DAG-Width Calculator

directed graph width

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About DAG-Width Calculator

A DAG-width calculator computing dagw(G): width of optimal DAG decomposition for digraphs. Generalizes treewidth to directed graphs via DAG structure. dagw = 1 iff acyclic. Obdržálek (2006). Parity games solvable in O(n^(dagw+1)). Client-side.

DAG-Width Calculator Features

  • dagw(G)
  • Directed
  • DAG=1
  • Parity games
  • Common digraphs
DAG-width dagw(G): directed graph width parameter. Decomposition uses a DAG (not tree). dagw=1 iff G is a DAG. Generalizes treewidth to digraphs. Obdržálek (2006): parity games solvable in n^O(dagw). Important for verification and games.

How to Use

Select digraph:

  • dagw: DAG-width
  • Directed: DAG decomp
  • Acyclic: dagw=1?

DAG Decomposition

Like tree decomposition but the skeleton is a DAG, not a tree. Bags of vertices. Width = max bag size - 1. Captures directed reachability structure. More expressive than directed treewidth for some applications.

Applications

Parity games: central to verification (model checking μ-calculus). Bounded dagw → polynomial parity games. Also: directed network analysis, circuit complexity, information flow in directed networks.

Step-by-Step Instructions

  1. 1Select digraph.
  2. 2Build DAG decomp.
  3. 3Measure bag width.
  4. 4Check acyclicity.
  5. 5Apply parity games.

DAG-Width Calculator — Frequently Asked Questions

Why directed width parameters?+

Treewidth ignores edge directions. Directed graphs need parameters respecting direction. DAG-width captures how 'DAG-like' a digraph is. Essential for verification, games, and reachability problems.

What's the difference from directed treewidth?+

Multiple directed width parameters exist: directed treewidth, DAG-width, Kelly-width, entanglement. DAG-width ≥ directed treewidth. DAG-width has better algorithmic properties for parity games.

Is DAG-width computable?+

Computing exact dagw is hard. For fixed k: recognizing dagw ≤ k is decidable but the complexity is not fully settled. Active research area in parameterized complexity for directed graphs.

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