Graph-Based Algorithms for Boolean Function Manipulation
IEEE Transactions on Computers
Journal of the ACM (JACM)
Theory of linear and integer programming
Theory of linear and integer programming
Finding the optimal variable ordering for binary decision diagrams
DAC '87 Proceedings of the 24th ACM/IEEE Design Automation Conference
Improving the Variable Ordering of OBDDs Is NP-Complete
IEEE Transactions on Computers
Size of ordered binary decision diagrams representing threshold functions
Theoretical Computer Science
Algorithms and Data Structures in VLSI Design
Algorithms and Data Structures in VLSI Design
BDDs in a branch and cut framework
WEA'05 Proceedings of the 4th international conference on Experimental and Efficient Algorithms
An improved branch and bound algorithm for exact BDD minimization
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
On the OBDD Complexity of Threshold Functions and the Variable Ordering Problem
SOFSEM '09 Proceedings of the 35th Conference on Current Trends in Theory and Practice of Computer Science
On the size of (generalized) OBDDs for threshold functions
Information Processing Letters
Manipulating MDD relaxations for combinatorial optimization
CPAIOR'11 Proceedings of the 8th international conference on Integration of AI and OR techniques in constraint programming for combinatorial optimization problems
| Hi-index | 0.00 |
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 output-sensitive 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 ordering is an NP-hard problem. We derive a 0/1 IP for finding an optimal variable ordering of a threshold BDD. This 0/1 IP formulation provides the basis for the computation of the variable ordering spectrum of a threshold function. We introduce our new tool azove 2.0 as an enhancement to azove 1.1 which is a tool for counting and enumerating 0/1 points. Computational results on benchmarks from the literature show the strength of our new method.