A Modular Systolic Linearizat of the Wars ha1 I- Floyd Algorithm

In this paper, we use a variant of the geometric method to derive efficient modular linear systolic algorithms for the transitive cIosurI? and shortest path problems. Furthermore, we show that partially-pipelined modular linear systolic algorithms with an output operation, for matrix multiplication, can be as fast as the fully-pipelined existing ones and, moreover, they need less cells.

[1]  Jean Frédéric Myoupo,et al.  Designing Modular Linear Systolic Arrays Using Dependance Graph Regular Partitions , 1992, CONPAR.

[2]  Viktor K. Prasanna,et al.  On Mapping Algorithms to Linear and Fault-Tolerant Systolic Arrays , 1989, IEEE Trans. Computers.

[3]  Henry S. Warren,et al.  A modification of Warshall's algorithm for the transitive closure of binary relations , 1975, Commun. ACM.

[4]  Tanguy Risset Linear systolic arrays for matrix multiplication: comparisons of existing synthesis methods and new results , 1991, Algorithms and Parallel VLSI Architectures.

[5]  H. T. Kung,et al.  Synchronizing Large VLSI Processor Arrays , 1985, IEEE Trans. Computers.

[6]  Viktor K. Prasanna,et al.  Designing Linear Systolic Arrays , 1989, J. Parallel Distributed Comput..

[7]  Jan L. A. van de Snepscheut A Derivation of a Distributed Implementation of Warshall's Algorithm , 1986, Sci. Comput. Program..

[8]  H. T. Kung,et al.  Direct VLSI Implementation of Combinatorial Algorithms , 1979 .

[9]  PEIZONG LEE,et al.  Synthesizing Linear Array Algorithms from Nested For Loop Algorithms , 2015, IEEE Trans. Computers.

[10]  H. T. Kung,et al.  Synchronizing Large VLSI Processor Arrays , 1983, IEEE Transactions on Computers.

[11]  I. V. Ramakrishnan,et al.  Dynamic Programming and Transitive Closure on Linear Pipelines. , 1984 .

[12]  H. T. Kung Why systolic architectures? , 1982, Computer.

[13]  I. V. Ramakrishnan,et al.  Synthesis of an Optimal Family of Matrix Multiplication Algorithms on Linear Arrays , 1986, IEEE Transactions on Computers.

[14]  Stephen Warshall,et al.  A Theorem on Boolean Matrices , 1962, JACM.

[15]  W. Shang,et al.  On Time Mapping of Uniform Dependence Algorithms into Lower Dimensional Processor Arrays , 1992, IEEE Trans. Parallel Distributed Syst..