Variable ordering for the application of BDDs to the maximum independent set problem

Authors:
David Bergman;Andre A. Cire;Willem-Jan van Hoeve;John N. Hooker
Affiliations:
Tepper School of Business, Carnegie Mellon University, Pittsburgh, PA;Tepper School of Business, Carnegie Mellon University, Pittsburgh, PA;Tepper School of Business, Carnegie Mellon University, Pittsburgh, PA;Tepper School of Business, Carnegie Mellon University, Pittsburgh, PA
Venue:
CPAIOR'12 Proceedings of the 9th international conference on Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems
Year:
2012

Citing 13
Cited 1

Graph-Based Algorithms for Boolean Function Manipulation

IEEE Transactions on Computers
Improving the Variable Ordering of OBDDs Is NP-Complete

IEEE Transactions on Computers
Counting stable sets on Cartesian products of graphs

Discrete Mathematics
The Number of Independent Sets in a Grid Graph

SIAM Journal on Discrete Mathematics
On Counting Independent Sets in Sparse Graphs

SIAM Journal on Computing
Binary Decision Diagrams

IEEE Transactions on Computers
Approximate Compilation of Constraints into Multivalued Decision Diagrams

CP '08 Proceedings of the 14th international conference on Principles and Practice of Constraint Programming
The number of independent sets in a regular graph

Combinatorics, Probability and Computing
A constraint store based on multivalued decision diagrams

CP'07 Proceedings of the 13th international conference on Principles and practice of constraint programming
A systematic approach to MDD-based constraint programming

CP'10 Proceedings of the 16th international conference on Principles and practice of constraint programming
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
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

BDD-based heuristics for binary optimization

Journal of Heuristics

Quantified Score

Hi-index	0.00

Visualization

Abstract

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 variable orderings for the BDD, we show that the width of an exact BDD can be given a theoretical upper bound for certain classes of graphs. In addition, we draw an interesting connection between the Fibonacci numbers and the width of exact BDDs for general graphs. We propose variable ordering heuristics inspired by these results, as well as a k-layer look-ahead heuristic applicable to any problem domain. We find experimentally that orderings that result in smaller exact BDDs have a strong tendency to produce tighter bounds in relaxation BDDs.