文章基本信息

标题：Quantum Algorithm for Finding the Optimal Variable Ordering for Binary Decision Diagrams
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作者：Seiichiro Tani
期刊名称：LIPIcs : Leibniz International Proceedings in Informatics
电子版ISSN：1868-8969
出版年度：2020
卷号：162
页码：36:1-36:19
DOI：10.4230/LIPIcs.SWAT.2020.36
出版社：Schloss Dagstuhl -- Leibniz-Zentrum fuer Informatik
摘要：An ordered binary decision diagram (OBDD) is a directed acyclic graph that represents a Boolean function. Since OBDDs have many nice properties as data structures, they have been extensively studied for decades in both theoretical and practical fields, such as VLSI (Very Large Scale Integration) design, formal verification, machine learning, and combinatorial problems. Arguably, the most crucial problem in using OBDDs is that they may vary exponentially in size depending on their variable ordering (i.e., the order in which the variables are to be read) when they represent the same function. Indeed, it is NP hard to find an optimal variable ordering that minimizes an OBDD for a given function. Friedman and Supowit provided a clever deterministic algorithm with time/space complexity O^â^-(3â¿), where n is the number of variables of the function, which is much better than the trivial brute-force bound O^â^-(n!2â¿). This paper shows that a further speedup is possible with quantum computers by presenting a quantum algorithm that produces a minimum OBDD together with the corresponding variable ordering in O^â^-(2.77286â¿) time and space with an exponentially small error probability. Moreover, this algorithm can be adapted to constructing other minimum decision diagrams such as zero-suppressed BDDs.
关键词：Binary Decision Diagram; Variable Ordering; Quantum Algorithm