Finding a Reconfiguration Sequence between Longest Increasing Subsequences

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 l...

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Veröffentlicht in:IEICE Transactions on Information and Systems 2024/04/01, Vol.E107.D(4), pp.559-563
Hauptverfasser: AOIKE, Yuuki, KIYOMI, Masashi, KOBAYASHI, Yasuaki, OTACHI, Yota
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Sprache:eng
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Zusammenfassung: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).
ISSN:0916-8532
1745-1361
DOI:10.1587/transinf.2023EDL8067