A graph-theoretic sufficient condition for FPGA/FPIC switch-module routability

Switch modules are the most important component of the routing resources in FPGAs/FPICs. We consider in this paper an FPGA/FPIC switch-module analyse's problem: The inputs consist of a switch-module description and the number of nets required to be routed through the switch module; the question is to determine if there exists a feasible routing for the routing requirements on the switch module. This problem is applicable to the routability evaluation of FPGA/FPIC switch modules, the switch-module design for FPGAs/FPICs, and FPGA/FPIC routing. We present a graph-theoretic sufficient condition for the analyse's problem. The implications of the condition are: (1) there exist several classes of efficient approximation algorithms for the analysis problem; (2) there exist several classes of switch-module architectures on which the analysis problem can be solved efficiently.