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Binary decision diagrams (BDDs in short) are a staple of computer science, that are used to represent Boolean functions in a compact manner. BDDs are described at length in the volume 4, fascicule 1 of Knuth's "The art of computer programming", who calls them "wonderful". In the last few months, I have been playing a lot with BDDs and related structures, and the more I play with them the more I lo
Graphillion is a Python library for efficient graphset operations. Unlike existing graph tools such as NetworkX, which are designed to manipulate just a single graph at a time, Graphillion handles a large set of graphs very efficiently. Surprisingly, trillions of trillions of graphs can be processed on a single computer with Graphillion. You may be curious about an uncommon concept of graphset, bu
Take a map of mainland USA, and consider the following problems: Suppose you want to visit every state capitol exactly once, traveling on highways. Which route is shortest? Which route is longest? What is the mean and standard deviation of all the routes? Weight the states by any means, for example, by reading their two-letter code as a number in base 36. Then find a set of states such that no two
ç§ã®ããã¯ãã¼ã¯ 決å®ã°ã©ããç¨ãããã¼ã¿æ§é ç§å¦æè¡æ¯èæ©æ§ãERATOæ¹é¢æ£æ§é å¦çç³»ããã¸ã§ã¯ããç ç©¶å¡ å·å ç´ ã¯ããã«BDD (Binary Decision Diagramãäºå決å®ã°ã©ã) ã¯nå¤æ°0/1è«çé¢æ°ãå¹çè¯ã表ç¾ãããã¼ã¿æ§é ã§ããã BDDã¯80年代ãã90年代å¾åã«ããã¦çãã«ç 究ããã¦ããã 主ã«LSIåè·¯è¨è¨ãã¢ãã«æ¤æ»ã®åéã«ããã¦åºã使ãããæè¡ã¨ãªã£ãã 2000年代以éã¯ãBDDããã®æ´¾çå½¢ãã ãã¼ã¿ãã¤ãã³ã°ãç¥èçºè¦ã確çæ¨è«ãåæã¢ã«ã´ãªãºã è¨è¨ããã¤ãªã¤ã³ãã©ããã£ãã¯ã¹çã æ å ±ç§å¦ã®æ§ã ãªåéã«é©ç¨ããåããåºãã£ã¦ããã ã¾ããçµåãéåï¼éåæï¼ã表ç¾ãã ZDDï¼Zero-Suppressed BDDï¼ããæååéåã表ç¾ãã SeqBDD (Sequence BDD)ã ç½®æã®éåã表ç¾ãã ÏDD (PiDD, Per
TdZdd is an efficient C++ library for manipulating ordered decision diagrams (DDs). Unlike the ordinary DD libraries that are optimized for efficient operations between multiple DDs, TdZdd focuses on direct construction of a non-trivial DD structure from scratch. It has three basic functions: Top-down/breadth-first DD construction Reduction as BDDs/ZDDs Bottom-up/breadth-first DD evaluation The DD
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Take a map of mainland USA, and consider the following problems: Suppose you want to visit every state capitol exactly once, traveling on highways. Which route is shortest? Which route is longest? What is the mean and standard deviation of all the routes? Weight the states by any means, for example, by reading their two-letter code as a number in base 36. Then find a set of states such that no two
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