Computational Complexity of Multi-way, Dataaow Constraint Problems Computational Complexity of Multi-way, Dataaow Constraint Problems

Although it is widely acknowledged that multi-way dataaow constraints make it easier to specify certain relationships in interactive applications, concerns about their eeciency have impeded their acceptance. Some of the local propagation algorithms that solve these constraints are polynomial, others (such as SkyBlue) are exponential. In fact, every system handles a speciic problem and the innuence of any particular restriction on the computational complexity is not yet precisely determined. In this report, we present theoretical results that allow us to classify existing multi-way constraint problems. We especially prove that the problem handled by SkyBlue is NP-hard. Complexitt thhorique de probllmes de contraintes fonctionnelles multi-directionnelles RRsumm Les contraintes fonctionnelles multi-directionnelles permettent de spciier facilement certaines relations dans les applications graphiques interactives. Elles sont pourtant encore peu utilisses cause de doutes concernant l'eecacitt des techniques de rrsolution par propagation locale : certains al-gorithmes de rrsolution par propagation locale sont polynomiaux, d'autres (comme SkyBlue) sont exponentiels. En fait, chaque systtme existant traite un probllme spciique et les conssquences des diverses restrictions dans le formalisme des contraintes traittes sur la complexitt thhorique ne sont pas ddterminnes prrcissment. Ce rapport prrsente des rrsultats de complexitt thhorique qui permettent de classiier les diiirents probllmes traitts par les systtmes existants. Nous montrons en particulier que le probllme traitt par SkyBlue est NP-diicile.