A Non-binary Constraint Satisfaction Solver: The One- Face Hyperpolyhedron Heuristic. Miguel A. Salido, Adriana Giret, Federico Barber Dpto. Sistemas Informáticos y Computación Universidad Politécnica de Valencia, Camino de Vera s/n 46071 Valencia, Spain {msalido,agiret,fbarber}@dsic.upv.es Abstract. Constraint satisfaction is gaining a great deal of attention because many combinatorial problems especially in areas of Artificial Intelligence can be expressed in a natural way as a Constraint Satisfaction Problem (CSP). It is well known that a non-binary CSP can be transformed into an equivalent binary CSP using some of the actual techniques. However, when the CSP is not discrete or the number of constraints is high relative to the number of variables, these techniques become impractical. In this paper, we propose an heuristic called "One-face Hyperpolyhedron Heuristic" as an incremental and non-binary CSP solver. This non-binary CSP solver does not increase its temporal complexity with the variable domain size. It carries out the search through a hyperpolyhedron that maintains those solutions that satisfy all metric non-binary temporal constraints. Thus, we can manage more complex and expressive problems with high number of constraints and very large domains.  ,QWURGXFWLRQ Nowadays, many researches are working on non-binary constraints, mainly influenced by the growing number of real-life applications. Modelling a problem with non-binary constraints has several advantages. It facilitates the expression of the problem, enables more powerful constraint propagation as more global information is available, etc. Problems of these kind can either be solved directly by means of non- binary CSPs by a search method or transformed into a binary one [7] and then solved by using binary CSP techniques. However, this transformation may not be practical in problems with some particular properties [1][3], for example when the number of constraints is high relative to the number of variables, when the constraints are not tight or when the CSP is non-discrete [2]. In this paper, we propose an algorithm called " 2QHIDFH +\SHUSRO\KHGURQ +HXULVWLF " (OFHH) that manages non-binary CSPs with very large domains, and many variables. OFHH maintains only one vertex in each hyperpolyhedron face. Thus the temporal cost of the hyperpolyhedron algorithm is reduced to O(Q), while the complete hyperpolyhedron maintains  vertices in each face.