The Optimal Knight Exchange Puzzle is NP-Hard

Henry Siegel

The Optimal Knight Exchange Puzzle is NP-Hard

离散数学 2026-06-28 v1 计算复杂性

作者: Henry Siegel

摘要

This paper explores the hardness of two popular recreational chess puzzles: The Knight's Tour and the Knight Exchange (Swap). The problem of finding a Knight's Tour is known to be NP-hard for any chessboard with holes and constant-time decidable for rectangular chessboards, so a natural direction is to explore the hardness of the problem for intermediate chessboard restrictions. In this paper, we show that Knight's Tour is NP-hard for connected boards. We also give a short polynomial-time reduction between the two problems, showing that the optimality version of Knight Exchange is NP-hard.

引用

@article{arxiv.2606.29153,
  title  = {The Optimal Knight Exchange Puzzle is NP-Hard},
  author = {Henry Siegel},
  journal= {arXiv preprint arXiv:2606.29153},
  year   = {2026}
}

备注

13 pages, 10 figures and tables