vol. 9, no. 9, pp. 861-871, Sept. 1998, doi:10.1109/71.722220
Usage of this product signifies your acceptance of the Terms of Use.