Preface

The Summer Workshop on Interval Methods (SWIM) is an annual meeting initiated in 2008 by the French MEA working group on Set Computation and Interval Techniques of the French research group on Automatic Control. A special focus of the MEA group is on promoting interval analysis techniques and applications to a broader community of researchers, facilitated by such multidisciplinary workshops. Since 2008, SWIM has become a keystone event for researchers dealing with various aspects of interval and set-based methods. In 2019, the 12th edition in this workshop series was held at ENSTA Paris, France, with a total of 25 talks. Traditionally, workshops in the series of SWIM provide a platform for both theoretical and applied researchers who work on the development, implementation, and application of interval methods, verified numerics, and other related (set-membership) techniques.For this edition, given talks were in the fields of the verified solution of initial value problems for ordinary differential equations, differential-algebraic system models, and partial differential equations, scientific computing with guaranteed error bounds, the design of robust and fault-tolerant control systems, the implementation of corresponding software libraries, and the usage of the mentioned approaches for a large variety of system models in areas such as control engineering, data analysis, signal and image processing. Seven papers were selected for submission to this Acta Cybernetica special issue. After a two turn peer-review process, six high-quality articles were selected for publication in this special issue. Three papers propose a contribution regarding differential equations, two papers focus on robust control, and one paper considers fault detection.

Optimal Region Search with Submodular Maximization

Region search is an important problem in location-based services due to its wide applications. In this paper, we study the problem of optimal region search with submodular maximization (ORS-SM). This problem considers a region as a connected subgraph. We compute an objective value over the locations in the region using a submodular function and a budget value by summing up the costs of edges in the region, and aim to search the region with the largest objective score under a budget value constraint. ORS-SM supports many applications such as the most diversified region search. We prove that the problem is NP-hard and develop two approximation algorithms with guaranteed error bounds. We conduct experiments on two applications using three real-world datasets. The results demonstrate that our algorithms can achieve high-quality solutions and are faster than a state-of-the-art method by orders of magnitude.