The key highlights and insights of this paper are:
The authors present a (3n+o(n))-bit representation for a Baxter permutation π of size n that can support π(i) and π−1(j) queries in O(f1(n)) and O(f2(n)) time respectively, where f1(n) and f2(n) are any increasing functions satisfying ω(log n) and ω(log2 n).
The representation is based on traversing the minimum Cartesian tree (MinC(π)) of the Baxter permutation using a two-stack algorithm that visits the nodes in ascending order of their labels. This allows efficient decoding of the node labels, which was a key challenge in prior representations.
The authors also provide a (2n+o(n))-bit representation for alternating Baxter permutations, which can support the same queries in the same time bounds.
As applications, the authors show how their succinct representations of Baxter and separable permutations can be used to construct efficient succinct data structures for mosaic/slicing floorplans and plane bipolar orientations that support various navigational queries.
The proposed representations circumvent previous lower bound results on the trade-offs between redundancy and query time for general permutations, by exploiting the structural properties of Baxter and separable permutations.
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by Sankardeep C... at arxiv.org 09-26-2024
https://arxiv.org/pdf/2409.16650.pdfDeeper Inquiries