Crash Course: graph

Table of Contents

• Introduction
• Data structures
  • Adjacency matrix
  • Graphviz dot language
• Flow builder
  • Tasks and resources
  • Fake resources and order of execution
  • Sync points
  • Execution graph

Introduction

EnTT doesn't aim to offer everything one needs to work with graphs. Therefore, anyone looking for this in the graph submodule will be disappointed.
Quite the opposite is true though. This submodule is minimal and contains only the data structures and algorithms strictly necessary for the development of some tools such as the flow builder.

Data structures

As anticipated in the introduction, the aim isn't to offer all possible data structures suitable for representing and working with graphs. Many will likely be added or refined over time. However I want to discourage anyone expecting tight scheduling on the subject.
The data structures presented in this section are mainly useful for the development and support of some tools which are also part of the same submodule.

Adjacency matrix

The adjacency matrix is designed to represent either a directed or an undirected graph:

entt::adjacency_matrix<entt::directed_tag> adjacency_matrix{};

The directed_tag type creates the graph as directed. There is also an undirected_tag counterpart which creates it as undirected.
The interface deviates slightly from the typical double indexing of C and offers an API that is perhaps more familiar to a C++ programmer. Therefore, the access and modification of an element takes place via the contains, insert and erase functions rather than a double call to an operator[]:

if(adjacency_matrix.contains(0u, 1u)) {
    adjacency_matrix.erase(0u, 1u);
} else {
    adjacency_matrix.insert(0u, 1u);
}

Both insert anderase are idempotent functions which have no effect if the element already exists or has already been deleted.
The first one returns an std::pair containing the iterator to the element and a boolean value indicating whether the element was newly inserted or not. The second one returns the number of deleted elements (0 or 1).

An adjacency matrix is initialized with the number of elements (vertices) when constructing it but can also be resized later using the resize function:

entt::adjacency_matrix<entt::directed_tag> adjacency_matrix{3u};

To visit all vertices, the class offers a function named vertices that returns an iterable object suitable for the purpose:

for(auto &&vertex: adjacency_matrix.vertices()) {
    // ...
}

The same result is obtained with the following snippet, since the vertices are plain unsigned integral values:

for(auto last = adjacency_matrix.size(), pos = {}; pos < last; ++pos) {
    // ...
}

As for visiting the edges, a few functions are available.
When the purpose is to visit all the edges of a given adjacency matrix, the edges function returns an iterable object that is used to get them as pairs of vertices:

for(auto [lhs, rhs]: adjacency_matrix.edges()) {
    // ...
}

If the goal is to visit all the in- or out-edges of a given vertex instead, the in_edges and out_edges functions are meant for that:

for(auto [lhs, rhs]: adjacency_matrix.out_edges(3u)) {
    // ...
}

Both the functions expect the vertex to visit (that is, to return the in- or out-edges for) as an argument.
Finally, the adjacency matrix is an allocator-aware container and offers most of the functionalities one would expect from this type of containers, such as clear or 'get_allocator` and so on.

Graphviz dot language

As it's one of the most popular formats, the library offers minimal support for converting a graph to a Graphviz dot snippet.
The simplest way is to pass both an output stream and a graph to the dot function:

std::ostringstream output{};
entt::dot(output, adjacency_matrix);

It's also possible to provide a callback to which the vertices are passed and which can be used to add (dot) properties to the output as needed:

std::ostringstream output{};
 
entt::dot(output, adjacency_matrix, [](auto &output, auto vertex) {
    out << "label=\"v\"" << vertex << ",shape=\"box\"";
});

This second mode is particularly convenient when the user wants to associate externally managed data to the graph being converted.

Flow builder

A flow builder is used to create execution graphs from tasks and resources.
The implementation is as generic as possible and doesn't bind to any other part of the library.

This class is designed as a sort of state machine to which a specific task is attached for which the resources accessed in read-only or read-write mode are specified.
Most of the functions in the API also return the flow builder itself, according to what is the common sense API when it comes to builder classes.

Once all tasks are registered and resources assigned to them, an execution graph in the form of an adjacency matrix is returned to the user.
This graph contains all the tasks assigned to the flow builder in the form of vertices. The vertex itself is used as an index to get the identifier passed during registration.

Tasks and resources

Although these terms are used extensively in the documentation, the flow builder has no real concept of tasks and resources.
This class works mainly with identifiers, that is, values of type id_type. In other terms, both tasks and resources are identified by integral values.
This allows not to couple the class itself to the rest of the library or to any particular data structure. On the other hand, it requires the user to keep track of the association between identifiers and operations or actual data.

Once a flow builder is created (which requires no constructor arguments), the first thing to do is to bind a task. This tells to the builder who intends to consume the resources that are specified immediately after:

entt::flow builder{};
builder.bind("task_1"_hs);

The example uses the EnTT hashed string to generate an identifier for the task.
Indeed, the use of id_type as an identifier type isn't by accident. In fact, it matches well with the internal hashed string class. Moreover, it's also the same type returned by the hash function of the internal RTTI system, in case the user wants to rely on that.
However, being an integral value, it leaves the user full freedom to rely on his own tools if necessary.

Once a task is associated with the flow builder, it's also assigned read-only or read-write resources as appropriate:

builder
    .bind("task_1"_hs)
        .ro("resource_1"_hs)
        .ro("resource_2"_hs)
    .bind("task_2"_hs)
        .rw("resource_2"_hs)

As mentioned, many functions return the builder itself and it's therefore easy to concatenate the different calls.
Also in the case of resources, they are identified by numeric values of type id_type. As above, the choice is not entirely random. This goes well with the tools offered by the library while leaving room for maximum flexibility.

Finally, both the ro andrw functions also offer an overload that accepts a pair of iterators, so that one can pass a range of resources in one go.

Rebinding

The flow class is resource based rather than task based. This means that graph generation is driven by resources and not by the order of appearance of tasks during flow definition.
Although this concept is particularly important, it's almost irrelevant for the vast majority of cases. However, it becomes relevant when rebinding resources or tasks.

In fact, nothing prevents rebinding elements to a flow.
However, the behavior changes slightly from case to case and has some nuances that it's worth knowing about.

Directly rebinding a resource without the task being replaced trivially results in the task's access mode for that resource being updated:

builder.bind("task"_hs).rw("resource"_hs).ro("resource"_hs)

In this case, the resource is accessed in read-only mode, regardless of the first call to rw.
Behind the scenes, the call doesn't actually replace the previous one but is queued after it instead, overwriting it when generating the graph. Thus, a large number of resource rebindings may even impact processing times (very difficult to observe but theoretically possible).

Rebinding resources and also combining it with changes to tasks has far more implications instead.
As mentioned, graph generation takes place starting from resources and not from tasks. Therefore, the result may not be as expected:

builder
    .bind("task_1"_hs)
        .ro("resource"_hs)
    .bind("task_2"_hs)
        .ro("resource"_hs)
    .bind("task_1"_hs)
        .rw("resource"_hs);

What happens here is that the resource first sees a read-only access request from the first task, then a read-write request from the second task and finally a new read-only request from the first task.
Although this definition would probably be counted as an error, the resulting graph may be unexpected. This in fact consists of a single edge outgoing from the second task and directed to the first task.
To intuitively understand what happens, it's enough to think of the fact that a task never has an edge pointing to itself.

While not obvious, this approach has its pros and cons like any other solution. For example, creating loops is actually simple in the context of resource-based graph generations:

builder
    .bind("task_1"_hs)
        .rw("resource"_hs)
    .bind("task_2"_hs)
        .rw("resource"_hs)
    .bind("task_1"_hs)
        .rw("resource"_hs);

As expected, this definition leads to the creation of two edges that define a loop between the two tasks.

As a general rule, rebinding resources and tasks is highly discouraged because it could lead to subtle bugs if users don't know what they're doing.
However, once the mechanisms of resource-based graph generation are understood, it can offer to the expert user a flexibility and a range of possibilities otherwise inaccessible.

Fake resources and order of execution

The flow builder doesn't offer the ability to specify when a task should execute before or after another task.
In fact, the order of registration on the resources also determines the order in which the tasks are processed during the generation of the execution graph.

However, there is a way to force the execution order of two processes.
Briefly, since accessing a resource in opposite modes requires sequential rather than parallel scheduling, it's possible to make use of fake resources to rule on the execution order:

builder
    .bind("task_1"_hs)
        .ro("resource_1"_hs)
        .rw("fake"_hs)
    .bind("task_2"_hs)
        .ro("resource_2"_hs)
        .ro("fake"_hs)
    .bind("task_3"_hs)
        .ro("resource_2"_hs)
        .ro("fake"_hs)

This snippet forces the execution of task_1 before task_2 and task_3. This is due to the fact that the former sets a read-write requirement on a fake resource that the other tasks also want to access in read-only mode.
Similarly, it's possible to force a task to run after a certain group:

builder
    .bind("task_1"_hs)
        .ro("resource_1"_hs)
        .ro("fake"_hs)
    .bind("task_2"_hs)
        .ro("resource_1"_hs)
        .ro("fake"_hs)
    .bind("task_3"_hs)
        .ro("resource_2"_hs)
        .rw("fake"_hs)

In this case, since there are a number of processes that want to read a specific resource, they will do so in parallel by forcing task_3 to run after all the others tasks.

Sync points

Sometimes it's useful to assign the role of sync point to a node.
Whether it accesses new resources or is simply a watershed, the procedure for assigning this role to a vertex is always the same. First it's tied to the flow builder, then the sync function is invoked:

builder.bind("sync_point"_hs).sync();

The choice to assign an identity to this type of nodes lies in the fact that, more often than not, they also perform operations on resources.
If this isn't the case, it will still be possible to create no-op vertices to which empty tasks are assigned.

Execution graph

Once both the resources and their consumers have been properly registered, the purpose of this tool is to generate an execution graph that takes into account all specified constraints to return the best scheduling for the vertices:

entt::adjacency_matrix<entt::directed_tag> graph = builder.graph();

Searching for the main vertices (that is, those without in-edges) is usually the first thing required:

for(auto &&vertex: graph) {
    if(auto in_edges = graph.in_edges(vertex); in_edges.begin() == in_edges.end()) {
        // ...
    }
}

Then it's possible to instantiate an execution graph by means of other functions such as out_edges to retrieve the children of a given task or edges to get the identifiers.