Showing papers by "Gerth Stølting Brodal published in 2019"

Dynamic Planar Convex Hull

Abstract: In this article, we determine the amortized computational complexity of the planar dynamic convex hull problem by querying. We present a data structure that maintains a set of n points in the plane under the insertion and deletion of points in amortized O(log n) time per operation. The space usage of the data structure is O(n). The data structure supports extreme point queries in a given direction, tangent queries through a given point, and queries for the neighboring points on the convex hull in O(log n) time. The extreme point queries can be used to decide whether or not a given line intersects the convex hull, and the tangent queries to determine whether a given point is inside the convex hull. We give a lower bound on the amortized asymptotic time complexity that matches the performance of this data structure.

Data Structures for the Cloud and External Memory Data (Dagstuhl Seminar 19051)

Abstract: This report documents the program and the outcomes of Dagstuhl Seminar 16101 "Data Structures for the Cloud and External Memory Data". In today's computing environment vast amounts of data are processed, exchanged and analyzed. The manner in which information is stored profoundly influences the efficiency of these operations over the data. In spite of the maturity of the field many data structuring problems are still open, while new ones arise due to technological advances. The seminar covered both recent advances in the "classical" data structuring topics as well as new models of computation adapted to modern architectures, scientific studies that reveal the need for such models, applications where large data sets play a central role, modern computing platforms for very large data, and new data structures for large data in modern architectures. The extended abstracts included in this report contain both recent state of the art advances and lay the foundation for new directions within data structures research.