On Threshold BDDs and the Optimal Variable Ordering Problem

Abstract. Many combinatorial optimization problems can be formulated as 0/1 integer programs (0/1 IPs). The investigation of the structure of these problems raises the following tasks: count or enumerate the feasible solutions and find an optimal solution according to a given linear objective function. All these tasks can be accomplished using binary decision diagrams (BDDs), a very popular and effective datastructure in computational logics and hardware verification. We present a novel approach for these tasks which consists of an outputsensitive algorithm for building a BDD for a linear constraint (a so-called threshold BDD) and a parallel AND operation on threshold BDDs. In particular our algorithm is capable of solving knapsack problems, subset sum problems and multidimensional knapsack problems. BDDs are represented as a directed acyclic graph. The size of a BDD is the number of nodes of its graph. It heavily depends on the chosen variable ordering. Finding the optimal variable...

• Type: Conference
• Year: 2007
• Where: COCOA
• Authors: Markus Behle
• Keywords: COCOA 2007, Optimal Variable Ordering, Threshold Bdd, Variable Ordering