Parameterized Complexity of the k-anonymity Problem

The problem of publishing personal data without giving up privacy is becoming increasingly important. An interesting formalization that has been recently proposed is the $k$-anonymity. This approach requires that the rows of a table are partitioned in clusters of size at least $k$ and that all the rows in a cluster become the same tuple, after the suppression of some entries. The natural optimization problem, where the goal is to minimize the number of suppressed entries, is known to be APX-hard even when the records values are over a binary alphabet and $k=3$, and when the records have length at most 8 and $k=4$ . In this paper we study how the complexity of the problem is influenced by different parameters. In this paper we follow this direction of research, first showing that the problem is W[1]-hard when parameterized by the size of the solution (and the value $k$). Then we exhibit a fixed parameter algorithm, when the problem is parameterized by the size of the alphabet and the number of columns. Finally, we investigate the computational (and approximation) complexity of the $k$-anonymity problem, when restricting the instance to records having length bounded by 3 and $k=3$. We show that such a restriction is APX-hard.Comment: 22 pages, 2 figure

Articulated Multi-Instrument 2D Pose Estimation Using Fully Convolutional Networks

Instrument detection, pose estimation and tracking in surgical videos is an important vision component for computer assisted interventions. While significant advances have been made in recent years, articulation detection is still a major challenge. In this paper, we propose a deep neural network for articulated multi-instrument 2D pose estimation, which is trained on a detailed annotations of endoscopic and microscopic datasets. Our model is formed by a fully convolutional detection-regression network. Joints and associations between joint pairs in our instrument model are located by the detection subnetwork and are subsequently refined through a regression subnetwork. Based on the output from the model, the poses of the instruments are inferred using maximum bipartite graph matching. Our estimation framework is powered by deep learning techniques without any direct kinematic information from a robot. Our framework is tested on single-instrument RMIT data, and also on multi-instrument EndoVis and in vivo data with promising results. In addition, the dataset annotations are publicly released along with our code and model

Dynamic discrete tomography

We consider the problem of reconstructing the paths of a set of points over time, where, at each of a finite set of moments in time the current positions of points in space are only accessible through some small number of their X-rays. This particular particle tracking problem, with applications, e.g., in plasma physics, is the basic problem in dynamic discrete tomography. We introduce and analyze various different algorithmic models. In particular, we determine the computational complexity of the problem (and various of its relatives) and derive algorithms that can be used in practice. As a byproduct we provide new results on constrained variants of min-cost flow and matching problems.Comment: In Pres

A Framework for Semantic Similarity Measures to enhance Knowledge Graph Quality

Precisely determining similarity values among real-world entities becomes a building block for data driven tasks, e.g., ranking, relation discovery or integration. Semantic Web and Linked Data initiatives have promoted the publication of large semi-structured datasets in form of knowledge graphs. Knowledge graphs encode semantics that describes resources in terms of several aspects or resource characteristics, e.g., neighbors, class hierarchies or attributes. Existing similarity measures take into account these aspects in isolation, which may prevent them from delivering accurate similarity values. In this thesis, the relevant resource characteristics to determine accurately similarity values are identified and considered in a cumulative way in a framework of four similarity measures. Additionally, the impact of considering these resource characteristics during the computation of similarity values is analyzed in three data-driven tasks for the enhancement of knowledge graph quality. First, according to the identified resource characteristics, new similarity measures able to combine two or more of them are described. In total four similarity measures are presented in an evolutionary order. While the first three similarity measures, OnSim, IC-OnSim and GADES, combine the resource characteristics according to a human defined aggregation function, the last one, GARUM, makes use of a machine learning regression approach to determine the relevance of each resource characteristic during the computation of the similarity. Second, the suitability of each measure for real-time applications is studied by means of a theoretical and an empirical comparison. The theoretical comparison consists on a study of the worst case computational complexity of each similarity measure. The empirical comparison is based on the execution times of the different similarity measures in two third-party benchmarks involving the comparison of semantically annotated entities. Ultimately, the impact of the described similarity measures is shown in three data-driven tasks for the enhancement of knowledge graph quality: relation discovery, dataset integration and evolution analysis of annotation datasets. Empirical results show that relation discovery and dataset integration tasks obtain better results when considering semantics encoded in semantic similarity measures. Further, using semantic similarity measures in the evolution analysis tasks allows for defining new informative metrics able to give an overview of the evolution of the whole annotation set, instead of the individual annotations like state-of-the-art evolution analysis frameworks

Heuristics for New Problems Arising in the Transport of People and Goods

The Vehicle Routing Problem (VRP) and its numerous variants are amongst the most widely studied in the entire Operations Research literature, with applications in fields includ- ing supply chain management, journey planning and vehicle scheduling. In this thesis, we focus on three problems from two fields with a wide reach; the design of public trans- port systems and the robust routing of delivery vehicles. Each chapter investigates a new setting, formulates an optimization problem, introduces various solution methods and presents computational experiments highlighting salient points. The first problem involves commuters who use a flexible shuttle service to travel to a main transit hub, where they catch a fixed route public transport service to their true destina- tion. In our variant, passengers must forgo some of the choices they had in previous ver- sions; the service provider chooses the specific hub passengers are taken to (provided all relevant timing constraints are satisfied). This introduces both complexities and opportu- nities not seen in other VRP variants, so we present two solution methods tailored for this problem. An extensive computational study over a range of networks shows this flexibility allows significant cost savings with little impact on the quality of service received. The second problem involves dynamic ridesharing schemes and one of their most per- sistent drawbacks: the requirement to attract a large number of users during the start up phase. Although this is influenced by many factors, a significant consideration is the per- ceived uncertainty around finding a match. To address this, the service provider may wish to employ a small number of their own private drivers, to serve riders who would oth- erwise remain unmatched. We explore how this could be formulated as an optimization problem and discuss the objectives and constraints the service provider may have. We then describe a special structure inherent to the problem and present three different so- lution methods which exploit this. Finally, a broad computational study demonstrates the potential benefits of these dedicated drivers and identifies environments in which they are most useful. The third problem comes from the field of logistics and involves a large delivery firm serving an uncertain customer set. The firm wishes to build low cost delivery routes that remain efficient after the appearance and removal of some customers. We formulate this problem and present a heuristic which is both computationally cheaper and more versatile than comparative exact methods. A wide computational study illustrates our heuristic’s predictive power and its efficacy compared to natural alternative strategies