# The combined basic LP and affine IP relaxation for promise VCSPs on infinite domains

arXiv: https://arxiv.org/abs/2007.01779 · HTML: https://mlsanity.com/paper/2007.01779/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Jul 2020.

## Built on by (most cited first, 1 of 1)

- [On Classifying Continuous Constraint Satisfaction Problems](https://mlsanity.com/paper/2106.02397/) (2021)

## Abstract (arXiv)

Convex relaxations have been instrumental in solvability of constraint satisfaction problems (CSPs), as well as in the three different generalisations of CSPs: valued CSPs, infinite-domain CSPs, and most recently promise CSPs. In this work, we extend an existing tractability result to the three generalisations of CSPs combined: We give a sufficient condition for the combined basic linear programming and affine integer programming relaxation for exact solvability of promise valued CSPs over infinite-domains. This extends a result of Brakensiek and Guruswami [SODA'20] for promise (non-valued) CSPs (on finite domains).