DeepAI

# Spined categories: generalizing tree-width beyond graphs

We develop a general theory of categories that admit a functorial invariant (the triangulation functor) which generalizes the tree-width of graphs. Our triangulation functor provides a uniform construction for various tree-width-like invariants including hypergraph tree-width, and the tree-width of the modular quotient in the category of modular partition functions.

• 6 publications
• 4 publications
05/18/2022

### Monoidal Width: Capturing Rank Width

Monoidal width was recently introduced by the authors as a measure of th...
02/15/2022

### Monoidal Width

We introduce monoidal width as a measure of the difficulty of decomposin...
06/23/2022

### On the parameterized complexity of computing tree-partitions

We study the parameterized complexity of computing the tree-partition-wi...
10/01/2019

### Parameterized complexity of quantum invariants

We give a general fixed parameter tractable algorithm to compute quantum...
11/03/2021

### The Algorithmic Complexity of Tree-Clique Width

Tree-width has been proven to be a useful parameter to design fast and e...
07/13/2022

### Structured Decompositions: Structural and Algorithmic Compositionality

We introduce structured decompositions: category-theoretic generalizatio...
09/28/2022

### Efficient parameterized algorithms on graphs with heterogeneous structure: Combining tree-depth and modular-width

Many computational problems admit fast algorithms on special inputs, how...