Circuit Partitioning Notes
Introduction
This lecture covers circuit partitioning in VLSI design, emphasizing its significance and methods.
Key concepts include motivation for partitioning, problem definition, circuit models, and main algorithms for partitioning.
Motivation for Partitioning
Purpose of Partitioning:
Data management: Reduces the amount of data handled by each designer/tool, leading to improved focus and efficiency.
Parallel implementation: Facilitates simultaneous work on different design parts, improving collaboration and development speeds in large teams.
Algorithm support: Aids other algorithms like placement, ensuring optimized layouts and timing closures.
Disadvantages:
Less optimization potential: Partitions may depend on neighboring partitions, limiting the optimization due to interdependencies.
Assembly stage: Requires an assembly stage post-partitioning, which may add complexity and extra steps in the design process.
Applications:
For FPGA emulation, to distribute large designs across multiple FPGAs, enabling hardware testing while minimizing resource conflicts.
Supports early software development through the shift-left strategy, allowing for software to be tested against hardware in earlier design stages.
Problem Definition
Circuit partitioning translates to a graph partitioning problem. Each component of the circuit is represented by a vertex in a graph, allowing complexity to be managed through effective problem representation.
Graphs allow representation of circuits where each logical unit is a node and edges represent connections, showcasing the relationship between the components.
Key Terms:
Cells: Logical units represented as nodes in a graph, reflecting the physical components of the circuit.
Weights: Associated with edges, representing connectivity strength; higher weights indicate stronger connections, influencing partitioning strategies.
Cut (Cut Set): All edges that cross from one partition to another; minimizing cut sets is critical for maintaining performance and reducing signal delays.
Graph Models for Partitioning
Graph Conversion:
Convert circuit partitioning to a graph partitioning problem, allowing the use of existing algorithms in a more abstract form.
Methods:
Clique Conversion for Multifanout Nets: Convert multi-fanout nets into cliques to align more than two connections through an edge, simplifying the representation of complex interdependencies.
Hypergraph Representation: Each edge connects multiple vertices, ideal for circuit descriptions since they can capture the multi-dimensional relationships in the design.
Partitioning Algorithms
Types of Algorithms:
Kernighan-Lin (KL) Algorithm
Divides a graph into two parts to minimize the cut cost while ensuring equal partition size.
Operates by swapping nodes between partitions to decrease the total weight of the cut set, which emphasizes a balanced approach to both size and connectivity.
Fiduccia-Mattheyses (FM) Algorithm
Optimizes by operating on a hypergraph and moves one cell at a time, maintaining the balance between partitions more effectively than KL.
More efficient than KL, especially with unbalanced sets, as it quickly converges to a near-optimal solution.
Kernighan-Lin Algorithm
Steps:
Start with two partitions of equal sizes.
Generate swaps of node pairs (one from each partition).
Continue until no further improvements can be made, thereby refining the partition.
Key Concept:
The algorithm is deterministic, producing a stable solution repeatably from the same starting point, ensuring reliability and predictability in results.
Fiduccia-Mattheyses Algorithm
Improvements Over KL:
Allows handling of imbalance, accommodating designs where sizes of partitions may differ significantly without sacrificing performance.
Works directly with the hypergraph representation, providing a more detailed analysis of relationships between components.
Maintains linear complexity relative to the circuit size, offering more efficient performance in larger designs, which is crucial in modern VLSI applications.
Additional Definitions
Cut State of a Net: Defines whether all cells connected to a net are in the same block or different blocks, affecting optimization considerations in terms of latency and power consumption.
Critical Net: A net whose state changes if a connected cell is moved across partitions, needing careful evaluation for optimal performance, particularly in timing analysis and layout optimization.
Complexity and Performance
KL Complexity: - indicates the algorithm's efficiency but can become limiting as the circuit grows larger.
FM Complexity: - shows how quickly the algorithm can perform as the number of connections (pins) increases, reflecting its practicality in modern applications.
Strategies to Improve Runs:
Randomly generate initial partitions and run multiple trials to find the best outcome, enhancing the likelihood of achieving an optimal cut set.
Use