没有16线索数独：解决数独最小线索数问题
There is no 16-Clue Sudoku: Solving the Sudoku Minimum Number of Clues Problem
摘要：
数独最小线索数问题是以下问题：一个数独谜题最小的线索数是多少？多年来，人们一直认为答案是17。我们已经进行了详尽的计算机搜索16线索数独难题，并没有找到任何，从而证明答案确实是17。在这篇文章中，我们描述了我们的方法和实际的搜索。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。击中集问题是计算困难的，它是卡普的21个经典NP完全问题之一。一个寻找命中集的标准回溯算法，即使以今天超级计算机的速度，也不足以彻底搜索一个16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适当大小的命中集。
英文摘要：
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 for enumerating 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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
