Orbital Systolic Algorithms and Array Processors for Solution of the Algebraic Path Problem

• Published in: IEICE Transactions on Information and Systems Vol. E93.D; no. 3; pp. 534 - 541
• Main Authors: MIYAZAKI, Toshiaki, KURODA, Kenichi, SEDUKHIN, Stanislav G.
• Format: Journal Article
• Language: English
• Published: Oxford The Institute of Electronics, Information and Communication Engineers 2010; Oxford University Press
• Subjects: algebraic path problem; Applied sciences; array processors; data manipulation; Design. Technologies. Operation analysis. Testing; Electronics; Exact sciences and technology; Integrated circuits; Integrated circuits by function (including memories and processors); orbital systolic algorithms; Semiconductor electronics. Microelectronics. Optoelectronics. Solid state devices; orbital systolic algorithms; Array processor; data manipulation; Step method; Scheduling; Systolic network; Algorithm; Implementation; Pipeline processing; Three dimensional model; array processors; Posterior probability; algebraic path problem; Integrated circuit; Massive parallelism
• ISSN: 0916-8532; 1745-1361; 1745-1361
• DOI: 10.1587/transinf.E93.D.534

The algebraic path problem (APP) is a general framework which unifies several solution procedures for a number of well-known matrix and graph problems. In this paper, we present a new 3-dimensional (3-D) orbital algebraic path algorithm and corresponding 2-D toroidal array processors which solve the n × n APP in the theoretically minimal number of 3n time-steps. The coordinated time-space scheduling of the computing and data movement in this 3-D algorithm is based on the modular function which preserves the main technological advantages of systolic processing: simplicity, regularity, locality of communications, pipelining, etc. Our design of the 2-D systolic array processors is based on a classical 3-D→2-D space transformation. We have also shown how a data manipulation (copying and alignment) can be effectively implemented in these array processors in a massively-parallel fashion by using a matrix-matrix multiply-add operation.