**cluster_x, cluster_y = c.GetWeightedCenter()*. Here the weighted center of cluster *c* is the average location of all the standard cells in the cluster, weighted according to their area.
* Use (*cluster_x*, *cluster_y*) as the origin and *threshold* as the step, to divide the bounding box of *c* into different regions.
* The elements (macro pins, macros, ports and standard cells) in each region forms a new cluster.
The following figure shows an example: the left part shows the cluster *c<sub>1</sub>* before break-up process and the blue dot is the weighted center of *c<sub>1</sub>*; the right part shows the clusters after breakup-up process. The "center" cluster still has the cluster id of 1.
* Use (*cluster_x*, *cluster_y*) as the origin and *breakup_threshold* as the step, to divide the bounding box of *c* into different regions.
* The elements (macro pins, macros, ports and standard cells) in each region form a new cluster.
The following figure shows an example: the left part shows the cluster *c<sub>1</sub>* before breakup process and the blue dot is the weighted center of *c<sub>1</sub>*; the right part shows the clusters after breakupup process. The "center" cluster still has the cluster id of 1.
<palign="center">
<imgsrc="./breakup.png"width="1600"/>
</p>
<palign="center">
Figure 2. Illustration of breaking up a cluster.
</p>
Note that the netlist is generated by physical-aware synthesis, we know the (x, y) coordinate for each instance.
## **III. Recursively merge small adjacent clusters**
## **IV. Recursively merge small adjacent clusters**
After breaking up clusters which span large distance, there may be some small clusters with only tens of standard cells.
In this step, Circuit Training recursively merges small clusters to the most adjacent cluster if they are within a certain
distance *closeness* (*breakup_threshold* / 2.0), thus reducing number of clusters. A cluster is claimed as a small cluster
...
...
@@ -111,7 +115,7 @@ if the number of elements (macro pins,
macros, IO ports and standard cells) is less than or equal to *max_num_nodes*, where *max_num_nodes* = *number_of_vertices* // *number_of_clusters_after_breakup* // 4. The merging process is as following:
* flag = True
* While (flag == True):
* Create adjacency matrix *adj_matrix* where *adj_matrix\[i\]\[j\]* represents the number of connections between cluster *c_i* and cluster *c_j*. For example, in the above figure, suppose *A*, *B*, *C*, *D* and *E* respectively belong to cluster *c<sub>1</sub>*, ..., *c<sub>5</sub>*, we have *adj_matrix\[1\]\[2\]* = 1, *adj_matrix\[1\]\[3\]* = 1, ...., *adj_matrix\[5\]\[3\]* = 1 and *adj_matrix\[5\]\[4\]* = 1. We want to emphasize that although there is no hyperedges related to macros in the hypergraph, *adj_matrix* considers the "virtual" connections between macros and macro pins. That is to say, if a macro and its macros pins belong to different clusters, for example, macro A in cluster *c<sub>1</sub>* and its macro pins in cluster *c<sub>2</sub>*, we have *adj_matrix\[1\]\[2\]* = 1 and *adj_matrix\[2\]\[1\]* = 1.
* Create adjacency matrix *adj_matrix* where *adj_matrix\[i\]\[j\]* represents the number of connections between cluster *c<sub>i</sub>* and cluster *c<sub>j</sub>*. For example, in the Figure 1, suppose *A*, *B*, *C*, *D* and *E* respectively belong to cluster *c<sub>1</sub>*, ..., *c<sub>5</sub>*, we have *adj_matrix\[1\]\[2\]* = 1, *adj_matrix\[1\]\[3\]* = 1, ...., *adj_matrix\[5\]\[3\]* = 1 and *adj_matrix\[5\]\[4\]* = 1. We want to emphasize that although there is no hyperedges related to macros in the hypergraph, *adj_matrix* considers the "virtual" connections between macros and macro pins. That is to say, if a macro and its macros pins belong to different clusters, for example, macro A in cluster *c<sub>1</sub>* and its macro pins in cluster *c<sub>2</sub>*, we have *adj_matrix\[1\]\[2\]* = 1 and *adj_matrix\[2\]\[1\]* = 1.
* Calculate the weighted center for each cluster. (see the breakup section for details)
* For each cluster *c*
* If *c* is not a small cluster
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@@ -126,7 +130,7 @@ macros, IO ports and standard cells) is less than or equal to *max_num_nodes*, w
## **V. Pending Clarifications**
We call readers’ attention to the existence of significant aspects that are still pending clarification here.
While [Gridding](https://github.com/TILOS-AI-Institute/MacroPlacement/blob/main/CodeElements/Gridding/README.md) and
[Grouping](https://github.com/TILOS-AI-Institute/MacroPlacement/blob/main/CodeElements/Grouping/README.md) are hopefully well-understood,
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@@ -139,7 +143,7 @@ All methodologies that span synthesis and placement (of which we are aware) must
***[June 13]*****Update to Pending clarification #3:*** We are glad to see [grouping (clustering)](https://github.com/google-research/circuit_training/tree/main/circuit_training/grouping) added to the Circuit Training GitHub. The new scripts refer to (x,y) coordinates of nodes in the netlist, which leads to further pending clarifications (noted [here](https://github.com/google-research/circuit_training/issues/25)). The solution space for how the input to hypergraph clustering is obtained has expanded. A first level of options is whether **(A) a non-physical synthesis tool** (e.g., Genus, DesignCompiler or Yosys), or **(B) a physical synthesis tool** (e.g., Genus iSpatial or DesignCompiler Topological (Yosys cannot perform physical synthesis)), is used to obtain the netlist from starting RTL and constraints. In the regime of (B), to our understanding the commercial physical synthesis tools are invoked with a starting .def that includes macro placement. Thus, we plan to also enable a second level of sub-options for determining this macro placement: **(B.1)** use the auto-macro placement result from the physical synthesis tool, and **(B.2)** use a human PD expert (or, [OpenROAD RTL-MP](https://github.com/The-OpenROAD-Project/OpenROAD/tree/master/src/mpl2)) macro placement.
## **III. Our Implementation of Hypergraph Clustering.**
## **VI. Our Implementation of Hypergraph Clustering.**
Our implementation of hypergraph clustering takes the synthesized netlist and a .def file with placed IO ports as input,
then generates the clustered netlist (in lef/def format) using hMETIS (1998 binary).
In default mode, our implementation will also run RePlAce in GUI mode automatically to place the clustered netlist.
