多联骨牌上的最大独立皇后集是NP完全问题
Maximum independent queen set on polyominoes is NP-complete
浏览论文内容
中文总结 AI 辅助
研究多联骨牌上皇后图的独立集问题INDQUEENS，证明其为NP完全问题，证实相关猜想，且因归约简约进一步证明是#P完全的，还证明了多联骨牌上的INDROOKS虽是多项式时间可解但也是#P完全的。
中文摘要 AI 辅助
在图中找到一组互不相连的顶点（即独立集问题INDSET）是著名的NP完全问题。棋盘的皇后图以棋盘方格为顶点，若皇后能从一方格移动到另一方格则二者连边。我们将棋盘为多联骨牌的皇后图上的独立集问题称为INDQUEENS。我们证明了多联骨牌上的INDQUEENS是NP完全的，证实了Langlois - Rémillard - Müßig - Roldán的猜想。由于我们的归约是简约的，还能进一步证明它是#P完全的。此外，我们证明了多联骨牌上的INDROOKS虽是多项式时间可解的，但也是#P完全的。
英文摘要
Finding a set of vertices in a graph with no edges between them, INDSET, is a well-known NP-complete problem. The queen graph of a chessboard is constructed by taking vertices as the tiles of the chessboard and drawing edges between two tiles if a queen can move from one to the other. We call INDQUEENS the independent set problem on a queen graph where the chessboard is a polyomino. We prove that INDQUEENS on polyominoes is NP-complete, proving a conjecture of Langlois-Rémillard--Müßig--Roldán. As our reduction is parsimonious, we can further prove that it is #P-complete. We furthermore prove that INDROOKS on polyominoes is #P-complete, despite being solvable in polynomial time.
