Analyzing and exploiting the structure of the constraints in theILP approach to the scheduling problem
Chaudhuri, S.
Walker, R.A.
Mitchell, J.E.
Dept. of Electr., Comput. & Syst. Eng., Rensselaer Polytech. Inst., Troy, NY;
This paper appears in: Very Large Scale Integration (VLSI) Systems, IEEE Transactions on
Publication Date: Dec 1994
Volume: 2,
Issue: 4
On page(s): 456-471
ISSN: 1063-8210
References Cited: 32
CODEN: IEVSE9
INSPEC Accession Number: 4839251
Digital Object Identifier: 10.1109/92.335014
Current Version Published: 2002-08-06
Abstract
In integer linear programming (ILP), formulating a
“good” model is of crucial importance to solving that model.
In this paper, we begin with a mathematical analysis of the structure of
the assignment, timing, and resource constraints in high-level
synthesis, and then evaluate the structure of the scheduling polytope
described by these constraints. We then show how the structure of the
constraints can be exploited to develop a well-structured ILP
formulation, which can serve as a solid theoretical foundation for
future improvement. As a start in that direction, we also present two
methods to further tighten the formulation. The contribution of this
paper is twofold: 1) it provides the first in-depth formal analysis of
the structure of the constraints, and it shows how to exploit that
structure in a well-designed ILP formulation, and 2) it shows how to
further improve a well-structured formulation by adding new valid
inequalities
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