A comparative study of two Boolean formulations of FPGA detailed routing constraints
Nam, G.-J.
Aloul, F.
Sakallah, K.A.
Rutenbar, R.A.
IEEE;
This paper appears in: Computers, IEEE Transactions on
Publication Date: June 2004
Volume: 53,
Issue: 6
On page(s): 688- 696
ISSN: 0018-9340
INSPEC Accession Number: 8018740
Digital Object Identifier: 10.1109/TC.2004.1
Current Version Published: 2004-04-19
Abstract
We present empirical analyses of two Boolean satisfiability (SAT) formulations of FPGA (field programmable gate array) detailed routing constraints. Boolean SAT-based routing transforms a routing problem into a Boolean SAT instance by rendering geometric routing constraints as an atomic Boolean function. The generated Boolean function is satisfiable if and only if the corresponding routing is possible. Two different Boolean SAT-based routing models are analyzed: the track-based and the route-based routing constraint model. The track-based routing model transforms a routing task into a net-to-track assignment problem, whereas the route-based routing model reduces it into a routability-checking problem with explicitly enumerated set of detailed routes for nets. In both models, routing constraints are represented as CNF Boolean satisfiability clauses. Through comparative experiments, we demonstrate that the route-based formulation yields an easier-to-evaluate and more scalable routability Boolean function than the track-based method. This is empirical evidence that a smart/efficient Boolean formulation can achieve significant performance improvement in real-world applications.
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