This Article 
   
 Share 
   
 Bibliographic References 
   
 Add to: 
 
Digg
Furl
Spurl
Blink
Simpy
Google
Del.icio.us
Y!MyWeb
 
 Search 
   
A Decomposition Approach for Balancing Large-Scale Acyclic Data Flow Graphs
January 1990 (vol. 39 no. 1)
pp. 34-46

An efficient decomposition technique that provides a more systematic approach in solving the optimal buffer assignment problem of an acyclic data-flow graph (ADFG) with a large number of computational nodes is presented. The buffer assignment problem is formulated as an integer linear optimization problem that can be solved in pseudopolynomial time. However, if the size of an ADFG increases, then integer linear constraint equations may grow exponentially, making the optimization problem more intractable. The decomposition approach utilizes the critical path concept to decompose a directed ADFG into a set of connected subgraphs, and the integer linear optimization technique can be used to solve the buffer assignment problem in each subgraph. Thus, a large-scale integer linear optimization problem is divided into a number of smaller-scale subproblems, each of which can be easily solved in pseudopolynomial time. Examples are given to illustrate the proposed decomposition technique.

[1] H. M. Ahmed, J. M. Delosme, and M. Morf, "Highly concurrent computing structures for matrix arithmetic and signal processing,"IEEE Comput. Mag., vol. 15, no. 1, pp. 65-82, Jan. 1982.
[2] A. V. Aho, J. E. Hopcroft, and J. D. Ullman,The Design and Analysis of Computer Algorithms. Reading, MA: Addison-Wesley, 1974, pp. 195-199.
[3] S. Baase,Computer Algorithms: Introduction to Design and Analysis. Reading, MA: Addison-Wesley, 1978, pp. 145-148.
[4] J. D. Brock and L. B. Montz, "Translation and optimization of data flow programs," inProc. 1979 Int. Conf. Parallel Processing, Aug. 1979, pp. 46-54.
[5] J. B. Dennis and R. G. Gao, "Maximum pipelining of array operations on static data flow machine," inProc. 1983 Int. Conf. Parallel Processing, Aug. 1983, pp. 331-334.
[6] K. S. Fu, Ed.,VLSI for Pattern Recognition and Image Processing. New York: Springer-Verlag, 1984.
[7] G. L. Haviland and A. A. Tuszynski, "A CORDIC arithmetic processor chip,"IEEE Trans. Comput., vol. C-29, no. 2, pp. 68-79, Feb. 1980.
[8] F. H. Hsu, H. T. Kung, T. Nishizawa, and A. Sussman, "LINC: The link and interconnection chip," Dep. Comput. Sci., Carnegie-Mellon Univ., 1984.
[9] K. Hwang and Z. Xu, "Multipipeline networking for fast evaluation of vector compound functions," inProc. 1986 Int. Conf. Parallel Processing, Aug. 1986, pp. 495-502.
[10] H. T. Kung, "Why systolic architectures?,"IEEE Comput. Mag., pp. 37-46, Jan. 1982.
[11] H. T. Kung and M. Lam, "Wafer-scale integration and two-level pipelined implementation of systolic arrays,"J. Parallel Distrib. Comput., vol. 1, no. 1, pp. 32-63, Sept. 1984.
[12] S. Kung, H. Whitehouse, and T. Kailath,VLSI and Modern Signal Processing, Prentice Hall, Englewood Cliffs, N.J., 1985.
[13] E. L. Lawler,Combinatorial Optimization: Networks and Matroids. New York: Holt, Rinehart and Winston, 1976.
[14] C. S. G. Lee and P. R. Chang, "Efficient parallel algorithm for inverse dynamics computation,"IEEE Trans. Syst., Man, Cybern., vol. SMC-16, no. 4, pp. 532-542, July/Aug. 1986.
[15] C. S. G. Lee and P. R. Chang, "A maximum pipelined CORDIC architecture for robot inverse kinematic position computation,"IEEE J. Robot. Automat., vol. RA-3, no. 5, pp. 445-458, Oct. 1987.
[16] C. E. Leiserson and J. B. Saxe, "Optimizing synchronous systems,"J. VLSI Comput. Syst., vol. 1, pp. 41-68, 1983.
[17] C. Mead and L. Conway,Introduction to VLSI Systems. Reading, MA: Addison-Wesley, 1980, pp. 150-152.
[18] C. H. Papadimitriou, "On the complexity of integer programming,"J. Assoc. Comput. Mach., vol. 28, pp. 675-768, 1981.
[19] J. A. Starzyk and A. Konczykowska, "Flowgraph analysis of large electronic networks,"IEEE Trans. Circuits Syst., vol. CAS-33, pp. 302-315, Mar. 1986.
[20] J. E. Volder, "The CORDIC trigonometric computing technique,"IRE Trans. Electron. Comput., vol. EC-8, no. 3, pp. 330-334, Sept. 1959.

Index Terms:
decomposition approach; balancing large-scale acyclic data flow graphs; optimal buffer assignment problem; integer linear optimization problem; pseudopolynomial time; integer linear constraint equations; optimisation; parallel processing.
Citation:
P.R. Chang, C.S.G. Lee, "A Decomposition Approach for Balancing Large-Scale Acyclic Data Flow Graphs," IEEE Transactions on Computers, vol. 39, no. 1, pp. 34-46, Jan. 1990, doi:10.1109/12.46279
Usage of this product signifies your acceptance of the Terms of Use.