Theis Rauhe

New data structures for orthogonal range searching

We present new general techniques for static orthogonal range searching problems in two and higher dimensions. For the general range reporting problem in R/sup 3/, we achieve query time O(log n+k) using space O(n log/sup 1+/spl epsiv// n), where n denotes the number of stored points and k the number of points to be reported. For the range reporting problem on an n/spl times/n grid, we achieve query time O(log log n+k) using space O(n log/sup /spl epsiv// n). For the two-dimensional semi-group range sum problem we achieve query time O(log n) using space O(n log n).

Compact Labeling Scheme for Ancestor Queries

We consider the following problem. Given a rooted tree

Marked ancestor problems

T

Nearest common ancestors: a survey and a new distributed algorithm

, label the nodes of

Labeling Schemes for Small Distances in Trees

T

Small induced-universal graphs and compact implicit graph representations

in the most compact way such that, given the labels of two nodes

Optimal static range reporting in one dimension

u

Nearest Common Ancestors: A Survey and a New Algorithm for a Distributed Environment

and

Mona: Monadic Second-Order Logic in Practice

v

Optimal time-space trade-offs for sorting

, one can determine in constant time, by looking only at the labels, whether