Publica
Hier finden Sie wissenschaftliche Publikationen aus den FraunhoferInstituten. The clique problem with multiplechoice constraints under a cyclefree dependency graph
 Discrete applied mathematics 283 (2020), S.5977 ISSN: 0166218X 

 Englisch 
 Zeitschriftenaufsatz 
 Fraunhofer IIS () 
Abstract
The clique problem with multiplechoice constraints (CPMC) represents a very common substructure in many realworld applications, for example scheduling problems with precedence constraints. It consists in finding a clique in a graph whose nodes are partitioned into subsets, such that exactly one node from each subset is chosen. Even though we can show that (CPMC) is NPcomplete, we will be able to identify and characterize a new interesting subclass which is solvable in polynomial time. It arises whenever there are no circular dependencies between the subsets in the partition when it comes to the compatibilities of their elements. We will be able to show that this subclass is equivalent to the clique problem on a perfect graph with certain additional structure. This finding will allow us to give a full convexhull description. Although the convex hull can have exponentiallymany facets, we can state an efficient and practical separation algorithm. In an application from underground and railway timetabling, we show that, in comparison to a naive formulation, these results lead to significant reductions in computation time.