Global Placement Wire Length Minimization via Game Theory
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Solution Overview
Problem
The initial global placement in integrated circuits is a mathematically challenging problem that requires minimizing wire length while ensuring maximum population density constraints are met, which existing technologies struggle to address effectively.
Innovation Solution
The method employs a single player game theory approach to determine wire length minimization based on maximum population density constraints, using transformations such as partial contraction and spreading, and an evolutionary tree search to optimize placement.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Manufacturing precision
If traditional global placement methods are used, then the placement process is simpler, but wire length is not minimized effectively and population density constraints are not met
Solution Approach 1:
The placement algorithm is divided into multiple iterations of contraction and spreading phases. Each phase performs a specific function (contraction reduces wire length, spreading satisfies density constraints), allowing the complex optimization problem to be solved through repeated simpler operations that progressively improve placement quality
Solution Approach 2:
The algorithm performs preliminary contraction operations to reduce wire length before spreading to satisfy density constraints. This preliminary action of minimizing wire length first, then adjusting for density, creates a more efficient optimization sequence that achieves both objectives
2Manufacturing precision
If wire length minimization is prioritized, then connection efficiency improves, but population density constraints may be violated
Solution Approach 1:
The algorithm alternates periodically between contraction operations (which minimize wire length) and spreading operations (which satisfy density constraints). This periodic alternation ensures that neither objective is permanently compromised - wire length is continuously reduced while density constraints are continuously satisfied through the alternating phases
Solution Approach 2:
The algorithm uses feedback from density constraint violations to adjust the spreading phase. When contraction operations reduce wire length but violate density constraints, the spreading phase responds by redistributing cells to satisfy constraints while minimizing wire length degradation, creating a feedback loop that balances both objectives
Data Source
AI summary
Embodiments are provided for enhanced initial global placement in a circuit design in a computing system by a processor. A wire length minimization may be determined based on maximum population density constraints as a single player game theory for global placement of an integrated circuit.