add grouping explanation

CodeElements/Grouping/README.md

 # **Grouping**
+Grouping is an important preprocessing step of clustering.
 The grouping step in Circuit Training requires as inputs:
-the post-synthesis gate-level netlist (standard cells and hard macros)
-placed IOs (ports, or terminals), typically at the borders of the chip canvas
-the grid of n_rows rows and n_cols columns of gridcells, which defines the gridded layout canvas
-The purpose of grouping, to our understanding, is to ensure that closely-related logic is kept close to hard macros and to clumps of IOs. The clumps of IOs are induced by IO locations with respect to the row and column coordinates in the gridded layout canvas.
- 
+the post-synthesis gate-level netlist (standard cells and hard macros),
+placed IOs (ports, or terminals), typically at the borders of the chip canvas,
+the grid of **n_rows** rows and **n_cols** columns of _gridcells_, which defines the gridded layout canvas.
+The purpose of grouping, to our understanding, is to ensure that closely-related standard-cell logic, 
+which connect to the same macro or the same clump of IO (noted as IO cluster), belong to the same standard-cell clusters.
+
+
+
 ## **The Grouping Process**
-In the Circuit Training approach, a given SRAM’s immediate fanins and immediate fanouts (with respect to all of the SRAM’s pins) comprise a group. One group is created for each SRAM in the design.
+The grouping consists of three steps:
+- Group the macro pins of the same macro into a cluster.
+In Circuit Training, the netlist consists of four building elements: 
+standard cells, IO ports, macro pins and macros.
+The following figure shows an example of netlist representation in Circuit Training.
+The left part is the real netlist; The right part is the Netlist Protocol Buffer 
+representation in Circuit Training. The solid arrow means the real signal net and the dashed
+arrow means the virtual nets between macro A and its macro pins.
+<img src="./macro_example.png" width= "1600"/>
+
+As shown in above figure, the macro pins and the related macro are both basic elements in the netlist, whereas there is no pins of standard cells.  Thus, it's necessary to group the macros pins of the same macro into a cluster, because the macro pins of the same macro will always stay together during macro placement. Note that only the macro pins are grouped and the macro itself is not grouped. For example, in above figure, **D[0]**, **D[1]**, **D[2]**, **Q[0]**,
+**Q[1]**, **Q[2]** are grouped into $cluster\_1$, but $cluster\_1$ does not include macro A.
 
-Then, all of the IOs (ports) that are in each row-grid or column-grid of the boundary of the layout canvas are put into clumps.  There is one clump for each row-grid or column-grid of the boundary that contains at least one IO. A group is then comprised of the union of immediate fanins and immediate fanouts of a given clump. 
 
-Note that “immediate fanins” is equivalent to “transitive fanins up to level K_in = 1”, and that “immediate fanouts” is equivalent to “transitive fanouts up to level K_out = 1”. It is our understanding that both K_in and K_out are always set to a default value of 1 in Circuit Training. However, other values might be applied. 
+- Group the IOs that are within close proximity of each other boundary by boundary, 
+following the order of **LEFT** &#8595 **TOP**  &#8595  **RIGHT** &#8595 **BOTTOM**. 
+For the **LEFT**/**RIGHT**(**TOP**/**Bottom**) boundary, 
+we sort the all the ports on the boundary based on their
+y (x) coordinates in a non-decreasing order. 
+Starting from the first IO port on the boundary, we group
+the IO ports within each $grid\_height$ ($grid\_width$) into an IO cluster. 
+For example, in following figure, 
+we have three IO clusters on **TOP** boundary and two IO clusters on **RIGHT** boundary. 
+<img src="./IO_Groups.png" width= "1600"/>
+The **grid_width** and **grid_height** are calculated based on the **n_cols** and **n_rows**:
+-- **grid_width** = **canvas_width** / **n_cols**
+-- **grid_height** = **canvas_height** / **n_rows**
 
-**Tie-Breaking.** If a given standard-cell instance can belong to two or more groups, we break ties according to the following, ordered criteria:  (1) when in the regime of K_in > 1 or K_out > 1, assign to the group with topologically closer (i.e., fewer levels away) macro or port; else (2) assign to the group induced by a clump containing lexicographically smallest port name; else (3) assign to the group induced by a macro having lexicographically smallest macro name.
 
-## **A Simple “Cartoon”**
-The following cartoon was recently provided by a Google engineer to explain the grouping process. In the cartoon, there are three rows and four columns of gridcells. There are also three clumps of IOs and two hard macros. As a result, in the cartoon we see a total of five groups. To our understanding, a given SRAM hard macro is not part of the group (of standard cells) that it induces.  And, a given clump of (placed, fixed) IO ports is not part of the group (of standard cells) that it induces. 
+- Group the close-related standard cells,
+which connect to the same macro or the same IO cluster.
+Suppose that we have a design with 100 clusters of macro pins (i.e., 100 macros) and 10 clusters of IOs.
+Before we grouping the close-related standard cells to these clusters of macro pins or IOs,
+we assign each cluster with a cluster id from 0 to 119.
+Then for each cluster, we traverse the netlist and assign the same cluster id to the "immediate fanins" and "immediate fanouts" of its element (macro pin or IO).
+Note that "immediate fanin" is equivalent to "transitive fanins up to level K_in = 1", and that "immediate fanouts" is equivalent to "transitive fanouts up to level K_out = 1".
+It is our understanding that both K_in and K_out are always set to a default value of 1 
+in Circuit Training. However, other values might be applied. 
+In our implementation, we traverse the netlist in a depth-first-search manner.
+All the elements (standard cell, macro pin or IO ports) with the same cluster id form a cluster.  Each cluster is recorded in the ".fix file" that is part of the input to the hMETIS hypergraph partitioner when the standard cells are grouped into soft macros. 
+The part id of each cluster is the same as its cluster id.
+Note that a macro does not belong to any cluster, thus is not fixed 
+when we call the hMETIS hypergraph partitioner.
 
-<img src="./Cartoon.png" width= "1600"/>
  
 ## **How Groups Are Used**
 Each group is recorded in the “.fix file” that is part of the input to the hMETIS hypergraph partitioner when the gate-level netlist is clustered into soft macros.
@@ -26,8 +62,7 @@ Each group is recorded in the “.fix file” that is part of the input to the h
 We provide [(an example)](https://github.com/TILOS-AI-Institute/MacroPlacement/blob/main/CodeElements/Grouping/test/test.py) about the usage of our grouping scripts.
 Basically our grouping scripts take follows as inputs: (i) [(setup_file)](https://github.com/TILOS-AI-Institute/MacroPlacement/blob/main/CodeElements/Grouping/test/setup.tcl)
 including enablement information (lefs/libs), synthesized gate-level netlist (*.v),  def file with placed IOs (*.def); (ii) n_rows and n_cols determined by the [(Gridding)](https://github.com/TILOS-AI-Institute/MacroPlacement/tree/main/CodeElements/Gridding) step; (iii) K_in and K_out parameters; (iv) global_net_threshold for ignoring global nets. If a net has more than global_net_threshold instances, we ignore such net when we search "transitive" fanins and fanouts. After
-running grouping scripts,  you will get two files *.fix and *.fix.old.  The ".fix.old" file contains the IOs or macros in the corresponding group while *.fix file only contains standard cells in each group.
-
+running grouping scripts,  you will get the **.fix** file.  
 
 # Thanks
 We thank Google engineers for Q&A in a shared document, as well as live discussions on May 19, 2022, that explained the grouping method used in Circuit Training. All errors of understanding and implementation are the authors'. We will rectify such errors as soon as possible after being made aware of them.