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We present a new technique for half-space and simplex range query using <italic>&Ogr;</italic>(<italic>n</italic>) space and <italic>&Ogr;</italic>(<italic>n</italic><supscrpt><italic>a</italic></supscrpt>) query time, where <italic>a</italic> &lt; <italic>d</italic>(d-1)/<italic>d</italic>(<italic>d</italic>-1) + 1 + &#947; for all dimensions(More)
We present a simple randomized algorithm which solves linear programs with <italic>n</italic> constraints and <italic>d</italic> variables in expected <italic>O</italic>(<italic>nde</italic><supscrpt>(<italic>d</italic> ln(<italic>n</italic>+1))<supscrpt>1/4</supscrpt></supscrpt>) time in the unit cost model (where we count the number of arithmetic(More)
A simple randomized algorithm is developed which computes the smallest enclosing disk of a nite set of points in the plane in expected linear time. The algorithm is based on Seidel's recent Linear Programming algorithm, and it can be generalized to computing smallest enclosing balls or ellipsoids of point sets in higher dimensions in a straightforward way.(More)
In this work we study the problem of determining the throughput capacity of a wireless network. We propose a scheduling algorithm to achieve this capacity within an approximation factor. Our analysis is performed in the physical interference model, where nodes are arbitrarily distributed in Euclidean space. We consider the problem separately from the(More)
Suppose we are given (the edge graph of) an dimensional hypercube with its edges oriented so that every face has a unique sink. Such an orientation is called a unique sink orientation, and we are interested in finding the unique sink of the whole cube, when the orientation is given implicitly. The basic operation available is the socalled vertex evaluation,(More)
We are given a two-dimensional square grid of size N N, where N := 2 n and n 0. A space lling curve (SFC) is a numbering of the cells of this grid with numbers from c + 1 to c + N 2 , for some c 0. We call a SFC recursive (RSFC) if it can be recursively divided into four square RSFCs of equal size. Examples of well-known RSFCs include the Hilbert curve, the(More)