In-Place Randomized Slope-Selection

Slope selection is a well-known algorithmic tool used in the context of computing robust estimators for fitting a line to a collection $mathcal{P}$ of $n$ points in the plane. We demonstrate that it is possible to perform slope selection in expected $mathcal{O}(n log n)$ time using only constant extra space in addition to the space needed for representing the input. Our solution is based upon a space-efficient variant of Matouv{s}ek\u27s randomized interpolation search, and we believe that the techniques developed in this paper will prove helpful in the design of space-efficient randomized algorithms using samples. To underline this, we also sketch how to compute the repeated median line estimator in an in-place setting

Oblivious Median Slope Selection

We study the median slope selection problem in the oblivious RAM model. In this model memory accesses have to be independent of the data processed, i.e., an adversary cannot use observed access patterns to derive additional information about the input. We show how to modify the randomized algorithm of Matou\v{s}ek (1991) to obtain an oblivious version with O(n log^2 n) expected time for n points in R^2. This complexity matches a theoretical upper bound that can be obtained through general oblivious transformation. In addition, results from a proof-of-concept implementation show that our algorithm is also practically efficient.Comment: 14 pages, to appear in Proceedings of CCCG 202

Detecting Quasars in Large-Scale Astronomical Surveys

We present a classification-based approach to identify quasi-stellar radio sources (quasars) in the Sloan Digital Sky Survey and evaluate its performance on a manually labeled training set. While reasonable results can already be obtained via approaches working only on photometric data, our experiments indicate that simple but problem-specific features extracted from spectroscopic data can significantly improve the classification performance. Since our approach works orthogonal to existing classification schemes used for building the spectroscopic catalogs, our classification results are well suited for a mutual assessment of the approaches' accuracies.Comment: 6 pages, 8 figures, published in proceedings of 2010 Ninth International Conference on Machine Learning and Applications (ICMLA) of the IEE

A Unified Approach for Indexed and Non-Indexed Spatial Joins

The original publication is available at www.springerlink.comL. Arge, O. Procopiuc, S. Ramaswamy, T. Suel, J. Vahrenhold, and J. S. Vitter. “A Unified Approach for Indexed and Non-Indexed Spatial Joins,” Proceedings of the 7th International Conference on Extending Database Technology (EDBT ’00), Konstanz, Germany, March 2000, published in Lecture Notes in Computer Science, Springer, 1777, Berlin, Germany, 413–429

Line-segment intersection made in-place

We present a space-efficient algorithm for reporting all k intersections induced by a set of n line segments in the plane. Our algorithm is an in-place variant of Balaban’s algorithm and, in the worst case, runs in O(n log2 n+k) time using O(1) extra words of memory in addition to the space used for the input to the algorithm

A Simple Algorithm for I/O-efficiently Pruning Dense Spanners

Given a geometric graph $G=(S,E)$ in $R^d$ with constant dilation $t$, and a positive constant $epsilon$, we show how to construct a $(1+epsilon)$-spanner of $G$ with $O(|S|)$ edges using $O(sort(|E|))$ I/O operations