In this note, we consider the problem of finding a step-by-step transformation between two longest increasing subsequences in a sequence, namely Longest Increasing Subsequence Reconfiguration. We give a polynomial-time algorithm for deciding whether there is a reconfiguration sequence between two longest increasing subsequences in a sequence. This implies that Independent Set Reconfiguration and Token Sliding are polynomial-time solvable on permutation graphs, provided that the input two independent sets are largest among all independent sets in the input graph. We also consider a special case, where the underlying permutation graph of an input sequence is bipartite. In this case, we give a polynomial-time algorithm for finding a shortest reconfiguration sequence (if it exists).

翻译：本文考虑序列中两个最长递增子序列之间的逐步变换问题，即最长递增子序列重配置问题。我们提出了一种多项式时间算法，用于判定序列中两个最长递增子序列之间是否存在重配置序列。这一结果表明，在输入的两个独立集均为输入图中所有独立集中规模最大的前提下，置换图上的独立集重配置与令牌滑动问题可在多项式时间内求解。我们还考虑了一种特殊情况，即输入序列的基础置换图为二分图。针对该情形，我们给出了一种多项式时间算法，用于寻找最短重配置序列（若存在）。