Online Bin Covering with Limited Migration

Semi-online models where decisions may be revoked in a limited way have been studied extensively in the last years. This is motivated by the fact that the pure online model is often too restrictive to model real-world applications, where some changes might be allowed. A well-studied measure of the amount of decisions that can be revoked is the migration factor beta: When an object o of size s(o) arrives, the decisions for objects of total size at most beta * s(o) may be revoked. Usually beta should be a constant. This means that a small object only leads to small changes. This measure has been successfully investigated for different, classical problems such as bin packing or makespan minimization. The dual of makespan minimization - the Santa Claus or machine covering problem - has also been studied, whereas the dual of bin packing - the bin covering problem - has not been looked at from such a perspective. In this work, we extensively study the bin covering problem with migration in different scenarios. We develop algorithms both for the static case - where only insertions are allowed - and for the dynamic case, where items may also depart. We also develop lower bounds for these scenarios both for amortized migration and for worst-case migration showing that our algorithms have nearly optimal migration factor and asymptotic competitive ratio (up to an arbitrary small epsilon). We therefore resolve the competitiveness of the bin covering problem with migration

Around Kolmogorov complexity: basic notions and results

Algorithmic information theory studies description complexity and randomness and is now a well known field of theoretical computer science and mathematical logic. There are several textbooks and monographs devoted to this theory where one can find the detailed exposition of many difficult results as well as historical references. However, it seems that a short survey of its basic notions and main results relating these notions to each other, is missing. This report attempts to fill this gap and covers the basic notions of algorithmic information theory: Kolmogorov complexity (plain, conditional, prefix), Solomonoff universal a priori probability, notions of randomness (Martin-L\"of randomness, Mises--Church randomness), effective Hausdorff dimension. We prove their basic properties (symmetry of information, connection between a priori probability and prefix complexity, criterion of randomness in terms of complexity, complexity characterization for effective dimension) and show some applications (incompressibility method in computational complexity theory, incompleteness theorems). It is based on the lecture notes of a course at Uppsala University given by the author

Supervised semantic labeling of places using information extracted from sensor data

Indoor environments can typically be divided into places with different functionalities like corridors, rooms or doorways. The ability to learn such semantic categories from sensor data enables a mobile robot to extend the representation of the environment facilitating interaction with humans. As an example, natural language terms like “corridor” or “room” can be used to communicate the position of the robot in a map in a more intuitive way. In this work, we first propose an approach based on supervised learning to classify the pose of a mobile robot into semantic classes. Our method uses AdaBoost to boost simple features extracted from sensor range data into a strong classifier. We present two main applications of this approach. Firstly, we show how our approach can be utilized by a moving robot for an online classification of the poses traversed along its path using a hidden Markov model. In this case we additionally use as features objects extracted from images. Secondly, we introduce an approach to learn topological maps from geometric maps by applying our semantic classification procedure in combination with a probabilistic relaxation method. Alternatively, we apply associative Markov networks to classify geometric maps and compare the results with a relaxation approach. Experimental results obtained in simulation and with real robots demonstrate the effectiveness of our approach in various indoor environments

AMICO galaxy clusters in KiDS-DR3: sample properties and selection function

We present the first catalogue of galaxy cluster candidates derived from the third data release of the Kilo Degree Survey (KiDS-DR3). The sample of clusters has been produced using the Adaptive Matched Identifier of Clustered Objects (AMICO) algorithm. In this analysis AMICO takes advantage of the luminosity and spatial distribution of galaxies only, not considering colours. In this way, we prevent any selection effect related to the presence or absence of the red-sequence in the clusters. The catalogue contains 7988 candidate galaxy clusters in the redshift range 0.13.5 with a purity approaching 95% over the entire redshift range. In addition to the catalogue of galaxy clusters we also provide a catalogue of galaxies with their probabilistic association to galaxy clusters. We quantify the sample purity, completeness and the uncertainties of the detection properties, such as richness, redshift, and position, by means of mock galaxy catalogues derived directly from the data. This preserves their statistical properties including photo-z uncertainties, unknown absorption across the survey, missing data, spatial correlation of galaxies and galaxy clusters. Being based on the real data, such mock catalogues do not have to rely on the assumptions on which numerical simulations and semi-analytic models are based on. This paper is the first of a series of papers in which we discuss the details and physical properties of the sample presented in this work.Comment: 16 pages, 14 figures, 3 tables, submitted to MNRA

Probabilistic analysis of algorithms for dual bin packing problems

In the dual bin packing problem, the objective is to assign items of given size to the largest possible number of bins, subject to the constraint that the total size of the items assigned to any bin is at least equal to 1. We carry out a probabilistic analysis of this problem under the assumption that the items are drawn independently from the uniform distribution on [0, 1] and reveal the connection between this problem and the classical bin packing problem as well as to renewal theory.