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Update GraphGridLayout Documentation (#3325)

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@ -14,96 +14,97 @@
Basic familiarity with graph algorithms is recommended. Basic familiarity with graph algorithms is recommended.
# Terms used: # Terms used:
- **Vertex**, **node**, **block** - read description of graph for definition. Within this text - **Vertex**, **node**, **block** - see the definition of graph. Within this text
vertex and node are used interchangeably with block due to code being written for visualizing basic vertex/node/block are used interchangeably due to the code being purposed for visualizing basic
block control flow graph. block control flow graph.
- **edge** - read description of graph for definition for precise definition. - **edge** - see the definition of graph.
- **DAG** - directed acyclic graph, graph using directed edges which doesn't have cycles. DAG may - **DAG** - directed acyclic graph, a graph using directed edges which doesn't have cycles. A DAG
contain loops if following them would require going in both directions of edges. Example 1->2 1->3 may contain loops if following them would require going in both directions of edges. Example 1->2
3->2 is a DAG, 2->1 1->3 3->2 isn't a DAG. 1->3 3->2 is a DAG, 2->1 1->3 3->2 isn't a DAG.
- **DFS** - depth first search, a graph traversal algorithm - **DFS** - depth first search, a graph traversal algorithm
- **toposort** - topological sorting, process of ordering a DAG vertices that all edges go from - **toposort** - topological sorting, the process of ordering a DAG vertices that results in all
vertices earlier in the toposort order to vertices later in toposort order. There are multiple edges going from vertices earlier in the toposort order to vertices later in toposort order. There
algorithms for implementing toposort operation. Single DAG can have multiple valid topological are multiple algorithms implementing toposort. A single DAG can have multiple valid topological
orderings, a toposort algorithm can be designed to prioritize a specific one from all valid toposort orderings, a toposort algorithm can be designed to prioritize a specific one from all valid toposort
orders. Example: for graph 1->4, 2->1, 2->3, 3->4 valid topological orders are [2,1,3,4] and orders. Example: for graph 1->4, 2->1, 2->3, 3->4 valid topological orders are [2,1,3,4] and
[2,3,1,4]. [2,3,1,4].
# High level structure of the algorithm # High level algorithm structure
1. select subset of edges that form a DAG (remove cycles) 1. Select a subset of edges that form a DAG (remove cycles)
2. toposort the DAG 2. Toposort the DAG
3. choose a subset of edges that form a tree and assign layers 3. Choose a subset of edges that form a tree and assign layers
4. assign node positions within grid using tree structure, child subtrees are placed side by side 4. Assign node positions within grid using tree structure, child subtrees are placed side by side
with parent on top with parent on top
5. perform edge routing 5. Perform edge routing
6. calculate column and row pixel positions based on node sizes and amount edges between the rows 6. Calculate column and row pixel positions based on node sizes and amount edges between the rows
7. [optional] layout compacting 7. [optional] Layout compacting
Contrary to many other layered graph drawing algorithm this implementation doesn't perform node Contrary to many other layered graph-drawing algorithms this implementation doesn't perform node
reordering to minimize edge crossing. This simplifies implementation, and preserves original control reordering to minimize edge crossing. This simplifies the implementation, and preserves the original
flow structure for conditional jumps ( true jump on one side, false jump on other). Due to most of control-flow structure for conditional jumps ( true jump on one side, false jump on other). Due to
control flow being result of structured programming constructs like if/then/else and loops, most of the control flow resulting from structured programming constructs like if/then/else and
resulting layout is usually readable without node reordering within layers. loops, the resulting layout is usually readable without node reordering within layers.
# Description of grid. # Grid
To simplify the layout algorithm initial steps assume that all nodes have the same size and edges To simplify the layout algorithm, its initial steps assume that all nodes have the same size and
are zero width. After placing the nodes and routing the edges it is known which nodes are in in that edges are zero-width. After nodes placement and edges rounting, the row/column of nodes is
which row and column, how many edges are between each pair of rows. Using this information positions known as well as the amount of edges between each pair of rows. Using this information, positions
are converted from the grid cells to pixel coordinates. Routing 0 width edges between rows can also are converted from grid cells to pixel coordinates. Routing zero-width edges between rows can also
be interpreted as every second row and column being reserved for edges. The row numbers in code are be interpreted as every second row and column being reserved for edges. The row numbers in code are
using first interpretation. To allow better centering of nodes one above other each node is 2 using the first interpretation. To allow better centering of nodes one above other, each node is 2
columns wide and 1 row high. columns wide and 1 row high.
\image html graph_grid.svg \image html graph_grid.svg
# 1-2 Cycle removal and toposort # 1-2 Cycle removal and toposort
Cycle removal and toposort are done at the same time during single DFS traversal. In case entrypoint Cycle removal and toposort are done in a single DFS traversal. In case the entrypoint
is part of a loop DFS started from entrypoint. This ensures that entrypoint is at the top of is part of a loop, the DFS starts from the entrypoint. This ensures that the entrypoint is at the
resulting layout if possible. Resulting toposort order is used in many of the following layout steps top of resulting layout, if possible. The resulting toposort order is used in many of the following
that require calculating some property of a vertex based on child property or the other way around. layout steps that require calculating some property of a vertex based on a child property or the
Using toposort order such operations can be implemented iteration through array in either forward or other way around. Using toposort order, such operations can be implemented by array iteration in
reverse direction. To prevent running out of stack memory when processing large graphs DFS is either forward/backward direction. To prevent running out of stack memory when processing large
implemented non-recursively. graphs, DFS is implemented non-recursively.
# Row assignment # Row assignment
Rows are assigned in toposort order from top to bottom, with nodes row being max(predecessor.row)+1. Rows are assigned in toposort order from top to bottom, with nodes row being max(predecessor.row)+1.
This ensures that loop edges are only ones going from deeper levels to previous layers. This ensures that loop back-edges are the only edges going from lower to higher layers.
To further simply node placement a subset of edges is selected which forms a tree. This turns DAG To further simply node placement, a subset of edges is selected which forms a tree. This turns a DAG
drawing problem into a tree drawing problem. For each node in level n following nodes which have drawing problem into a tree drawing problem. For each node in level n the following nodes with
level exactly n+1 are greedily assigned as child nodes in tree. If a node already has parent level exactly n+1 are greedily assigned as child nodes in the tree. If a node already has a parent
assigned then corresponding edge is not part of tree. assigned then the corresponding edge is not part of the tree.
# Node position assignment # Node placement
Since the graph has been reduced to a tree, node placement is more or less putting subtrees side by Since the graph has been reduced to a tree, node placement is more or less putting subtrees side by
side with parent on top. There is some room for interpretation what exactly side by side means and side with parent on top. There is some room for interpretation as to what exactly 'side by side'
where exactly on top is. Drawing the graph either too dense or too big may make it less readable so means and where exactly 'on top' is: drawing the graph either too dense or too sparse may make it
there are configuration options which allow choosing these things resulting in more or less dense less readable, so there are configuration options which allow choosing these things resulting in
layout. more or less dense layout.
Once the subtrees are placed side by side. Parent node can be placed either in the middle of Once the subtrees are placed side by side, the parent node can be placed either in the middle of
horizontal bounds or in the middle of direct children. First option results in narrower layout and the horizontal bounds or in the middle of its direct children. The first option results in narrower
more vertical columns. Second option results in nodes being more spread out which may help seeing layout and more vertical columns, while the second option results in more spread out layout which
where each edge goes. may help seeing where each edge goes.
In more compact mode two subtrees are placed side by side taking into account their shape. In wider In compact mode two subtrees are placed side by side accounting for their shape. In wider
mode bounding box of shorter subtree is used instead of exact shape. This gives slightly sparse mode the bounding box of the shorter subtree is used instead of its exact shape. This gives slightly
layout without it being too wide. sparser layout without being too wide.
\image html graph_parent_placement.svg \image html graph_parent_placement.svg
# Edge routing # Edge routing
Edge routing can be split into: main column selection, rough routing, segment offset calculation. Edge routing can be split into: main column selection, rough routing, and segment offset
calculation.
Transition from source to target row is done using single vertical segment. This is called main Transition from source to target row is done using a single vertical segment. This segment is called
column. the 'main column'.
A sweep line is used for computing main columns: Blocks and edges are processed as events top to Main columns are computed using a sweep line: blocks and edges are processed as events top to
bottom based off their row (max(start row, end row) for edges). Blocked columns are tracked in a bottom based off their row (max(start row, end row) for edges). Blocked columns are tracked in a
tree structure which allows searching nearest column with at least last N rows empty. The column tree structure which allows searching nearest column with at least last N rows empty. The column
of the starting block is favored for the main column, otherwise the target block's column is chosen of the starting block is favored for the main column, otherwise the target block's column is chosen
@ -114,10 +115,9 @@ true or false branch. In case of upward edges it is allowed to choose a column o
is slightly further than nearest empty to reduce the chance of producing tilted figure 8 shaped is slightly further than nearest empty to reduce the chance of producing tilted figure 8 shaped
crossing between two blocks. crossing between two blocks.
Rough routing creates the path of edge using up to 5 segments using grid coordinates. Due to nodes being placed in a grid, horizontal segments of edges can't intersect with any nodes.
Due to nodes being placed in a grid. Horizontal segments of edges can't intersect with any nodes.
The path for edges is chosen so that it consists of at most 5 segments, typically resulting in The path for edges is chosen so that it consists of at most 5 segments, typically resulting in
sideways U shape or square Z shape. sideways U shape or square Z shape:
- short vertical segment from node to horizontal line - short vertical segment from node to horizontal line
- move to empty column - move to empty column
- vertical segment between starting row and end row - vertical segment between starting row and end row
@ -134,45 +134,49 @@ ensures that two segments don't overlap. Segment offsets within each column are
with some heuristics for assignment order to reduce amount of edge crossings and result in more with some heuristics for assignment order to reduce amount of edge crossings and result in more
visually pleasing output for a typical CFG graph. Each segment gets assigned an offset that is visually pleasing output for a typical CFG graph. Each segment gets assigned an offset that is
maximum of previously assigned offsets overlapping with current segment + segment spacing. maximum of previously assigned offsets overlapping with current segment + segment spacing.
Assignment order is chosen based on:
* direction of previous and last segment - helps reducing crossings and place the segments between Assignment order is based on:
- direction of previous and last segment - helps reducing crossings and place the segments between
nodes nodes
* segment length - reduces crossing when segment endpoints have the same structure as valid - segment length - reduces crossing when segment endpoints have the same structure as valid
parentheses expression parentheses expression
* edge length - establishes some kind of order when single node is connected to many edges, - edge length - establishes some kind of order when single node is connected to many edges,
typically a block with switch statement or block after switch statement. typically a block with switch statement or block after switch statement.
# Layout compacting # Layout compacting
Doing the layout within a grid causes minimal spacing to be limited by widest and tallest block Doing the layout on a grid limits the minimal spacing to the widest block within a column and
within each column and row. One common case is block with function entrypoint being wider due to tallest block within a row. One common case is a function-entry block being wider due to the
function name causing wide horizontal space between branching blocks. Another case is rows in two function name, causing wide horizontal space between branching blocks. Another case is rows in two
parallel columns being aligned. parallel columns being aligned.
\image html layout_compacting.svg \image html layout_compacting.svg
Both problems are mitigated by squishing graph. Compressing in each of the two direction is done Both problems are mitigated by squishing the graph. Compressing in each of the two direction is done
separately. The process is defined as liner program. Each variable represents a position of edge separately. The process is defined as liner program. Each variable represents a position of edge
segment or node in the direction being optimized. segment or node in the direction being optimized.
Following constraints are used The following constraints are used:
- Keep the order with nearest segments. - Keep the order with nearest segments.
- If the node has two outgoing edges, one to the node on left side and other to the right, keep them - If a node has two outgoing edges, one to the left and one to the right, keep them
on the corresponding side of node's center. on the corresponding side of the node's center.
- For all edges keep the node which is above above. This helps when vertical block spacing is set
bigger than double edge spacing and edge shadows relationship between two blocks.
- Equality constraint to keep relative position between nodes and and segments directly connected to - Equality constraint to keep relative position between nodes and and segments directly connected to
them. them.
- Equality constraint to keep the node centered when control flow merges - For all blocks connected by forward edge, keep the vertical distance at least as big as configured
In the vertical direction objective function minimizes y positions of nodes and lengths of vertical block vertical spacing. This helps when vertical block-spacing is set bigger than double edge
segments. In the horizontal direction objective function minimizes lengths of horizontal segments. spacing and an edge shadows relationship between two blocks.
- Equality constraint to keep a node centered when control flow merges.
In the resulting linear program all constraints beside x_i >= 0 consist of exactly two variables: In the vertical direction the objective function minimizes y positions of nodes and lengths of
vertical segments. In the horizontal direction the objective function minimizes the lengths of
horizontal segments.
In the resulting linear program all constraints besides x_i >= 0 consist of exactly two variables:
either x_i - x_j <= c_k or x_i = x_j + c_k. either x_i - x_j <= c_k or x_i = x_j + c_k.
Since it isn't necessary get perfect solution and to avoid worst case performance current Since a perfect solution isn't necessary and to avoid worst case performance, the current
implementation isn't using a general purpose linear programming solver. Each variable is changed implementation isn't using a general purpose linear solver. Instead, each variable is modified
until constraint is reached and afterwards variables are grouped and changed together. until a constraint is satisfied and afterwards variables are grouped and modified together.
*/ */