An In-Place Sorting with O(n log n) Comparisons and O(n) Moves

We present the first in-place algorithm for sorting an array of size n that performs, in the worst case, at most O(n log n) element comparisons and O(n) element transports. This solves a long-standing open problem, stated explicitly, e.g., in [J.I. Munro and V. Raman, Sorting with minimum data movement, J. Algorithms, 13, 374-93, 1992], of whether there exists a sorting algorithm that matches the asymptotic lower bounds on all computational resources simultaneously

Cache-Oblivious Data Structures and Algorithms for Undirected Breadth-First Search and Shortest Paths

We present improved cache-oblivious data structures and algorithms for breadth-first search (BFS) on undirected graphs and the single-source shortest path (SSSP) problem on undirected graphs with non-negative edge weights. For the SSSP problem, our result closes the performance gap between the currently best cache-aware algorithm and the cache-oblivious counterpart. Our cache-oblivious SSSP-algorithm takes nearly full advantage of block transfers for dense graphs. The algorithm relies on a new data structure, called bucket heap, which is the first cache-oblivious priority queue to efficiently support a weak DECREASEKEY operation. For the BFS problem, we reduce the number of I/Os for sparse graphs by a factor of nearly sqrt{B}, where B is the cache-block size, nearly closing the performance gap between the currently best cache-aware and cache-oblivious algorithms

Permuting and Batched Geometric Lower Bounds in the I/O Model

We study permuting and batched orthogonal geometric reporting problems in the External Memory Model (EM), assuming indivisibility of the input records. Our main results are twofold. First, we prove a general simulation result that essentially shows that any permutation algorithm (resp. duplicate removal algorithm) that does alpha*N/B I/Os (resp. to remove a fraction of the existing duplicates) can be simulated with an algorithm that does alpha phases where each phase reads and writes each element once, but using a factor alpha smaller block size. Second, we prove two lower bounds for batched rectangle stabbing and batched orthogonal range reporting queries. Assuming a short cache, we prove very high lower bounds that currently are not possible with the existing techniques under the tall cache assumption

Modeling Endogenous Mobility in Earnings Determination

We evaluate the bias from endogenous job mobility in fixed-effects estimates of worker- and firm-specific earnings heterogeneity using longitudinally linked employer-employee data from the LEHD infrastructure file system of the U.S. Census Bureau. First, we propose two new residual diagnostic tests of the assumption that mobility is exogenous to unmodeled determinants of earnings. Both tests reject exogenous mobility. We relax the exogenous mobility assumptions by modeling the evolution of the matched data as an evolving bipartite graph using a Bayesian latent class framework. Our results suggest that endogenous mobility biases estimated firm effects toward zero. To assess validity, we match our estimates of the wage components to out-of-sample estimates of revenue per worker. The corrected estimates attribute much more of the variation in revenue per worker to variation in match quality and worker quality than the uncorrected estimates

Aspects of k-k-Routing in Meshes and OTIS Networks

Aspects of k-k Routing in Meshes and OTIS-Networks Abstract Efficient data transport in parallel computers build on sparse interconnection networks is crucial for their performance. A basic transport problem in such a computer is the k-k routing problem. In this thesis, aspects of the k-k routing problem on r-dimensional meshes and OTIS-G networks are discussed. The first oblivious routing algorithms for these networks are presented that solve the k-k routing problem in an asymptotically optimal running time and a constant buffer size. Furthermore, other aspects of the k-k routing problem for OTIS-G networks are analysed. In particular, lower bounds for the problem based on the diameter and bisection width of OTIS-G networks are given, and the k-k sorting problem on the OTIS-Mesh is considered. Based on OTIS-G networks, a new class of networks, called Extended OTIS-G networks, is introduced, which have smaller diameters than OTIS-G networks.Für die Leistungfähigkeit von Parallelrechnern, die über ein Verbindungsnetzwerk kommunizieren, ist ein effizienter Datentransport entscheidend. Ein grundlegendes Transportproblem in einem solchen Rechner ist das k-k Routing Problem. In dieser Arbeit werden Aspekte dieses Problems in r-dimensionalen Gittern und OTIS-G Netzwerken untersucht. Es wird der erste vergessliche (oblivious) Routing Algorithmus vorgestellt, der das k-k Routing Problem in diesen Netzwerken in einer asymptotisch optimalen Laufzeit bei konstanter Puffergröße löst. Für OTIS-G Netzwerke werden untere Laufzeitschranken für das untersuchte Problem angegeben, die auf dem Durchmesser und der Bisektionsweite der Netzwerke basieren. Weiterhin wird ein Algorithmus vorgestellt, der das k-k Sorting Problem mit einer Laufzeit löst, die nahe an der Bisektions- und Durchmesserschranke liegt. Basierend auf den OTIS-G Netzwerken, wird eine neue Klasse von Netzwerken eingeführt, die sogenannten Extended OTIS-G Netzwerke, die sich durch einen kleineren Durchmesser von OTIS-G Netzwerken unterscheiden