There Is No 16-Clue Sudoku: Solving the Sudoku Minimum Number of Clues Problem via Hitting Set Enumeration
There Is No 16-Clue Sudoku: Solving the Sudoku Minimum Number of Clues Problem via Hitting Set Enumeration
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DOI：
10.1080/10586458.2013.870056
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发表时间：
2012-01
影响因子：
0.5
通讯作者：
G. McGuire;Bastian Tugemann;G. Civario
中科院分区：
文献类型：
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作者：
G. McGuire;Bastian Tugemann;G. Civario
数独最小线索数问题是这样一个问题：数独谜题最小线索数是多少？几年来，人们一直猜测答案是17。我们对16条线索数独谜题进行了详尽的计算机搜索，但没有找到任何答案，从而证明答案确实是17。本文介绍了我们的方法和实际搜索。作为这个项目的一部分，我们开发了一种新的方法来枚举命中集。碰集问题是一个计算困难的问题，它是Karp的21个经典NP-完全问题之一。即使在今天的超级计算机速度下，寻找命中集的标准回溯算法也不足以详尽地搜索包含16条线索的数独谜题。为了使穷举搜索成为可能，我们设计了一种算法，使我们能够有效地枚举合适大小的命中集。
The sudoku minimum number of clues problem is the following question: what is the smallest number of clues that a sudoku puzzle can have? For several years it had been conjectured that the answer is 17. We have performed an exhaustive computer search for 16-clue sudoku puzzles and did not find any, thus proving that the answer is indeed 17. In this article we describe our method and the actual search. As a part of this project, we developed a novel way to enumerate hitting sets. The hitting set problem is computationally hard; it is one of Karp’s 21 classic NP-complete problems. A standard backtracking algorithm for finding hitting sets would not be fast enough to search for a 16-clue sudoku puzzle exhaustively, even at today’s supercomputer speeds. To make an exhaustive search possible, we designed an algorithm that allowed us to efficiently enumerate hitting sets of a suitable size.