Graph-Based Algorithms for Boolean Function Manipulation
IEEE Transactions on Computers
Zero-suppressed BDDs for set manipulation in combinatorial problems
DAC '93 Proceedings of the 30th international Design Automation Conference
ZRES: The Old Davis-Putman Procedure Meets ZBDD
CADE-17 Proceedings of the 17th International Conference on Automated Deduction
The Art of Computer Programming, Volume 4, Fascicle 1: Bitwise Tricks & Techniques; Binary Decision Diagrams
| Hi-index | 0.00 |
Permutations and combinations are two basic concepts in elementary combinatorics. Permutations appear in various problems such as sorting, ordering, matching, coding and many other real-life situations. While conventional SAT problems are discussed in combinatorial space, "permutatorial" SAT and CSPs also constitute an interesting and practical research topic. In this paper, we propose a new type of decision diagram named "pDD," for compact and canonical representation of a set of permutations. Similarly to an ordinary BDD or ZDD, pDD has efficient algebraic set operations such as union, intersection, etc. In addition, pDDs hava a special Cartesian product operation which generates all possible composite permutations for two given sets of permutations. This is a beautiful and powerful property of pDDs. We present two examples of pDD applications, namely, designing permutation networks and analysis of Rubik's Cube. The experimental results show that a pDD-based method can explore billions of permutations within feasible time and space limits by using simple algebraic operations.