Parallel preprocessing for path queries without concurrent reading
Information and Computation
High-order entropy-compressed text indexes
SODA '03 Proceedings of the fourteenth annual ACM-SIAM symposium on Discrete algorithms
LATIN '00 Proceedings of the 4th Latin American Symposium on Theoretical Informatics
A survey on tree edit distance and related problems
Theoretical Computer Science
Range mode and range median queries on lists and trees
Nordic Journal of Computing
Succinct ordinal trees with level-ancestor queries
ACM Transactions on Algorithms (TALG)
Lower bounds for 2-dimensional range counting
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
FOCS '08 Proceedings of the 2008 49th Annual IEEE Symposium on Foundations of Computer Science
Range mode and range median queries in constant time and sub-quadratic space
Information Processing Letters
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
Range Quantile Queries: Another Virtue of Wavelet Trees
SPIRE '09 Proceedings of the 16th International Symposium on String Processing and Information Retrieval
Data Structures for Range Median Queries
ISAAC '09 Proceedings of the 20th International Symposium on Algorithms and Computation
Improved bounds for range mode and range median queries
SOFSEM'08 Proceedings of the 34th conference on Current trends in theory and practice of computer science
Counting inversions, offline orthogonal range counting, and related problems
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Theoretical Computer Science
Orthogonal range searching on the RAM, revisited
Proceedings of the twenty-seventh annual symposium on Computational geometry
Range selection and median: tight cell probe lower bounds and adaptive data structures
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Space-Efficient and fast algorithms for multidimensional dominance reporting and counting
ISAAC'04 Proceedings of the 15th international conference on Algorithms and Computation
Succinct data structures for path queries
ESA'12 Proceedings of the 20th Annual European conference on Algorithms
Succinct representations of weighted trees supporting path queries
Journal of Discrete Algorithms
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We consider the problem of supporting several different path queries over a tree on n nodes, each having a weight drawn from a set of σ distinct values, where σ≤n. One query we support is the path median query, which asks for the median weight on a path between two given nodes. For this and the more general path selection query, we present a linear space data structure that answers queries in $O(\lg \sigma)$ time under the word RAM model. This greatly improves previous results on the same problem, as previous data structures achieving $O(\lg n)$ query time use $O(n \lg^2 n)$ space, and previous linear space data structures require O(nε) time to answer a query for any positive constant ε [16]. Our linear space data structure also supports path counting queries in $O(\lg \sigma)$ time. This matches the result of Chazelle [8] when σ is close to n, but has better performance when σ is significantly smaller than n. Finally, the same data structure can also support path reporting queries in $O(\lg \sigma + occ \lg \sigma)$ time, where occ is the size of output. In addition, we present a data structure that answers path reporting queries in $O(\lg \sigma + occ \lg\lg\sigma)$ time, using $O(n\lg\lg\sigma)$ space. These are the first data structures that answer path reporting queries.