The predecessor problem is a key component of the fundamental sorting-and-searching
core of algorithmic problems. While binary search is the optimal solution in the comparison …

We present a number of new results about range searching for colored (or" categorical")
data: 1. For a set of $ n $ colored points in three dimensions, we describe randomized data …

We revisit the classic problem of simplex range searching and related problems in
computational geometry. We present a collection of new results which improve previous …

In this paper we present new data structures for two extensively studied variants of the
orthogonal range searching problem. First, we describe a data structure that supports two …

Given a set of points P and a set of regions O, an incidence is a pair (p, o)∈ P× O such that
p∈ o. We obtain a number of new results on a classical question in combinatorial geometry …

Range searching on categorical, or “colored”, data has been studied extensively for over two
decades. In this paper, we obtain the current best results for perhaps the most basic, and …

Let T [1, n] be a string of length n and T [i, j] be the substring of T starting at position i and
ending at position j. A substring T [i, j] of T is a repeat if it occurs more than once in T; …

We introduce the first index that can be built in $ o (n) $ time for a text of length $ n $, and
can also be queried in $ o (q) $ time for a pattern of length $ q $. On an alphabet of size …

Top-k search, which reports the k elements of the highest importance from all the elements
in an underlying dataset that satisfy a certain predicate, has attracted significant attention …

We study the orthogonal range reporting and rectangle stabbing problems in moderate
dimensions, ie, when the dimension is c log⁡(n) for some constant c. In orthogonal range …