Year: 2011
Type: preprint
Abstract: We describe fully retroactive dynamic data structures for approximate range reporting and approximate nearest neighbor reporting. We show how to maintain, for any positive constant $d$, a set of $n$ points in $\R^d$ indexed by time such that we can perform insertions or deletions at any point in the timeline in $O(\log n)$ amortized time. We support, for any small constant $ε>0$, $(1+ε)$-approximate range reporting queries at any point in the timeline in $O(\log n + k)$ time, where $k$ is the output size. We also show how to answer $(1+ε)$-approximate nearest neighbor queries for any point in the past or present in $O(\log n)$ time.
Source: arXiv (Cornell University)
Authors: Goodrich, Michael T., Simons, Joseph A.
Institution: University of California, Irvine
Language: English
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2951132861