The Firefighter Problem: A Structural Analysis

We consider the complexity of the firefighter problem where b>=1 firefighters are available at each time step. This problem is proved NP-complete even on trees of degree at most three and budget one (Finbow et al.,2007) and on trees of bounded degree b+3 for any fixed budget b>=2 (Bazgan et al.,2012). In this paper, we provide further insight into the complexity landscape of the problem by showing that the pathwidth and the maximum degree of the input graph govern its complexity. More precisely, we first prove that the problem is NP-complete even on trees of pathwidth at most three for any fixed budget b>=1. We then show that the problem turns out to be fixed parameter-tractable with respect to the combined parameter "pathwidth" and "maximum degree" of the input graph

The ESO Slice Project (ESP) galaxy redshift survey: III. The Sample

The ESO Slice Project (ESP) is a galaxy redshift survey extending over about 23 square degrees, in a region near the South Galactic Pole. The survey is ~85% complete to the limiting magnitude b_J=19.4 and consists of 3342 galaxies with redshift determination. The ESP survey is intermediate between shallow, wide angle samples and very deep, one-dimensional pencil beams; the spanned volume is ~ 5 x 10^4 Mpc^3 at the sensitivity peak (z ~ 0.1). In this paper we present the description of the observations and of the data reduction, the ESP redshift catalogue and the analysis of the quality of the velocity determinations.Comment: 10 pages, 4 encapsulated figures, uses A&A LATEX; A&A Supplements in press (June 1998 issue

Spatial and kinematic alignments between central and satellite halos

Based on a cosmological N-body simulation we analyze spatial and kinematic alignments of satellite halos within six times the virial radius of group size host halos (Rvir). We measure three different types of spatial alignment: halo alignment between the orientation of the group central substructure (GCS) and the distribution of its satellites, radial alignment between the orientation of a satellite and the direction towards its GCS, and direct alignment between the orientation of the GCS and that of its satellites. In analogy we use the directions of satellite velocities and probe three further types of alignment: the radial velocity alignment between the satellite velocity and connecting line between satellite and GCS, the halo velocity alignment between the orientation of the GCS and satellite velocities and the auto velocity alignment between the satellites orientations and their velocities. We find that satellites are preferentially located along the major axis of the GCS within at least 6 Rvir (the range probed here). Furthermore, satellites preferentially point towards the GCS. The most pronounced signal is detected on small scales but a detectable signal extends out to 6 Rvir. The direct alignment signal is weaker, however a systematic trend is visible at distances < 2 Rvir. All velocity alignments are highly significant on small scales. Our results suggest that the halo alignment reflects the filamentary large scale structure which extends far beyond the virial radii of the groups. In contrast, the main contribution to the radial alignment arises from the adjustment of the satellite orientations in the group tidal field. The projected data reveal good agreement with recent results derived from large galaxy surveys. (abridged)Comment: accepted for publication in Ap

The Opacity of Nearby Galaxies from Counts of Background Galaxies: II. Limits of the Synthetic Field Method

Recently, we have developed and calibrated the Synthetic Field Method (SFM) to derive the total extinction through disk galaxies. The method is based on the number counts and colors of distant background field galaxies that can be seen through the foreground object, and has been successfully applied to NGC 4536 and NGC 3664, two late-type galaxies located, respectively, at 16 and 11 Mpc. Here, we study the applicability of the SFM to HST images of galaxies in the Local Group, and show that background galaxies cannot be easily identified through these nearby objects, even with the best resolution available today. In the case of M 31, each pixel in the HST images contains 50 to 100 stars, and the background galaxies cannot be seen because of the intrinsic granularity due to strong surface brightness fluctuations. In the LMC, on the other hand, there is only about one star every six linear pixels, and the lack of detectable background galaxies results from a ``secondary'' granularity, introduced by structure in the wings of the point spread function. The success of the SFM in NGC 4536 and NGC 3664 is a natural consequence of the reduction of the intensity of surface brightness fluctuations with distance. When the dominant confusion factor is structure in the PSF wings, as is the case of HST images of the LMC, and would happen in M 31 images obtained with a 10-m diffraction- limited optical telescope, it becomes in principle possible to improve the detectability of background galaxies by subtracting the stars in the foreground object. However, a much better characterization of optical PSFs than is currently available would be required for an adequate subtraction of the wings. Given the importance of determining the dust content of Local Group galaxies, efforts should be made in that direction.Comment: 45 pages, 10 Postscript figure

Decision Tree Classifiers for Star/Galaxy Separation

We study the star/galaxy classification efficiency of 13 different decision tree algorithms applied to photometric objects in the Sloan Digital Sky Survey Data Release Seven (SDSS DR7). Each algorithm is defined by a set of parameters which, when varied, produce different final classification trees. We extensively explore the parameter space of each algorithm, using the set of $884,126$ SDSS objects with spectroscopic data as the training set. The efficiency of star-galaxy separation is measured using the completeness function. We find that the Functional Tree algorithm (FT) yields the best results as measured by the mean completeness in two magnitude intervals: $14\le r\le21$ ($85.2$) and $r\ge19$ ($82.1$). We compare the performance of the tree generated with the optimal FT configuration to the classifications provided by the SDSS parametric classifier, 2DPHOT and Ball et al. (2006). We find that our FT classifier is comparable or better in completeness over the full magnitude range $15\le r\le21$, with much lower contamination than all but the Ball et al. classifier. At the faintest magnitudes ($r>19$), our classifier is the only one able to maintain high completeness ($>$80%) while still achieving low contamination ($\sim2.5$). Finally, we apply our FT classifier to separate stars from galaxies in the full set of $69,545,326$ SDSS photometric objects in the magnitude range $14\le r\le21$.Comment: Submitted to A