Abstract: After a brief introduction to intersection graphs, I will survey the past 10 years of research on Bk-VPG graphs, the intersection graphs of k-bend paths on a grid. They have become the source of many interesting pure mathematical and algorithmic problems. Originally, the study of these graphs was motivated by applications from chip manufacturing and circuit layout where paths (wires) on a grid are constrained by the number of bends per wire for reasons of feasibility and to reduce the cost of the chip.

Interest in the topic began with the paper "Vertex Intersection Graphs of Paths on a Grid" by Andrei Asinowski, Elad Cohen, Martin Charles Golumbic, Vincent Limouzy, Marina Lipshteyn and Michal Stern in the Journal of Graph Algorithms and Applications (2012). Subsequently, dozens of researchers have investigated theoretical and computational aspects of Bk-VPG graphs in more than 50 published works including recognition and coloring problems, approximation algorithms and mathematical characterizations.

Abstract: How do we identify and prioritize risks so as to make smart choices based on limited resources? How do we secure against and withstand potential threats that may affect critical resources located within a given region. Proactive and coordinated efforts are necessary so as to maintain system resilience and strengthen the functioning of critical infrastructures. Recent years have witnessed the explosive growth of MAVs--Mobile Autonomous Vehicles--be they underwater, earth-bound or air-born as a communication and data gathering tool to provide efficient mitigation strategies. One is interested to know how communication capabilities of an autonomous system affects its performance.

Motivated from questions related to the interaction between the knowledge the MAVs have and the capabilities of the underlying wireless network we discuss several challenging optimization problems whose solution has occupied and will continue to occupy computer scientists. Topics discussed include: Collision Avoidance, Domain Protection, Fault Tolerance, Evacuation, Patrolling, Search, and Swarm Detection. The central theme in all these problems involves the interaction of communication and mobility of the participating autonomous entities. Goal of this talk is to outline existing models and ideas and discuss related open problems and future research directions, pertaining to optimization problems in the interface of communication and mobility.

Abstract: We discuss temporal graphs as an abstract model of dynamic networks. We focus on the impact of different ways of determining the temporal availability of links in such networks. We do this by presenting and analyzing several notions and problems. We demonstrate that different rules of temporal availability of links lead to quite different approaches and conclusions about the complexity of problems on temporal graphs.

Abstract: Methods developed in the field of combinatorial testing for identifying inputs that trigger software faults and failures also have interesting applications in artificial intelligence and machine learning. The talk will explain how methods and tools for measuring similarity and differences in combination coverage of input space can be applied to generate explanations or justifications of decisions produced by machine learning algorithms. These methods are also beginning to show promise for many aspects of the transfer learning problem, to evaluate the potential for applying AI/ML trained for one environment or input space to a different environment.

Abstract: Bringing AI methods and techniques into practice require to verify that their corresponding systems fulfill their requirements in order to show dependability. In case of autonomous systems and especially in autonomous driving, we have to assure safety. In this tutorial, I am going to discuss a novel approach for software and system testing that is based on ontologies capturing potential interactions with the environment of such system. The approach takes ontologies and computes test cases that comprise combinations of environmental concepts for finding critical scenarios that have been overlocked during development. We discuss the motivation behind the testing approach, the foundations behind ontology-based testing, as well as results obtained when using the approach for testing an automated driving function. In the latter, we showed that the approach is able to come up with critical scenarios revealing faults in the implemented function.