190 research outputs found

    Relating the Time Complexity of Optimization Problems in Light of the Exponential-Time Hypothesis

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    Obtaining lower bounds for NP-hard problems has for a long time been an active area of research. Recent algebraic techniques introduced by Jonsson et al. (SODA 2013) show that the time complexity of the parameterized SAT(⋅\cdot) problem correlates to the lattice of strong partial clones. With this ordering they isolated a relation RR such that SAT(RR) can be solved at least as fast as any other NP-hard SAT(⋅\cdot) problem. In this paper we extend this method and show that such languages also exist for the max ones problem (MaxOnes(Γ\Gamma)) and the Boolean valued constraint satisfaction problem over finite-valued constraint languages (VCSP(Δ\Delta)). With the help of these languages we relate MaxOnes and VCSP to the exponential time hypothesis in several different ways.Comment: This is an extended version of Relating the Time Complexity of Optimization Problems in Light of the Exponential-Time Hypothesis, appearing in Proceedings of the 39th International Symposium on Mathematical Foundations of Computer Science MFCS 2014 Budapest, August 25-29, 201

    65 Cybele in the thermal infrared: Multiple observations and thermophysical analysis

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    We investigated the physical and thermal properties of 65 Cybele}, one of the largest main-belt asteroids. Based on published and recently obtained thermal infrared observations, including ISO measurements, we derived through thermophysical modelling (TPM) a size of 302x290x232 km (+/- 4 %) and an geometric visible albedo of 0.050+/-0.005. Our model of a regolith covered surface with low thermal inertia and "default" roughness describes the wavelengths and phase angle dependent thermal aspects very well. Before/after opposition effect and beaming behaviour can be explained in that way. We found a constant emissivity of 0.9 at wavelengths up to about 100 micron and lower values towards the submillimetre range, indicating a grain size distribution dominated by 200 micron particle sizes. The spectroscopic analysis revealed an emissivity increase between 8.0 and 9.5 micron. We compared this emissivity behaviour with the Christiansen features of carbonaceous chondrite meteorites, but a conclusive identification was not possible. A comparison between the Standard Thermal Model (STM) and the applied TPM clearly demonstrates the limitations and problems of the STM for the analysis of multi-epoch and -wavelengths observations. While the TPM produced a unique diameter/albedo solution, the calculated STM values varied by +/-30 % and showed clear trends with wavelength and phase angle. Cybele can be considered as a nice textbook case for the thermophysical analysis of combined optical and thermal infrared observations.Comment: 11 pages, 8 figures, accepted for publication by A&

    Solar System Objects in the ISOPHOT 170 micron Serendipity Survey

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    The ISOPHOT Serendipity Survey (ISOSS) covered approximately 15 % of the sky at a wavelength of 170 micron while the ISO satellite was slewing from one target to the next. By chance ISOSS slews went over many solar system objects (SSOs). We identified the comets, asteroids and planets in the slews through a fast and effective search procedure based on N-body ephemeris and flux estimates. The detections were analysed from a calibration and scientific point of view. Through the measurements of the well-known asteroids Ceres, Pallas, Juno and Vesta and the planets Uranus and Neptune it was possible to improve the photometric calibration of ISOSS and to extend it to higher flux regimes. We were also able to establish calibration schemes for the important slew end data. For the other asteroids we derived radiometric diameters and albedos through a recent thermophysical model. The scientific results are discussed in the context of our current knowledge of size, shape and albedos, derived from IRAS observations, occultation measurements and lightcurve inversion techniques. In all cases where IRAS observations were available we confirm the derived diameters and albedos. For the five asteroids without IRAS detections only one was clearly detected and the radiometric results agreed with sizes given by occultation and HST observations. Four different comets have clearly been detected at 170 micron and two have marginal detections. The observational results are presented to be used by thermal comet models in the future. The nine ISOSS slews over Hale-Bopp revealed extended and asymmetric structures related to the dust tail. We attribute the enhanced emission in post-perihelion observations to large particles around the nucleus. The signal patterns are indicative of a concentration of the particles in trail direction.Comment: 15 pages, 6 figures, 6 tables; Accepted for publication in Astronomy and Astrophysic

    (1173) Anchises - Thermophysical and Dynamical Studies of a Dynamically Unstable Jovian Trojan

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    We have performed detailed thermophysical and dynamical modelling of Jovian Trojan (1173) Anchises. Our results reveal a most unusual object. By examining observational data taken by IRAS, Akari and WISE between 11.5 and 60 microns, along with variations in its optical lightcurve, we find Anchises is most likely an elongated body, with an axes-ratio of ~1.4. This yields calculated best-fit dimensions of 170x121x121km (an equivalent diameter of 136+18/-11km). We find the observations are best fit by Anchises having a retrograde sense of rotation, and an unusually high thermal inertia (25 to 100 Jm-2s-0.5K-1). The geometric albedo is found to be 0.027 (+0.006/-0.007). Anchises therefore has one of the highest published thermal inertias of any object larger than 100km in diameter, at such large heliocentric distances, and is one of the lowest albedo objects ever observed. More observations are needed to see if there is a link between the very shallow phase curve, with almost no opposition effect, and the derived thermal properties for this large Trojan asteroid. Our dynamical investigation of Anchises' orbit has revealed it to be dynamically unstable on timescales of hundreds of Myr, similar to the unstable Neptunian Trojans 2001 QR322 and 2008 LC18. Unlike those objects, we find that Anchises' dynamical stability is not a function of its initial orbital elements, the result of the exceptional precision with which its orbit is known. This is the first time that a Jovian Trojan has been shown to be dynamically unstable, and adds weight to the idea that planetary Trojans represent a significant ongoing contribution to the Centaur population, the parents of the short-period comets. The observed instability does not rule out a primordial origin for Anchises, but when taken in concert with the result of our thermophysical analysis, suggest that it would be a fascinating target for future study.Comment: 5 figures, 3 tables, accepted for publication in Monthly Notices of the Royal Astronomical Societ

    Catalogue of ISO LWS observations of asteroids

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    (Abridged) The Long Wavelength Spectrometer (LWS) onboard the Infrared Space Observatory (ISO) observed the four large main-belt asteroids (1) Ceres, (2) Pallas, (4) Vesta, and (10) Hygiea multiple times. The photometric and spectroscopic data cover the wavelength range between 43 and 197 um, and are a unique dataset for future investigations and detailed characterisations of these bodies. The standard ISO archive products, produced through the last post-mission LWS pipeline, were still affected by instrument artefacts. Our goal was to provide the best possible data products to exploit the full scientific potential of these observations. We performed a refined reduction of all measurements, corrected for various instrumental effects, and re-calibrated the data. We outline the data reduction process and give an overview of the available data and the quality of the observations. We apply a thermophysical model to the flux measurements to derive far-IR based diameter and albedo values of the asteroids. The measured thermal rotational lightcurve of (4) Vesta is compared to model predictions. The absolute photometric accuracy of the data products was foubd to be better than 10%. The calibrated spectra will serve as source for future mineralogical studies of dwarf planets and dwarf planet candidates.Comment: 11 pages, 6 figures, accepted for publication in A&

    Crossing Paths with Hans Bodlaender:A Personal View on Cross-Composition for Sparsification Lower Bounds

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    On the occasion of Hans Bodlaender’s 60th birthday, I give a personal account of our history and work together on the technique of cross-composition for kernelization lower bounds. I present several simple new proofs for polynomial kernelization lower bounds using cross-composition, interlaced with personal anecdotes about my time as Hans’ PhD student at Utrecht University. Concretely, I will prove that Vertex Cover, Feedback Vertex Set, and the H-Factor problem for every graph H that has a connected component of at least three vertices, do not admit kernels of (formula presented) bits when parameterized by the number of vertices n for any (formula presented), unless (formula presented). These lower bounds are obtained by elementary gadget constructions, in particular avoiding the use of the Packing Lemma by Dell and van Melkebeek.</p
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