---
title: "Valued Constraint Satisfaction Problems: Hard and Easy Problems"
authors:
  - "Thomas Schiex"
  - "Hélène Fargier"
  - "Gérard Verfaillie"
doi: ""
url: "https://ijcai.org/proceedings/1995/83"
pdf: "https://ijcai.org/proceedings/1995/0083.pdf"
venue: "Proceedings of the Fourteenth International Joint Conference on Artificial Intelligence"
year: 1995
pages: "631-638"
track: "Constraint Satisfaction"
keywords:
---

# Valued Constraint Satisfaction Problems: Hard and Easy Problems

Thomas Schiex, Hélène Fargier, Gérard Verfaillie

*Proceedings of the Fourteenth International Joint Conference on Artificial Intelligence*, pages 631-638.

## Abstract

In order to deal with over-constrained Constraint Satisfaction Problems, various extensions of the CSP framework have been considered by taking into account costs, uncertainties, preferences, priorities ... Each extension uses a specific mathematical operator (+,max .. .) to aggregate constraint violations. In this paper, we consider a simple algebraic framework, related to Partial Constraint Satisfaction, which subsumes most of these proposals and use it to characterize existing proposals in terms of rationality and computational complexity. We exhibit simple relationships between these proposals, try to extend some traditional CSP algorithms and prove that some of these extensions may be computationally expensive.