Maximizing Revenues for Online-Dial-a-Ride

In the classic Dial-a-Ride Problem, a server travels in some metric space to serve requests for rides. Each request has a source, destination, and release time. We study a variation of this problem where each request also has a revenue that is earned if the request is satisfied. The goal is to serve requests within a time limit such that the total revenue is maximized. We first prove that the version of this problem where edges in the input graph have varying weights is NP-complete. We also prove that no algorithm can be competitive for this problem. We therefore consider the version where edges in the graph have unit weight and develop a 2-competitive algorithm for this problem

On the probabilistic min spanning tree Problem

We study a probabilistic optimization model for min spanning tree, where any vertex vi of the input-graph G(V,E) has some presence probability pi in the final instance G′ ⊂ G that will effectively be optimized. Suppose that when this “real” instance G′ becomes known, a spanning tree T, called anticipatory or a priori spanning tree, has already been computed in G and one can run a quick algorithm (quicker than one that recomputes from scratch), called modification strategy, that modifies the anticipatory tree T in order to fit G ′. The goal is to compute an anticipatory spanning tree of G such that, its modification for any G ′ ⊆ G is optimal for G ′. This is what we call probabilistic min spanning tree problem. In this paper we study complexity and approximation of probabilistic min spanning tree in complete graphs under two distinct modification strategies leading to different complexity results for the problem. For the first of the strategies developed, we also study two natural subproblems of probabilistic min spanning tree, namely, the probabilistic metric min spanning tree and the probabilistic min spanning tree 1,2 that deal with metric complete graphs and complete graphs with edge-weights either 1, or 2, respectively

The Stochastic Container Relocation Problem

The Container Relocation Problem (CRP) is concerned with finding a sequence of moves of containers that minimizes the number of relocations needed to retrieve all containers, while respecting a given order of retrieval. However, the assumption of knowing the full retrieval order of containers is particularly unrealistic in real operations. This paper studies the stochastic CRP (SCRP), which relaxes this assumption. A new multi-stage stochastic model, called the batch model, is introduced, motivated, and compared with an existing model (the online model). The two main contributions are an optimal algorithm called Pruning-Best-First-Search (PBFS) and a randomized approximate algorithm called PBFS-Approximate with a bounded average error. Both algorithms, applicable in the batch and online models, are based on a new family of lower bounds for which we show some theoretical properties. Moreover, we introduce two new heuristics outperforming the best existing heuristics. Algorithms, bounds and heuristics are tested in an extensive computational section. Finally, based on strong computational evidence, we conjecture the optimality of the “Leveling” heuristic in a special “no information” case, where at any retrieval stage, any of the remaining containers is equally likely to be retrieved next

Scheduling over Scenarios on Two Machines

We consider scheduling problems over scenarios where the goal is to find a single assignment of the jobs to the machines which performs well over all possible scenarios. Each scenario is a subset of jobs that must be executed in that scenario and all scenarios are given explicitly. The two objectives that we consider are minimizing the maximum makespan over all scenarios and minimizing the sum of the makespans of all scenarios. For both versions, we give several approximation algorithms and lower bounds on their approximability. With this research into optimization problems over scenarios, we have opened a new and rich field of interesting problems.Comment: To appear in COCOON 2014. The final publication is available at link.springer.co

An optimally concentrated Gabor transform for localized time-frequency components

Gabor analysis is one of the most common instances of time-frequency signal analysis. Choosing a suitable window for the Gabor transform of a signal is often a challenge for practical applications, in particular in audio signal processing. Many time-frequency (TF) patterns of different shapes may be present in a signal and they can not all be sparsely represented in the same spectrogram. We propose several algorithms, which provide optimal windows for a user-selected TF pattern with respect to different concentration criteria. We base our optimization algorithm on $l^p$-norms as measure of TF spreading. For a given number of sampling points in the TF plane we also propose optimal lattices to be used with the obtained windows. We illustrate the potentiality of the method on selected numerical examples

Relaxing the Irrevocability Requirement for Online Graph Algorithms

Online graph problems are considered in models where the irrevocability requirement is relaxed. Motivated by practical examples where, for example, there is a cost associated with building a facility and no extra cost associated with doing it later, we consider the Late Accept model, where a request can be accepted at a later point, but any acceptance is irrevocable. Similarly, we also consider a Late Reject model, where an accepted request can later be rejected, but any rejection is irrevocable (this is sometimes called preemption). Finally, we consider the Late Accept/Reject model, where late accepts and rejects are both allowed, but any late reject is irrevocable. For Independent Set, the Late Accept/Reject model is necessary to obtain a constant competitive ratio, but for Vertex Cover the Late Accept model is sufficient and for Minimum Spanning Forest the Late Reject model is sufficient. The Matching problem has a competitive ratio of 2, but in the Late Accept/Reject model, its competitive ratio is 3/2

Shaping Biological Knowledge: Applications in Proteomics

The central dogma of molecular biology has provided a meaningful principle for data integration in the field of genomics. In this context, integration reflects the known transitions from a chromosome to a protein sequence: transcription, intron splicing, exon assembly and translation. There is no such clear principle for integrating proteomics data, since the laws governing protein folding and interactivity are not quite understood. In our effort to bring together independent pieces of information relative to proteins in a biologically meaningful way, we assess the bias of bioinformatics resources and consequent approximations in the framework of small-scale studies. We analyse proteomics data while following both a data-driven (focus on proteins smaller than 10 kDa) and a hypothesis-driven (focus on whole bacterial proteomes) approach. These applications are potentially the source of specialized complements to classical biological ontologies

Optimal online and offline algorithms for robot-assisted restoration of barrier coverage

Cooperation between mobile robots and wireless sensor networks is a line of research that is currently attracting a lot of attention. In this context, we study the following problem of barrier coverage by stationary wireless sensors that are assisted by a mobile robot with the capacity to move sensors. Assume that $n$ sensors are initially arbitrarily distributed on a line segment barrier. Each sensor is said to cover the portion of the barrier that intersects with its sensing area. Owing to incorrect initial position, or the death of some of the sensors, the barrier is not completely covered by the sensors. We employ a mobile robot to move the sensors to final positions on the barrier such that barrier coverage is guaranteed. We seek algorithms that minimize the length of the robot's trajectory, since this allows the restoration of barrier coverage as soon as possible. We give an optimal linear-time offline algorithm that gives a minimum-length trajectory for a robot that starts at one end of the barrier and achieves the restoration of barrier coverage. We also study two different online models: one in which the online robot does not know the length of the barrier in advance, and the other in which the online robot knows the length of the barrier. For the case when the online robot does not know the length of the barrier, we prove a tight bound of $3/2$ on the competitive ratio, and we give a tight lower bound of $5/4$ on the competitive ratio in the other case. Thus for each case we give an optimal online algorithm.Comment: 20 page

On Conceptually Simple Algorithms for Variants of Online Bipartite Matching

We present a series of results regarding conceptually simple algorithms for bipartite matching in various online and related models. We first consider a deterministic adversarial model. The best approximation ratio possible for a one-pass deterministic online algorithm is $1/2$, which is achieved by any greedy algorithm. D\"urr et al. recently presented a $2$-pass algorithm called Category-Advice that achieves approximation ratio $3/5$. We extend their algorithm to multiple passes. We prove the exact approximation ratio for the $k$-pass Category-Advice algorithm for all $k \ge 1$, and show that the approximation ratio converges to the inverse of the golden ratio $2/(1+\sqrt{5}) \approx 0.618$ as $k$ goes to infinity. The convergence is extremely fast --- the $5$-pass Category-Advice algorithm is already within $0.01\%$ of the inverse of the golden ratio. We then consider a natural greedy algorithm in the online stochastic IID model---MinDegree. This algorithm is an online version of a well-known and extensively studied offline algorithm MinGreedy. We show that MinDegree cannot achieve an approximation ratio better than $1-1/e$, which is guaranteed by any consistent greedy algorithm in the known IID model. Finally, following the work in Besser and Poloczek, we depart from an adversarial or stochastic ordering and investigate a natural randomized algorithm (MinRanking) in the priority model. Although the priority model allows the algorithm to choose the input ordering in a general but well defined way, this natural algorithm cannot obtain the approximation of the Ranking algorithm in the ROM model

Neo: an object model for handling electrophysiology data in multiple formats

Neuroscientists use many different software tools to acquire, analyze and visualize electrophysiological signals. However, incompatible data models and file formats make it difficult to exchange data between these tools. This reduces scientific productivity, renders potentially useful analysis methods inaccessible and impedes collaboration between labs. A common representation of the core data would improve interoperability and facilitate data-sharing. To that end, we propose here a language-independent object model, named “Neo,” suitable for representing data acquired from electroencephalographic, intracellular, or extracellular recordings, or generated from simulations. As a concrete instantiation of this object model we have developed an open source implementation in the Python programming language. In addition to representing electrophysiology data in memory for the purposes of analysis and visualization, the Python implementation provides a set of input/output (IO) modules for reading/writing the data from/to a variety of commonly used file formats. Support is included for formats produced by most of the major manufacturers of electrophysiology recording equipment and also for more generic formats such as MATLAB. Data representation and data analysis are conceptually separate: it is easier to write robust analysis code if it is focused on analysis and relies on an underlying package to handle data representation. For that reason, and also to be as lightweight as possible, the Neo object model and the associated Python package are deliberately limited to representation of data, with no functions for data analysis or visualization. Software for neurophysiology data analysis and visualization built on top of Neo automatically gains the benefits of interoperability, easier data sharing and automatic format conversion; there is already a burgeoning ecosystem of such tools. We intend that Neo should become the standard basis for Python tools in neurophysiology.EC/FP7/269921/EU/Brain-inspired multiscale computation in neuromorphic hybrid systems/BrainScaleSDFG, 103586207, GRK 1589: Verarbeitung sensorischer Informationen in neuronalen SystemenBMBF, 01GQ1302, Nationaler Neuroinformatik Knote