Detlef Seese

Easy problems for tree-decomposable graphs

Abstract Using a variation of the interpretability concept we show that all graph properties definable in monadic second-order logic (MS properties) with quantification over vertex and edge sets can be decided in linear time for classes of graphs of fixed bounded treewidth given a tree-decomposition. This gives an alternative proof of a recent result by Courcelle. We allow graphs with directed and/or undirected edges, labeled on edges and/or vertices with labels taken from a finite set. We extend MS properties to extended monadic second-order (EMS) problems involving counting or summing evaluations over sets definable in monadic second-order logic. Our technique allows us also to solve some EMS problems in linear time or in polynomial or pseudopolynomial time for classes of graphs of fixed bounded treewidth. Moreover, it is shown that each EMS problem is in NC for graphs of bounded treewidth. Most problems for which linear time algorithms for graphs of bounded treewidth were previously known to exist, and many others, are EMS problems.

An algebraic theory of graph reduction

We show how membership in classes of graphs definable in monadic second order logic and of bounded treewidth can be decided by finite sets of terminating reduction rules. The method is constructive in the sense that we describe an algorithm which will produce, from a formula in monadic second order logic and an integer k such that the class defined by the formula is of treewidth ≤ k, a set of rewrite rules that reduces any member of the class to one of finitely many graphs, in a number of steps bounded by the size of the graph. This reduction system corresponds to an algorithm that runs in time linear in the size of the graph.

Width Parameters Beyond Tree-width and their Applications

Besides the very successful concept of tree-width (see [Bodlaender, H. and Koster, A. (2007) Combinatorial optimisation on graphs of bounded treewidth. These are special issues on Parameterized Complexity]), many concepts and parameters measuring the similarity or dissimilarity of structures compared to trees have been born and studied over the past years. These concepts and parameters have proved to be useful tools in many applications, especially in the design of efficient algorithms. Our presented novel look at the contemporary developments of these ‘width’ parameters in combinatorial structures delivers—besides traditional tree-width and derived dynamic programming schemes—also a number of other useful parameters like branch-width, rank-width (clique-width) or hypertree-width. In this contribution, we demonstrate how ‘width’ parameters of graphs and generalized structures (such as matroids or hypergraphs), can be used to improve the design of parameterized algorithms and the structural analysis in other applications on an abstract level.

On Measuring the Understandability of Process Models

Much efforts are aimed at unveiling the factors that influence a person’s comprehension of a business process model. While various potential factors have been proposed and studied in an experimental setting, little attention is being paid to reliability and validity requirements on measuring a person’s structural understanding of a process model. This paper proposes the concepts to meaningfully argue about these notions, for the sake of improving future measurement instruments. The findings from an experiment, involving 178 students from three different universities, underline the importance of this topic. In particular, it is shown that the coverage of model-related questions is important. This paper provides various recommendations to properly measure structural model comprehension.

Problems Easy for Tree-Decomposable Graphs (Extended Abstract)

Using a variation of the interpretability concept we show that all graph properties definable in monadic second order logic (MS properties) with quantification over vertex and edge sets can be decided in linear time for classes of graphs of fixed bounded tree-width, giving an alternative proof of a recent result by Courcelle. We allow graphs with directed and/or undirected edges, labeled on edges and/or vertices with labels taken from a finite set. We extend MS properties to Extended Monadic Second-order (EMS) problems involving counting or summing evaluations given with the graph over sets definable in monadic second order logic. Our tecnique allowes us to solve also some EMS problems in linear time or in polynomial or pseudopolynomial time for classes of graphs of fixed bounded tree-width. Most problems for wich linear time algorithms for graphs of bounded tree width where previously known to exist, and many others, are EMS problems.

A hybrid heuristic approach to discrete multi-objective optimization of credit portfolios

A hybrid heuristic approach combining multi-objective evolutionary and problem-specific local search methods is proposed to support the risk-return analysis of credit portfolios. Its goal is to compute approximations of discrete sets of Pareto-efficient portfolio structures concerning both the respective portfolio return and the respective portfolio risk using the non-linear, non-convex Credit-Value-at-Risk downside risk measure which is relevant to real world credit portfolio optimization. In addition, constraints like capital budget restrictions are considered in the hybrid heuristic framework. The computational complexity of selected parts of the algorithm is analyzed. Moreover, empirical results indicate that the hybrid method is superior in convergence speed to a non-hybrid evolutionary approach and finds approximations of risk-return efficient portfolios within reasonable time.

A Conceptual Framework for the Governance of Service-Oriented Architectures

With the widespread adoption of service-oriented architecture (SOA) as the leading paradigm for the development of business applications, the need for adequate governance mechanisms to keep control of the increasing complexity inherently introduced by SOA arises. However, current approaches to SOA governance are often limited to either design time or runtime aspects of SOA governance, despite the need for adequate governance mechanisms covering the complete SOA lifecycle. Furthermore, no common understanding of SOA governance exists today, as many solution vendors misleadingly label SOA management products as solutions for SOA governance. This work presents a reference model for SOA governance that is based on the OASIS Reference Model for Service Oriented Architecture. It aims at establishing a common understanding of SOA governance and is intended to serve as a basis for comparing and developing concrete SOA governance solutions.

Monadic Second Order Logic, Tree Automata and Forbidden Minors

N.Robertson and P.D.Seymour proved that each minor closed class K of graphs is characterized by finitely many minimal forbidden minors. If these minors are given then they can be used to find an efficient membership test for such classes (see [Rob Sey 86b]). From these minors one can get a monadic second order description of the class K. Main result of the article is that from a monadic second order description of the class K. Main result of the article is that from a monadic second order description of K the minimal forbidden minors can be constructed, when K contains only graphs of universally bounded tree width. The result is applied to the class of partial 2-pathes.

Handbook on Information Technology in Finance

This Handbook contains surveys of state-of-the-art concepts, systems, applications, best practices as well as contemporary research in the intersection between IT and finance. Included are recent trends and challenges, IT systems and architectures in finance, essential developments and case studies on management information systems, service oriented architecture modelling, IT architectures for securities trading, IT-systems in banking, process-oriented systems in corporate treasuries, grid computing and networking. The IT applications in banking, trading and insurance cover risk management and controlling, financial portals, electronic payment and others. In addition, also finance-related IT applications in non-financial companies are considered. The concept-oriented part of the book focuses on IT methods in finance like financial models and modelling financial data, planning and processes, security, algorithms and complexity.

Visualization and Clustering of Business Process Collections Based on Process Metric Values

Motivated by ideas of software measurement, the area of process measurement has attracted attention in recent time. Numerous process metrics have been proposed to measure (often structural) properties of business processes.In this paper, we propose heatmaps, a visualization technique for high-dimensional data originally used in genetics, for visualizing the process metric values of business process collections. So, new insights into the distribution of the metric values among the processes could be gained. Additionally, we use clustering for analyzing (1) the correlations between different process metrics and (2) finding (structurally) similar processes among business process collections. Our approach has been successfully applied to the SAP Reference Model processes.