# Conditional lexicographic orders in constraint satisfaction problems

@article{Wallace2006ConditionalLO, title={Conditional lexicographic orders in constraint satisfaction problems}, author={Richard J. Wallace and Nic Wilson}, journal={Annals of Operations Research}, year={2006}, volume={171}, pages={3-25} }

The lexicographically-ordered CSP (“lexicographic CSP” or “LO-CSP” for short) combines a simple representation of preferences with the feasibility constraints of ordinary CSPs. Preferences are defined by a total ordering across all assignments, such that a change in assignment to a given variable is more important than any change in assignment to any less important variable. In this paper, we show how this representation can be extended to handle conditional preferences in two ways. In the…

## 8 Citations

Lexicographically-ordered constraint satisfaction problems

- Computer ScienceConstraints
- 2009

The simple structure of lexicographic CSPs can support specialised algorithms: a branch and bound algorithm with an implicit cost function, and an iterative algorithm that obtains optimal values for successive variables in the importance ordering, both of which can be combined with appropriate variable ordering heuristics to improve performance.

Lexicographic Preference Trees with Hard Constraints

- Computer ScienceCanadian Conference on AI
- 2019

A recursive backtrack search algorithm that is called Search-LP to find the most preferable feasible outcome for an LP-tree extended to a set of hard constraints, which it is proved is preferable to every other feasible outcome.

Conditional and Composite Constraints with Preferences

- Computer ScienceFLAIRS Conference
- 2008

This paper extends the conditional and composite CSP framework, managing CSPs in a dynamic environment, in order to handle preferences, and favors the MAC principle as the constraint propagation strategy to be used within the branch and bound procedure.

Managing dynamic CSPs with preferences

- Computer ScienceApplied Intelligence
- 2012

A new framework, managing Constraint Satisfaction Problems (CSPs) with preferences in a dynamic environment, which supports four types, namely: unary and binary constraint preferences, composite preferences and conditional preferences, and which is handled by four variants of the branch and bound algorithm.

Conditional and Composite Temporal Constraints with Preferences

- Computer ScienceThirteenth International Symposium on Temporal Representation and Reasoning (TIME'06)
- 2006

This paper extends the temporal reasoning framework, managing numeric and symbolic information, in order to handle preferences, and proposes a variant of the branch and bound algorithm, which offers more expressive power in representing a wide variety of temporal constraint problems.

Constrained Optimization with Qualitative Preferences

- Computer ScienceArXiv
- 2021

It is shown that the Constrained CPR-net has one single optimal outcome that the authors can obtain without dominance testing, and it is proved that the first feasible outcome returned by Search-LP is also preferable to any other feasible outcome.

Learning Lexicographic Preference Trees From Positive Examples

- Computer ScienceAAAI
- 2018

This paper presents an algorithm to learn several classes of lexicographic preference trees, proves convergence properties of the algorithm, and experiment on both synthetic data and on a real-world bench in the domain of recommendation in interactive configuration.

Managing Temporal Constraints with Preferences

- Computer ScienceSpatial Cogn. Comput.
- 2008

This paper proposes a variant of the branch and bound algorithm, which supports four types of preferences, namely: numeric and symbolic temporal preferences, composite preferences and conditional preferences, and offers more expressive power in representing a wide variety of temporal constraint problems.

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