On threshold BDDs and the optimal variable ordering problem

On Threshold BDDs and the Optimal Variable Ordering Problem

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...

Variable Ordering of BDDs with Parallel Geneti

Variable Ordering for the Application of BDDs to the Maximum Independent Set Problem

The ordering of variables can have a significant effect on the size of the reduced binary decision diagram (BDD) that represents the set of solutions to a combinatorial optimization problem. It also influences the quality of the objective function bound provided by a limited-width relaxation of the BDD. We investigate these effects for the maximum independent set problem. By identifying variabl...

Improving BDD Variable Ordering Using Abstract BDDs and Sampling

Variable ordering for BDDs has been extensively investigated. Recently, sampling based ordering techniques have been proposed to overcome problems with structure based static ordering methods and sifting based dynamic reordering techniques. However, existing sampling techniques can lead to an unacceptably large deviation in the size of the final BDD. In this paper, we propose a sampling techniq...

On the OBDD Complexity of Threshold Functions and the Variable Ordering Problem