Binary and multivalued decision diagrams are closely related to dynamic programming (DP) but differ in some important ways. This paper makes the relationship more precise by interpreting the DP state transition graph as a weighted... more
Binary and multivalued decision diagrams are closely related to dynamic programming (DP) but differ in some important ways. This paper makes the relationship more precise by interpreting the DP state transition graph as a weighted decision diagram and incorporating the state-dependent costs of DP into the theory of decision diagrams. It generalizes a well-known uniqueness theorem by showing that, for a given optimization problem and variable ordering, there is a unique reduced weighted decision diagram with “canonical” edge costs. This can lead to simplification of DP models by transforming the costs to canonical costs and reducing the diagram, as illustrated by a standard inventory management problem. The paper then extends the relationship between decision diagrams and DP by introducing the concept of nonserial decision diagrams as a counterpart of nonserial dynamic programming.
The typical constraint store transmits a limited amount of information because it consists only of variable domains. We propose a richer constraint store in the form of a limited-width multivalued de- cision diagram (MDD). It reduces to a... more
The typical constraint store transmits a limited amount of information because it consists only of variable domains. We propose a richer constraint store in the form of a limited-width multivalued de- cision diagram (MDD). It reduces to a traditional domain store when the maximum width is one but allows greater pruning of the search tree for larger widths. MDD propagation
We present a propagator that achieves MDD consistency for a separable equality over an MDD (multivalued decision diagram) store in pseudo-polynomial time. We integrate the propagator into a constraint solver based on an MDD store... more
We present a propagator that achieves MDD consistency for a separable equality over an MDD (multivalued decision diagram) store in pseudo-polynomial time. We integrate the propagator into a constraint solver based on an MDD store introduced in (1). Our experiments show that the new propagator provides substantial computational advantage over propagation of two inequality constraints, and that the advantage increases
Abstract. This paper describes a new data structure, difference decision diagrams (DDDs), for representing a Boolean logic over inequalities of the form x − y ≤ c where the variables are integer or real-valued. We give algorithms for... more
Abstract. This paper describes a new data structure, difference decision diagrams (DDDs), for representing a Boolean logic over inequalities of the form x − y ≤ c where the variables are integer or real-valued. We give algorithms for manipulating DDDs and for determining validity, ...
We explore the idea of obtaining valid inequalities for a 0–1 model from a finite-domain constraint programming formulation of the problem. In particular, we formulate a graph coloring problem as a system of all-different constraints. By... more
We explore the idea of obtaining valid inequalities for a 0–1 model from a finite-domain constraint programming formulation of the problem. In particular, we formulate a graph coloring problem as a system of all-different constraints. By analyzing the polyhedral structure of all-different systems, we obtain facet-defining inequalities that can be mapped to valid cuts in the classical 0–1 model of the problem. We focus on cuts corresponding to cycles and webs and show that they are stronger than known cuts for these structures. We also identify path cuts and show they do not strengthen the bound. Computational experiments for a set of benchmark instances reveal that finite-domain cycle cuts often deliver tighter bounds, in less time, than classical 0–1 cuts.
