Abstract
One of the most important parameters that determines the size of a decision diagram is the variable ordering. In this chapter we formally study the impact of variable ordering on the size of exact decision diagrams for the maximum independent set problem. We provide worst-case bounds on the size of the exact decision diagram for particular classes of graphs. For general graphs, we show that the size is bounded by the Fibonacci numbers. Lastly, we demonstrate experimentally that variable orderings that produce small exact decision diagrams also produce better bounds from relaxed decision diagrams.
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© 2016 Springer International Publishing Switzerland
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Bergman, D., Cire, A.A., van Hoeve, WJ., Hooker, J. (2016). Variable Ordering. In: Decision Diagrams for Optimization. Artificial Intelligence: Foundations, Theory, and Algorithms. Springer, Cham. https://doi.org/10.1007/978-3-319-42849-9_7
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DOI: https://doi.org/10.1007/978-3-319-42849-9_7
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Publisher Name: Springer, Cham
Print ISBN: 978-3-319-42847-5
Online ISBN: 978-3-319-42849-9
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