Samit Chaudhuri

Introduction to the scheduling problem

Scheduling-a central task in high-level synthesis-involves determining the execution order of operations in a behavioral description. After introducing the scheduling problem, this paper describes four scheduling algorithms commonly used to solve it. >

A solution methodology for exact design space exploration in a three-dimensional design space

This paper describes an exact solution methodology, implemented in Rensselaers Voyager design space exploration system, for solving the scheduling problem in a three-dimensional (3-D) design space: the usual two-dimensional (2-D) design space (which trades off area and schedule length), plus a third dimension representing clock length. Unlike design space exploration methodologies which rely on bounds or estimates, this methodology is guaranteed to find the globally optimal solution to a 3-D scheduling problem. Furthermore, this methodology efficiently prunes the search space, eliminating provably inferior design points through the following: 1) a careful selection of candidate clock lengths and 2) tight bounds on the number of functional units or on the schedule length. Both chaining and multicycle operations are supported.

Computing lower bounds on functional units before scheduling

The authors present a new polynomial-time algorithm for computing lower bounds on the number of functional units (FUs) of each type required to schedule a data flow graph in a specified number of control steps. A formal approach is presented that is guaranteed to find the tightest possible bounds that can be found by relaxing either the precedence constraints or integrality constraints on the scheduling problem. This tight, yet fairly efficient, bounding method can be used to estimate FU area, to generate resource constraints for reducing the search space, or in conjunction with exact techniques for efficient optimal design space exploration.

An efficient linear time algorithm for scan chain optimization and repartitioning

Proposes a linear-time algorithm for post-placement scan chain optimization that works efficiently on large designs and that allows user-specified tradeoffs between runtime and solution quality. This algorithm is also efficiently applied on scan chain partitioning. Presents repartitioning algorithm that takes advantage of the linear-time scan chain optimization algorithm presented in the first part. The idea is simply to connect all the scan flipflops of all the scan chains together in a new chain. Then the algorithm optimizes this new chain and splits it in individual chains of the size of the initial chains. Later it assigns individual chains to their closest scan primary input/output pair.

An exact methodology for scheduling in a 3D design space

Abstract: This paper describes an exact solution methodology, implemented in Rensselaers Voyager design space exploration system, for solving the scheduling problem in a 3-dimensional (3D) design space: the usual 2D design space (which trades off area and schedule length), plus a third dimension representing clock length. Unlike design space exploration methodologies which rely on bounds or estimates, this methodology is guaranteed to find the globally optimal solution to the 3D scheduling problem. Furthermore, this methodology efficiently prunes the search space, eliminating provably inferior design points through: a careful selection of candidate clock lengths; and tight bounds on the number of functional units of each type or on the schedule length.

ILP-based scheduling with time and resource constraints in high level synthesis

Presents a formal analysis of the constraints of the scheduling problem, and evaluates the structure of the scheduling polytope described by those constraints. Polyhedral theory and duality theory are used to demonstrate that efficient solutions of the scheduling problem can be expected from a carefully formulated integer linear program (ILP). Furthermore, the authors present an algorithm to lower bound the resource requirement of the time-constrained scheduling problem that enables them to solve the ILP more efficiently.<<ETX>>

The structure of assignment, precedence, and resource constraints in the ILP approach to the scheduling problem

Presents a general treatment of the combinatorial approach to the scheduling problem, enhancing previous formulations in the literature. The focus of this paper is a formal analysis of the integer linear programming (ILP) approach, which we use to evaluate the structure of our formulation. Polyhedral theory and duality theory are used to demonstrate that efficient solutions of the scheduling problem can be expected from a carefully formulated integer linear program. Furthermore, we use the theory of valid inequalities to tighten the constraints and make the formulation more efficient.<<ETX>>

Bounding algorithms for design space exploration

This paper describes several new algorithms for computing lower bounds on the length of the schedule and the number of functional units in high-level synthesis.