We present a data structure to maintain a set of intervals on the real line subject to fast insertions and deletions of the intervals, stabbing queries, and local updates. Intuitively, a local update replaces an interval by another one of roughly the same size and location. We inves-tigate whether local updates can be implemented faster than a deletion followed by an insertion. We present the first results for this problem for sets of possibly over-lapping intervals. If the maximum depth of the overlap (a.k.a. ply) is bounded by a constant, our data structure performs insertions, dele-tions and stabbing queries in time O(log n), and local updates in time O(log n/ log log n), where n is the number of intervals. We also analyze the dependence on the ply when it is not constant. Our results are adap-tive: the times depend on the current ply at the time of each operation.
CITATION STYLE
Khramtcova, E., & LöO?Er, M. (2017). Dynamic stabbing queries with sub-logarithmic local updates for overlapping intervals. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 10304 LNCS, pp. 176–190). Springer Verlag. https://doi.org/10.1007/978-3-319-58747-9_17
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