Update README.md

CodeElements/Clustering/README.md

@@ -42,27 +42,30 @@ Finally, the Methods section of the [Nature paper](https://www.nature.com/articl
 
 * **"Synthesis of the input netlist.** We use a commercial tool to synthesize the netlist from RTL. Synthesis is physical-aware, in the sense that it has access to the floorplan size and the locations of the input/output pins, which were informed by inter- and intra-block-level information."
 
-All hypergraph partitioning applications in physical design (of which we are aware) perform some kind of thresholding to ignore large hyperedges.
-Circuit Training ignore all hyperedges of size greater than or equal to 500.
 
 
 ## **II. What *exactly* is the Hypergraph, and how is it partitioned?**
 From the above information sources, the description of the [Grouping](https://github.com/TILOS-AI-Institute/MacroPlacement/blob/main/CodeElements/Grouping/README.md) process, and information provided by Google engineers, we are fairly certain of the following.
 * (1) Clustering uses the hMETIS partitioner, which is run in “multiway” mode. 
-More specifically, hMETIS is **always** invoked with *nparts*=500, with unit vertex weights. 
+More specifically, hMETIS is **always** invoked with *npart* more than 500, with unit vertex weights. 
 The hyperparameters given in Extended Data Table 3 of the [Nature paper](https://www.nature.com/articles/s41586-021-03544-w.epdf?sharing_token=tYaxh2mR5EozfsSL0WHZLdRgN0jAjWel9jnR3ZoTv0PW0K0NmVrRsFPaMa9Y5We9O4Hqf_liatg-lvhiVcYpHL_YQpqkurA31sxqtmA-E1yNUWVMMVSBxWSp7ZFFIWawYQYnEXoBE4esRDSWqubhDFWUPyI5wK_5B_YIO-D_kS8%3D) are used. 
 (Additionally, Circuit Training explicitly sets reconst=1 and dbglvl=0.)
 
-* (2) The hypergraph that is fed to hMETIS consists **only** of standard cells and “fixed” 
-(i.e., specified as monolithic clusters of vertices, using the .fix input file mechanism of hMETIS) groups of standard cells.
+* (2) The hypergraph that is fed to hMETIS consists of macros, macro pins, IO ports and standard cells.
+The "fixed" file generated by [Grouping](https://github.com/TILOS-AI-Institute/MacroPlacement/blob/main/CodeElements/Grouping/README.md) process, is also fed as  .fix input file to hMETIS.
+
+
+* (3) All hypergraph partitioning applications in physical design (of which we are aware) perform some kind of thresholding to ignore large hyperedges.
+Circuit Training ignores all hyperedges of size greater than 500.
+
 
 
 Before going further, we provide a **concrete example** for (2).
 
-* Suppose that we have a design with 200,000 standard cells, 100 macros, and 1,000 ports. 
+* Suppose that we have a design with 200,000 standard cells, 100 macros, and 1,000 IO ports. 
 
 * Furthermore, using terms defined in [Grouping](https://github.com/TILOS-AI-Institute/MacroPlacement/blob/main/CodeElements/Grouping/README.md), suppose 
-that each of the 100 macros induces a *cluster* of 300 standard cells, and that the ports collectively induce 20 *IO clusters*, 
+that each of the 100 macros induces a *cluster* of 300 standard cells, and that the IO ports collectively induce 20 *IO clusters*, 
 each of which induces a cluster of 50 standard cells.
 
 * Then, there will be 100 + 20 = 120 clusters. Each element (macro pin, IO port or standard cell)
@@ -71,9 +74,14 @@ in these clusters corresponds to an entry of the .fix file. The cluster id start
 * The number of individual standard cells in the hypergraph that is actually partitioned by hMETIS is 200,000 - (100 * 300) - (20 * 50) = 169,000.
 
 * Suppose that each macro has 64 macro pins. The hypergraph that is actually partitioned by hMETIS has
-200,000 + 100 + 1000 + 100 * 64 = 207, 500 vertice.  Although there are both macro pins and macros in the hypergraph, all the nets related to macros are connected to macro pins and there is no hyperedges related to macros.
-And the hyperedges in the hypergraph cooresponds to the nets in the netlist.  Note that Circuit Training assumes that there is only one output pin for each standard cell, thus there is only one hyperedge {**A**, **B**, **C**, **D**, **E**} for the following case.  
+200,000 + 100 + 1000 + 100 * 64 = 207, 500 vertices.  Although there are both macro pins and macros in the hypergraph, all the nets related to macros are connected to macro pins and there is no hyperedges related to macros. Each hyperedge in the hypergraph cooresponds to a net in the netlist. Note that Circuit Training assumes that there is only one output pin for each standard cell, thus there is only one hyperedge {**A**, **B**, **C**, **D**, **E**} for the following case.  
+<p align="center">
 <img src="./net_model.png" width= "600"/>
+</p>
+<p align="center">
+ Figure 1.  Illustration of net model in Circuit Training.  
+</p>
+                                     
 
 * *nparts* = 500 + 120 = 620 is used when applying hMETIS to this hypergraph.