A block algorithm for the algebraic path problem and its execution on a systolic array

The solution of the algebraic path problem (APP) for arbitrarily sized graphs by a fixed-size systolic array processor (SAP) is addressed. The APP is decomposed into two subproblems, and SAP is designed for each one. Both SAPs combined produce a highly implementable versatile SAP. The proposed SAP has p×p processing elements (PEs) solving the APP of an N-vertex graph in N³/p²+N²/ p+3p-2 cycles. With slight modifications in the operations performed by the PEs, the problem is optimally solved in N³/p²+3p-2 cycles