Heaps and heapsort on secondary storage

AbstractA heap structure designed for secondary storage is suggested that tries to make the best use of the available buffer space in primary memory. The heap is a complete multi-way tree, with multi-page blocks of records as nodes, satisfying a generalized heap property. A special feature of the tree is that the nodes may be partially filled, as in B-trees. The structure is complemented with priority-queue operations insert and delete-max. When handling a sequence of S operations, the number of page transfers performed is shown to be O(∑i = 1S(1P) log(MP)(NiP)), where P denotes the number of records fitting into a page, M the capacity of the buffer space in records, and Ni, the number of records in the heap prior to the ith operation (assuming P ⩾ 1 and S > M ⩾ c · P, where c is a small positive constant). The number of comparisons required when handling the sequence is O(∑i = 1S log2 Ni). Using the suggested data structure we obtain an optimal external heapsort that performs O((NP) log(MP)(NP)) page transfers and O(N log2 N) comparisons in the worst case when sorting N records

The Open Graph Archive: A Community-Driven Effort

In order to evaluate, compare, and tune graph algorithms, experiments on well designed benchmark sets have to be performed. Together with the goal of reproducibility of experimental results, this creates a demand for a public archive to gather and store graph instances. Such an archive would ideally allow annotation of instances or sets of graphs with additional information like graph properties and references to the respective experiments and results. Here we examine the requirements, and introduce a new community project with the aim of producing an easily accessible library of graphs. Through successful community involvement, it is expected that the archive will contain a representative selection of both real-world and generated graph instances, covering significant application areas as well as interesting classes of graphs.Comment: 10 page

UBVRI photopolarimetry of the long period eclipsing AM Herculis binary V1309

We report simultaneous UBVRI photo-polarimetric observations of the long period (7.98 h) AM Her binary V1309 Ori. The length and shape of the eclipse ingress and egress varies from night to night. We suggest this is due to the variation in the brightness of the accretion stream. By comparing the phases of circular polarization zero-crossovers with previous observations, we confirm that V1309 Ori is well synchronized, and find an upper limit of 0.002 percent for the difference between the spin and orbital periods. We model the polarimetry data using a model consisting of two cyclotron emission regions at almost diametrically opposite locations, and centered at colatitude 35 (deg) and 145 (deg) on the surface of the white dwarf. We also present archive X-ray observations which show that the negatively polarised accretion region is X-ray bright.Comment: 11 pages, 12 figures (2 colour), Fig1 and Fig 4 are in lower resolution than in original paper, accepted for publication in Monthly Notices of the Royal Astronomical Societ

QuickXsort: Efficient Sorting with n log n - 1.399n +o(n) Comparisons on Average

In this paper we generalize the idea of QuickHeapsort leading to the notion of QuickXsort. Given some external sorting algorithm X, QuickXsort yields an internal sorting algorithm if X satisfies certain natural conditions. With QuickWeakHeapsort and QuickMergesort we present two examples for the QuickXsort-construction. Both are efficient algorithms that incur approximately n log n - 1.26n +o(n) comparisons on the average. A worst case of n log n + O(n) comparisons can be achieved without significantly affecting the average case. Furthermore, we describe an implementation of MergeInsertion for small n. Taking MergeInsertion as a base case for QuickMergesort, we establish a worst-case efficient sorting algorithm calling for n log n - 1.3999n + o(n) comparisons on average. QuickMergesort with constant size base cases shows the best performance on practical inputs: when sorting integers it is slower by only 15% to STL-Introsort

Discovery of polarised emission from the long period intermediate polar RX J2133.7+5107

Aims. We intended to investigate the magnetic field properties of the recently identified intermediate polar RX J2133.7+5107. Methods. We carried out UBVRI photopolarimetric observations of the target using TURPOL on the Nordic Optical Telescope over 2 nights in July/August 2006. Results. We found that RX J2133.7+5107 emits circularly polarized light in all UBVRI bands (up to 3%). This is the first detection of circular polarization in this object. The circular polarization modulations and flux variations give hints of cyclotron beaming effects and suggest that the field strength in RX J2133.7+5107 is possibly one of the highest found amongst the IPs. Conclusions. The highly asynchronous rotation of RX J2133.7+5107 (the spin to orbital period ratio is ~0.022), suggests that it has only recently come into contact and although it is likely to evolve into a polar, it is currently a long way from doing so. We suggest a possible link between the detection of a soft X-ray blackbody component and polarized optical emission in intermediate polars

Circular polarization survey of intermediate polars I. Northern targets in the range 17h<R.A.<23h

Context. The origin, evolution, and ultimate fate of magnetic cataclysmic variables are poorly understood. It is largely the nature of the magnetic fields in these systems that leads to this poor understanding. Fundamental properties, such as the field strength and the axis alignment, are unknown in a majority of these systems. Aims. We undertake to put all the previous circular polarization measurements into context and systematically survey intermediate polars for signs of circular polarization, hence to get an indication of their true magnetic field strengths and try to understand the evolution of magnetic cataclysmic variables. Methods. We used the TurPol instrument at the Nordic Optical Telescope to obtain simultaneous UBVRI photo-polarimetric observations of a set of intermediate polars, during the epoch 2006 July 31 - August 2. Results. Of this set of eight systems two (1RXS J213344.1+510725 and 1RXS J173021.5-055933) were found to show significant levels of circular polarization, varying with spin phase. Five others (V2306 Cyg, AO Psc, DQ Her, FO Aqr, and V1223 Sgr) show some evidence for circular polarization and variation of this with spin phase, whilst AE Aqr shows little evidence for polarized emission. We also report the first simultaneous UBVRI photometry of the newly identified intermediate polar 1RXS J173021.5-055933. Conclusions. Circular polarization may be ubiquitous in intermediate polars, albeit at a low level of one or two percent or less. It is stronger at longer wavelengths in the visible spectrum. Our results lend further support to the possible link between the presence of soft X-ray components and the detectability of circular polarization in intermediate polars.Comment: 14 pages. Accepted for publication in A&

Pulsations and orbital modulation of the intermediate polar 1WGA J1958.2+3232

We present optical photometry, spectroscopy and photopolarimetry, as well as ASCA X-ray observations, of the recently discovered intermediate polar 1WGA J1958.2+3232. Through the first detection of an optical beat frequency, we confirm the previously tentative suggestion that the spin period of the white dwarf is twice the X-ray and optical pulsation period, which we also confirm in each case. We detect an orbital modulation in each of the U, B, V, R and I bands for the first time, and suggest that the true orbital period is the -1d alias of that previously suggested. We also confirm the presence of circular polarization in this system, detecting a variable polarization which has opposite signs in each of the B and R bands. The double peaked pulse profile and oppositely signed polarization pulses suggest that 1WGA J1958.2+3232 accretes onto both magnetic poles via a disc which is truncated relatively close to the white dwarf.Comment: All figures now included as postscrip

Day-Scale Variability of 3C 279 and Searches for Correlations in Gamma-Ray, X-Ray, and Optical Bands

Light curves of 3C 279 are presented in optical (R-band), X-rays (RXTE/PCA), and gamma rays (CGRO/EGRET) for 1999 Jan-Feb and 2000 Jan-Mar. During both of those epochs the gamma-ray levels were high, and all three observed bands demonstrated substantial variation, on time scales as short as one day. Correlation analyses provided no consistent pattern, although a rather significant optical/gamma-ray correlation was seen in 1999, with a gamma-ray lag of ~2.5 days, and there are other suggestions of correlations in the light curves. For comparison, correlation analysis is also presented for the gamma-ray and X-ray light curves during the large gamma ray flare in 1996 Feb and the two gamma-bright weeks leading up to it; the correlation at that time was strong, with a gamma-ray/X-ray offset of no more than 1 day.Comment: 20 pages, including 7 figures; accepted by The Astrophysical Journa