Cell Placement Bipartite Graph Shadow Edge Ranking
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Solution Overview
Problem
Existing cell placement techniques for integrated circuit design are inefficient, difficult to implement, and take a long time to determine a feasible placement that meets capacity constraints, often resulting in uneven distribution of objects across the chip.
Innovation Solution
A method using a bipartite graph representation to rank and select edges for reassigning cell instances to regions, ensuring that the capacity constraints are met by minimizing the total movement cost, which is formulated as a relaxed capacity-constrained min-cost assignment problem.
Engineering Contradictions & Design Principles
Engineering Contradiction Analysis
1Manufacturing precision
If quadratic placement technique is used to minimize total wirelength, then wirelength optimization is improved, but the capacity constraints of regions are violated
Solution Approach 1:
The chip is divided into multiple regions with capacity constraints. The placement problem is segmented into finding optimal assignments of cell instances to regions while respecting regional capacity limits. This segmentation allows the solution to satisfy both wirelength optimization and capacity constraints by treating region assignment as a separate controllable variable.
Solution Approach 2:
The invention uses a dynamic approach where cell instances can be reassigned between regions based on current capacity availability and wirelength considerations. The system dynamically adjusts assignments rather than fixing them statically, allowing adaptation to capacity constraints while maintaining wirelength optimization goals.
2Reliability
If prior art techniques are used to determine feasible cell placement, then capacity constraints are satisfied, but computational efficiency deteriorates
Solution Approach 1:
The system uses shadow edges to automatically guide the selection process. Shadow edges provide self-service by indicating the next best assignment options without requiring complex external control mechanisms. This self-organizing property of the shadow edge system enables efficient computation while maintaining feasibility.
Solution Approach 2:
The invention replaces complex mechanical-style iterative adjustment procedures with a more efficient graph-theoretic approach using shadow edges. Instead of physically simulating or mechanically iterating through possible assignments, the system uses mathematical properties of the bipartite graph with shadow edges to directly determine optimal assignments, significantly improving computational efficiency.
3Reliability
If prior art techniques are used to determine feasible cell placement, then capacity constraints are satisfied, but implementation complexity increases
Solution Approach 1:
Shadow edges serve as intermediaries between cell instances and region assignments. Rather than directly managing complex constraints and interactions between all elements, the shadow edges mediate the assignment process by encoding capacity and cost information in a simplified structure that is easier to implement and maintain.
Solution Approach 2:
The invention changes the parameter representation from direct capacity constraint management to shadow edge cost values. By transforming the problem parameters into shadow edge weights and costs, the system simplifies the implementation while maintaining the ability to satisfy capacity constraints through standard graph algorithms.
4Manufacturing precision
If quadratic placement is used, then wirelength is minimized, but object distribution across chip becomes uneven
Solution Approach 1:
By segmenting the chip into regions with explicit capacity constraints, the invention prevents uneven distribution. Each region's capacity limit ensures that objects are distributed across multiple regions rather than concentrating in optimal wirelength positions, achieving both wirelength minimization and uniform distribution.
Solution Approach 2:
The invention applies local quality control by allowing different regions to have different capacity characteristics. This enables local optimization within each region while maintaining global distribution uniformity, as each region can be optimized independently subject to its own capacity constraints.
Data Source
AI summary
One embodiment of the present invention provides a system that determines a feasible cell placement for an integrated circuit design. During operation, the system receives an input cell placement, which is typically determined using a quadratic placement technique. Next, the system receives a set of regions within the integrated circuit design. Each region has a capacity constraint which specifies an upper limit on the total cell area that can be placed within the region. The system then generates a bi-partite graph which comprises instance vertices, region vertices, and edges. An instance vertex is associated with a cell instance, a region vertex is associated with a region, and each edge is incident on an instance vertex and a region vertex. Each edge is assigned a cost that indicates the cost of placing the associated cell instance in the associated region. Next, the system associates edges with shadow edges. Note that an edge and an associated shadow edge are incident to the same instance vertex. The system then ranks the edges using the costs of the shadow edges. Next, the system selects a set of edges using the edge rankings. Finally, the system determines the feasible cell placement using the set of edges.