Can someone explain in simple terms to me what a directed acyclic graph is?

Question

Can someone explain in simple terms to me what a directed acyclic graph is? I have looked on Wikipedia but it doesn\'t really make me see its use in programming.

Answer 1

The name tells you most of what you need to know of its definition: It's a graph where every edge only flows in one direction and once you crawl down an edge your path will never return you to the vertex you just left.

I can't speak to all the uses (Wikipedia helps there), but for me DAGs are extremely useful when determining dependencies between resources. My game engine for instance represents all loaded resources (materials, textures, shaders, plaintext, parsed json etc) as a single DAG. Example:

A material is N GL programs, that each need two shaders, and each shader needs a plaintext shader source. By representing these resources as a DAG, I can easily query the graph for existing resources to avoid duplicate loads. Say you want several materials to use vertex shaders with the same source code. It is wasteful to reload the source and recompile the shaders for every use when you can just establish a new edge to the existing resource. In this way you can also use the graph to determine if anything depends on a resource at all, and if not, delete it and free its memory, in fact this happens pretty much automatically.

By extension, DAGs are useful for expressing data processing pipelines. The acyclic nature means you can safely write contextual processing code that can follow pointers down the edges from a vertex without ever reencountering the same vertex. Visual programming languages like VVVV, Max MSP or Autodesk Maya's node-based interfaces all rely on DAGs.