We present memory-efficient deterministic algorithms for constructing #-nets and #-approximations of streams of geometric data. Unlike probabilistic approaches, these deterministic samples provide guaranteed bounds on their approximation factors. We show how our deterministic samples can be used to answer approximate online iceberg geometric queries on data streams. We use these techniques to approximate several robust statistics of geometric data streams, including Tukey depth, simplicial depth, regression depth, the Thiel-Sen estimator, and the least median of squares. Our algorithms use only a polylogarithmic amount of memory, provided the desired approximation factors are inverse-polylogarithmic. We also include a lower bound for non-iceberg geometric queries.

. We present an implementation of Luby's algorithm for the calculation of maximal independent sets in graphs on the Cray T3E. 1 Introduction Due to the increasing practical availability of powerful parallel architectures, the investigation of parallel algorithms has become a major research topic in the eld of theoretical computer science. A widely used model for the high level description of parallel algorithms is the PRAM-model, see e.g. [8]. A computational problem is considered to be eciently solvable in parallel, if it can be solved in polylogarithmic time, i.e., time O(log k (n)) for a xed k 0, with polynomially many processors on a PRAM. The class of all these computational problems is called NC, see e.g. [16]. The development of NC-algorithms for practically and theoretically relevant problems is a major research eld in theoretical computer science. In this paper we consider the problem of calculating a maximal independent set in a given graph, briey MIS problem. A ma...