Abstract
Consider a tree T on n nodes, each having a weight drawn from [1..σ]. In this paper, we design succinct data structures to encode T using \(n H(W_T) + o(n\lg \sigma)\) bits of space, such that we can support path counting queries in \(O(\frac{\lg \sigma}{\lg\lg n} + 1)\) time, path reporting queries in \(O((occ+1)(\frac{\lg \sigma}{\lg\lg n} + 1))\) time, and path median and path selection queries in \(O(\frac{\lg \sigma}{\lg\lg \sigma})\) time, where H(W T ) is the entropy of the multiset of the weights of the nodes in T. Our results not only improve the best known linear space data structures [15], but also match the lower bounds for these path queries [18,19,16] when \(\sigma = \Omega(n / \textrm{polylog}(n))\).
This work was supported by NSERC and the Canada Research Chairs Program.
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He, M., Munro, J.I., Zhou, G. (2012). Succinct Data Structures for Path Queries. In: Epstein, L., Ferragina, P. (eds) Algorithms – ESA 2012. ESA 2012. Lecture Notes in Computer Science, vol 7501. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-33090-2_50
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