Expanding the expressive power of Monadic Second-Order logic on restricted graph classes

We combine integer linear programming and recent advances in Monadic Second-Order model checking to obtain two new algorithmic meta-theorems for graphs of bounded vertex-cover. The first shows that cardMSO1, an extension of the well-known Monadic Second-Order logic by the addition of cardinality constraints, can be solved in FPT time parameterized by vertex cover. The second meta-theorem shows that the MSO partitioning problems introduced by Rao can also be solved in FPT time with the same parameter. The significance of our contribution stems from the fact that these formalisms can describe problems which are W[1]-hard and even NP-hard on graphs of bounded tree-width. Additionally, our algorithms have only an elementary dependence on the parameter and formula. We also show that both results are easily extended from vertex cover to neighborhood diversity.Comment: Accepted for IWOCA 201

Indexing Metric Spaces for Exact Similarity Search

With the continued digitalization of societal processes, we are seeing an explosion in available data. This is referred to as big data. In a research setting, three aspects of the data are often viewed as the main sources of challenges when attempting to enable value creation from big data: volume, velocity and variety. Many studies address volume or velocity, while much fewer studies concern the variety. Metric space is ideal for addressing variety because it can accommodate any type of data as long as its associated distance notion satisfies the triangle inequality. To accelerate search in metric space, a collection of indexing techniques for metric data have been proposed. However, existing surveys each offers only a narrow coverage, and no comprehensive empirical study of those techniques exists. We offer a survey of all the existing metric indexes that can support exact similarity search, by i) summarizing all the existing partitioning, pruning and validation techniques used for metric indexes, ii) providing the time and storage complexity analysis on the index construction, and iii) report on a comprehensive empirical comparison of their similarity query processing performance. Here, empirical comparisons are used to evaluate the index performance during search as it is hard to see the complexity analysis differences on the similarity query processing and the query performance depends on the pruning and validation abilities related to the data distribution. This article aims at revealing different strengths and weaknesses of different indexing techniques in order to offer guidance on selecting an appropriate indexing technique for a given setting, and directing the future research for metric indexes

On the Complexity of Partitioning Graphs for Arc-Flags

Precomputation of auxiliary data in an additional off-line step is a common approach towards improving the performance of shortest-path queries in large-scale networks. One such technique is the arc-flags algorithm, where the preprocessing involves computing a partition of the input graph. The quality of this partition significantly affects the speed-up observed in the query phase. It is evaluated by considering the search-space size of subsequent shortest-path queries, in particular its maximum or its average over all queries. In this paper, we substantially strengthen existing hardness results of Bauer et al. and show that optimally filling this degree of freedom is NP-hard for trees with unit-length edges, even if we bound the height or the degree. On the other hand, we show that optimal partitions for paths can be computed efficiently and give approximation algorithms for cycles and trees

Computations by fly-automata beyond monadic second-order logic

We present logically based methods for constructing XP and FPT graph algorithms, parametrized by tree-width or clique-width. We will use fly-automata introduced in a previous article. They make possible to check properties that are not monadic second-order expressible because their states may include counters, so that their sets of states may be infinite. We equip these automata with output functions, so that they can compute values associated with terms or graphs. Rather than new algorithmic results we present tools for constructing easily certain dynamic programming algorithms by combining predefined automata for basic functions and properties.Comment: Accepted for publication in Theoretical Computer Scienc

Novel models and algorithms for integrated production planning and scheduling

This thesis is concerned with production planning and scheduling in make-to-order manufacturing system. We seek effective modelling and efficient solution techniques that can help increase the productivity and the service level of an enterprise, together with reducing production costs, by supporting the management to make smarter decisions on these two levels of the planning hierarchy. In th

An Efficient Algorithm for Bulk-Loading xBR+ -trees

A major part of the interface to a database is made up of the queries that can be addressed to this database and answered (processed) in an efficient way, contributing to the quality of the developed software. Efficiently processed spatial queries constitute a fundamental part of the interface to spatial databases due to the wide area of applications that may address such queries, like geographical information systems (GIS), location-based services, computer visualization, automated mapping, facilities management, etc. Another important capability of the interface to a spatial database is to offer the creation of efficient index structures to speed up spatial query processing. The xBR + -tree is a balanced disk-resident quadtree-based index structure for point data, which is very efficient for processing such queries. Bulk-loading refers to the process of creating an index from scratch, when the dataset to be indexed is available beforehand, instead of creating the index gradually (and more slowly), when the dataset elements are inserted one-by-one. In this paper, we present an algorithm for bulk-loading xBR + -trees for big datasets residing on disk, using a limited amount of main memory. The resulting tree is not only built fast, but exhibits high performance in processing a broad range of spatial queries, where one or two datasets are involved. To justify these characteristics, using real and artificial datasets of various cardinalities, first, we present an experimental comparison of this algorithm vs. a previous version of the same algorithm and STR, a popular algorithm of bulk-loading R-trees, regarding tree creation time and the characteristics of the trees created, and second, we experimentally compare the query efficiency of bulk-loaded xBR + -trees vs. bulk-loaded R-trees, regarding I/O and execution time. Thus, this paper contributes to the implementation of spatial database interfaces and the efficient storage organization for big spatial data management