Edge bundling is a technique commonly used to reduce visual clutter and improve the comprehension of the drawings of large graphs. Here, we model edge bundling as a multi-objective optimization problem and employ clustering strategies, metaheuristic and Pareto analysis to identify non-dominated solutions for some classical graphs from the literature.

Multiway spatial joins are a commonly occurring and fundamental type of query for spatial data processing. This article presents models and algorithms to schedule this type of query in distributed database systems while attempting to strike a balance between makespan and communication costs. We propose three algorithms based on combinatorial optimization methods: the well-known linear relaxation technique of rounding a solution generated by linear programming (LP), a more sophisticated Lagrangian Relaxation method (LR), as well as a greedy heuristic (GR) for baseline comparison. Our evaluation shows that a schedule built using GR consumes, on average, 22% more processing and communication resources than a more elaborate schedule constructed via the LR method, when scheduling a query for 64 machines. The schedule provided by LR is also, on average, an order of magnitude closer to the optimal schedule for a query compared to GR. We show that scheduling Gigabyte-size multiway queries before execution can reduce its processing time by an order of magnitude compared to state-of-the-art frameworks for spatial data processing that do not have this capability, and can significantly reduce the amount of shuffled data in the network.

One of the commonly used techniques to improve the readability of large graph drawings is called edge bundling, which groups edges in such a way that reduces the visual complexity of the drawing. This paper proposes to treat this task as a clustering problem, using compatibility metrics to evaluate the generated solutions in an optimization pipeline, combined with a clustering ensemble approach. The goal was to solve the General-based Edge Bundling (GBEB) problem with relatively low computational costs using a method called Clustering Ensemble-based Edge Bundling (CEBEB) and evaluate the results. CEBEB proved to be a very promising alternative to solve GBEB, since it is capable of generating relatively good solutions with shorter run-times compared to an existing, well-established GBEB method.

Abstract This article presents a survey of the current status of the research on structural and qualitative systems theory that has been conducted in the last few decades. This theory can be traced back to the work of Samuelson on comparative static analysis of a national economy. His problem was to find the direction of change in economic equilibrium induced by small changes in the exogenous variables of a system based solely on qualitative information such as the sign pattern of the parameters that specify the system. In the field of engineering, the work of Iri et al. on structural analysis of systems of equations and Lin's research on the structural controllability of dynamic systems were quite influential. Following these pioneering works, a variety of research has been carried out by mathematicians and engineers, as well as by economists. A few examples of problems are the structural solvability and decomposability of systems of equations, the structural characterization of Tinbergen's rule of economic policy, the structural controllability and decouplability of dynamic systems, and the sign‐solvability of static systems. Using graph‐theoretic terms with explanatory examples, this paper surveys the established results on the structural and qualitative analysis of systems in areas ranging from control theory to economics.

Abstract The Steiner problem in graphs is concerned with finding a set of edges with minimum total weight which connects a given subset of points in a weighted graph. A branch and bound algorithm for solving this problem is presented together with an interesting application to a problem in molecular evolution. Computational experience gained in using the algorithm compares favorably, for certain classes of graphs, with that of existing methods.