2023/10/02 by Yuuki Aoike, Aoike, Yuuki, Masashi Kiyomi +5
Computer Science · Biochemistry, Genetics and Molecular Biology · #Algorithms and Data Compression #DNA and Biological Computing #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.2310.01066
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).