# Incremental Updates of Generalized Hypertree Decompositions

arXiv: https://arxiv.org/abs/2209.10375 · HTML: https://mlsanity.com/paper/2209.10375/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 5 of its 29 references that are in the map.
- First posted on arXiv 21 Sep 2022.

## Builds on (most cited first, 5 of 5)

- [FAQ: Questions Asked Frequently](https://mlsanity.com/paper/1504.04044/) (2015)
- [HyperBench: A Benchmark and Tool for Hypergraphs and Empirical Findings](https://mlsanity.com/paper/1811.08181/) (2018)
- [Semantic Width and the Fixed-Parameter Tractability of Constraint Satisfaction Problems](https://mlsanity.com/paper/2007.14169/) (2020)
- [General and Fractional Hypertree Decompositions: Hard and Easy Cases](https://mlsanity.com/paper/1611.01090/) (2016)
- [The HyperTrac Project: Recent Progress and Future Research Directions on Hypergraph Decompositions](https://mlsanity.com/paper/2012.14762/) (2020)

## Abstract (arXiv)

Structural decomposition methods, such as generalized hypertree decompositions, have been successfully used for solving constraint satisfaction problems (CSPs). As decompositions can be reused to solve CSPs with the same constraint scopes, investing resources in computing good decompositions is beneficial, even though the computation itself is hard. Unfortunately, current methods need to compute a completely new decomposition even if the scopes change only slightly. In this paper, we make the first steps toward solving the problem of updating the decomposition of a CSP P so that it becomes a valid decomposition of a new CSP P' produced by some modification of P. Even though the problem is hard in theory, we propose and implement a framework for effectively updating GHDs. The experimental evaluation of our algorithm strongly suggests practical applicability.