Selection Graph Coloring: Application to Constrained Encoding

This paper aims at introducing the concept of selection graph with an application to a non-trivial problem. A selection graph is made of a set of classes, each class having multiple realizations, and of an uncompatibility graph built on these realizations. Coloring a selection graph can be used to solve constrained scheduling, constrained ressource allocation, and dichotomy-based constrained encoding (DBCE). This paper shows how the later problem can be solved with selection graph coloring. This results in the first efficient polynomial-memory exact DBCE algorithm. Experimental results show that it outperforms the best known exact solvers.