Incremental Updates of Generalized Hypertree Decompositions

TL;DR

This paper introduces a framework for efficiently updating generalized hypertree decompositions (GHDs) when CSPs undergo minor modifications, reducing the need for recomputing decompositions from scratch and demonstrating practical effectiveness.

Contribution

It presents the first approach for incremental updates of GHDs in response to small CSP modifications, addressing a significant computational challenge.

Findings

The proposed algorithm effectively updates GHDs with minor CSP changes.

Experimental results show practical applicability of the incremental update method.

The framework reduces computational effort compared to recomputing GHDs from scratch.

Abstract

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.