Discrepancy-Sensitive Dynamic Fractional Cascading, Dominated Maxima Searching, and 2-d Nearest Neighbors in Any Minkowski Metric

  title={Discrepancy-Sensitive Dynamic Fractional Cascading, Dominated Maxima Searching, and 2-d Nearest Neighbors in Any Minkowski Metric},
  author={Mikhail J. Atallah and Marina Blanton and Michael T. Goodrich and Stanislas Polu},
This paper studies a discrepancy-sensitive approach to dynamic fractional cascading. We provide an efficient data structure for dominated maxima searching in a dynamic set of points in the plane, which in turn leads to an efficient dynamic data structure that can answer queries for nearest neighbors using any Minkowski metric. 
2 Citations
Dynamic Data Structures : Orthogonal Range Queries and Update Efficiency
English) We study dynamic data structures for different variants of orthogonal range reporting query problems. In particular, we consider (1) the planar orthogonal 3-sided range reporting problem:
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Finding nearest neighbors in growth-restricted metrics
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Navigating nets: simple algorithms for proximity search
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Fully-dynamic two dimensional orthogonal range and line segment intersection reporting in logarithmic time
If n is the number of stored elements, then these problems can be solved in worst case time Θ(log n) plus time proportional to the size of the output pr.
Nearest-Neighbor Searching and Metric Space Dimensions
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Dynamic fractional cascading
This paper shows that fractional cascading also supports insertions into and deletions from the lists efficiently and shows that queries, insertions, and deletion into segment trees or range trees can be supported in timeO(logn log logn), whenn is the number of segments (points).
Fractional cascading: I. A data structuring technique
This paper shows that, if ordered lists can be put in a one-to-one correspondence with the nodes of a graph of degreed so that the iterative search always proceeds along edges of that graph, then this structure can be built, called afractional cascading structure, in which all original searches after the first can be carried out at only logd extra cost per search.
Optimal Expected-Time Algorithms for Closest Point Problems
Algorithms for solving a number of closest-point problems in k- space, including nearest neighbor searching, finding all nearest neighbors, and computing planar minimum spanning trees can be implemented to solve practical problems very efficiently.
Fractional cascading: II. Applications
This paper presents several applications offractional cascading, a new searching technique which has been described in a companion paper. The applications center around a variety of geometric query
Fractional Cascading Revisited
  • Sandeep Sen
  • Mathematics, Computer Science
    J. Algorithms
  • 1995
This work presents an alternative implementation of the fractional cascading data structure of Chazelle and Guibas that performs iterative search for a key in multiple ordered lists and uses tools from branching process theory to derive some useful asymptotic bounds.