CS 269S, Winter 2011: Theory Seminar
ICS 243
6 May 2011:

Speaker: Joe Simons

Fully Retroactive Approximate Range and Nearest Neighbor Searching

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 epsilon>0, (1+ epsilon)-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+epsilon)-approximate nearest neighbor queries for any point in the past or present in O(log n) time. Joint work with Michael Goodrich.