Zig-zag Sort: A Simple Deterministic Data-Oblivious Sorting Algorithm Running in O(n log n) Time

We describe and analyze Zig-zag Sort--a deterministic data-oblivious sorting algorithm running in O(n log n) time that is arguably simpler than previously known algorithms with similar properties, which are based on the AKS sorting network. Because it is data-oblivious and deterministic, Zig-zag Sort can be implemented as a simple O(n log n)-size sorting network, thereby providing a solution to an open problem posed by Incerpi and Sedgewick in 1985. In addition, Zig-zag Sort is a variant of Shellsort, and is, in fact, the first deterministic Shellsort variant running in O(n log n) time. The existence of such an algorithm was posed as an open problem by Plaxton et al. in 1992 and also by Sedgewick in 1996. More relevant for today, however, is the fact that the existence of a simple data-oblivious deterministic sorting algorithm running in O(n log n) time simplifies the inner-loop computation in several proposed oblivious-RAM simulation methods (which utilize AKS sorting networks), and this, in turn, implies simplified mechanisms for privacy-preserving data outsourcing in several cloud computing applications. We provide both constructive and non-constructive implementations of Zig-zag Sort, based on the existence of a circuit known as an epsilon-halver, such that the constant factors in our constructive implementations are orders of magnitude smaller than those for constructive variants of the AKS sorting network, which are also based on the use of epsilon-halvers.Comment: Appearing in ACM Symp. on Theory of Computing (STOC) 201

Linear-Time Algorithms for Geometric Graphs with Sublinearly Many Edge Crossings

We provide linear-time algorithms for geometric graphs with sublinearly many crossings. That is, we provide algorithms running in O(n) time on connected geometric graphs having n vertices and k crossings, where k is smaller than n by an iterated logarithmic factor. Specific problems we study include Voronoi diagrams and single-source shortest paths. Our algorithms all run in linear time in the standard comparison-based computational model; hence, we make no assumptions about the distribution or bit complexities of edge weights, nor do we utilize unusual bit-level operations on memory words. Instead, our algorithms are based on a planarization method that "zeroes in" on edge crossings, together with methods for extending planar separator decompositions to geometric graphs with sublinearly many crossings. Incidentally, our planarization algorithm also solves an open computational geometry problem of Chazelle for triangulating a self-intersecting polygonal chain having n segments and k crossings in linear time, for the case when k is sublinear in n by an iterated logarithmic factor.Comment: Expanded version of a paper appearing at the 20th ACM-SIAM Symposium on Discrete Algorithms (SODA09

Isotope discrimination by the stearoyl desaturase of Neurospora crassa

In wild type Neurospora crassa, we previously observed an unexpectedly low proportion of label in unsaturated fatty acids that should have been derived from deuterated palmitate (16:0). Interpretation of whether the position of deuteration could account for these results was inconclusive, because wild type had a low proportion of total fatty acids derived from the deuterated supplement. The N. crassa cel-1 strain is ideally suited for studies of fatty acid enrichment, because cel-1 must obtain its fatty acids exogenously. We supplemented cel-1 with 16:0\u27s deuterated at different positions. With each of the labelled 16:0\u27s, cel-1 desaturated the stearate (18:0) derived from the 16:0 more efficiently than wild type. However, when the 16:0 was deuterated at the site of future desaturation, we indeed observed effects on fatty acid composition and label distribution consistent with inhibition of the 18:0 desaturase

More is Less: Perfectly Secure Oblivious Algorithms in the Multi-Server Setting

The problem of Oblivious RAM (ORAM) has traditionally been studied in a single-server setting, but more recently the multi-server setting has also been considered. Yet it is still unclear whether the multi-server setting has any inherent advantages, e.g., whether the multi-server setting can be used to achieve stronger security goals or provably better efficiency than is possible in the single-server case. In this work, we construct a perfectly secure 3-server ORAM scheme that outperforms the best known single-server scheme by a logarithmic factor. In the process, we also show, for the first time, that there exist specific algorithms for which multiple servers can overcome known lower bounds in the single-server setting.Comment: 36 pages, Accepted in Asiacrypt 201

Security by Spatial Reference:Using Relative Positioning to Authenticate Devices for Spontaneous Interaction

Spontaneous interaction is a desirable characteristic associated with mobile and ubiquitous computing. The aim is to enable users to connect their personal devices with devices encountered in their environment in order to take advantage of interaction opportunities in accordance with their situation. However, it is difficult to secure spontaneous interaction as this requires authentication of the encountered device, in the absence of any prior knowledge of the device. In this paper we present a method for establishing and securing spontaneous interactions on the basis of emphspatial references that capture the spatial relationship of the involved devices. Spatial references are obtained by accurate sensing of relative device positions, presented to the user for initiation of interactions, and used in a peer authentication protocol that exploits a novel mechanism for message transfer over ultrasound to ensures spatial authenticity of the sender

HST Imaging Polarimetry of the Gravitational Lens FSC10214+4724

We present imaging polarimetry of the extremely luminous, redshift 2.3 IRAS source FSC10214+4724. The observations were obtained with HST's Faint Object Camera in the F437M filter, which is free of strong emission lines. The 0.7 arcsec long arc is unresolved to 0.04 arcsec FWHM in the transverse direction, and has an integrated polarization of 28 +/- 3 percent, in good agreement with ground-based observations. The polarization position angle varies along the arc by up to 35 deg. The overall position angle is 62 +/- 3 deg east of north. No counterimage is detected to B = 27.5 mag ($3\sigma$), giving an observed arc to counterimage flux ratio greater than 250, considerably greater than the flux ratio of 100 measured previously in the I-band. This implies that the configuration of the object in the source plane at the B-band is different from that at I-band, and/or that the lensing galaxy is dusty.Comment: 17 pages, 3 figures. Accepted for publication in Astronomical Journal, February 199

Oxygen Isotope Ratios of Magnetite in CI-Like Clasts from a Polymict Ureilite

Polymict ureilites contain a variety of Less than or equal to mm to cm sized non-ureilitic clasts, many of which can be identifed as chondritic and achondritic meteorite types. Among them, dark clasts have been observed in polymict ureilites that are similar to CI chondrites in mineralogy, containing phyllosilicates, magnetite, sulfide and carbonates. Bulk oxygen isotope analyses of a dark clast in Nilpena plot along the CCAM line and above the terrestrial fractionation line, on the O-poor extension of the main group ureilite trend and clearly different from bulk CI chondrites. One possible origins of such dark clast is that they represent aqueously altered precursors of ureilite parent body (UPB) that were preserved on the cold surface of the UPB. Oxygen isotope analyses of dark clasts are key to better understanding their origins. Oxygen isotope ratios of magnetite are of special interest because they reflect the compositions of the fluids in asteroidal bodies. In primitive chondrites, Delta O (= Delta O - 0.52 Delta O) values of magnetites are always higher than those of the bulk meteorites and represent minimum Delta O values of the initial O-poor aqueous fluids in the parent body. Previous SIMS analyses on magnetite and fayalite in dark clasts from the DaG 319 polymict ureilite were analytically difficult due to small grain sizes, though data indicated positive Delta O values of 3-4 per mille, higher than that of the dark clast in Nilpena (1.49per mille)

A New Perspective on Clustered Planarity as a Combinatorial Embedding Problem

The clustered planarity problem (c-planarity) asks whether a hierarchically clustered graph admits a planar drawing such that the clusters can be nicely represented by regions. We introduce the cd-tree data structure and give a new characterization of c-planarity. It leads to efficient algorithms for c-planarity testing in the following cases. (i) Every cluster and every co-cluster (complement of a cluster) has at most two connected components. (ii) Every cluster has at most five outgoing edges. Moreover, the cd-tree reveals interesting connections between c-planarity and planarity with constraints on the order of edges around vertices. On one hand, this gives rise to a bunch of new open problems related to c-planarity, on the other hand it provides a new perspective on previous results.Comment: 17 pages, 2 figure

Fermi-surface topology of the iron pnictide LaFe2_2P2_2

We report on a comprehensive de Haas--van Alphen (dHvA) study of the iron pnictide LaFe$_2$P$_2$. Our extensive density-functional band-structure calculations can well explain the measured angular-dependent dHvA frequencies. As salient feature, we observe only one quasi-two-dimensional Fermi-surface sheet, i.e., a hole-like Fermi-surface cylinder around $\Gamma$, essential for $s_\pm$ pairing, is missing. In spite of considerable mass enhancements due to many-body effects, LaFe$_2$P$_2$ shows no superconductivity. This is likely caused by the absence of any nesting between electron and hole bands.Comment: 5 pages, 4 figure