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We consider the general problem known as job shop scheduling, in which multiple jobs consist of sequential operations that need to be executed or served by appropriate machines having limited capacities. For example, train journeys (jobs) consist of moves and stops (operations) to be served by rail tracks and stations (machines). A schedule is an assignment of the job operations to machines and times where and when they will be executed. The developers of computational methods for job scheduling need tools enabling them to explore how their methods work. At a high level of generality, we define the system of pertinent exploration tasks and a combination of visualizations capable of supporting the tasks. We provide general descriptions of the purposes, contents, visual encoding, properties, and interactive facilities of the visualizations and illustrate them with images from an example implementation in air traffic management. We justify the design of the visualizations based on the tasks, principles of creating visualizations for pattern discovery, and scalability requirements. The outcomes of our research are sufficiently general to be of use in a variety of applications.

A possible objective in analyzing trajectories of multiple simultaneously moving objects, such as football players during a game, is to extract and understand the general patterns of coordinated movement in different classes of situations as they develop. For achieving this objective, we propose an approach that includes a combination of query techniques for flexible selection of episodes of situation development, a method for dynamic aggregation of data from selected groups of episodes, and a data structure for representing the aggregates that enables their exploration and use in further analysis. The aggregation, which is meant to abstract general movement patterns, involves construction of new time-homomorphic reference systems owing to iterative application of aggregation operators to a sequence of data selections. As similar patterns may occur at different spatial locations, we also propose constructing new spatial reference systems for aligning and matching movements irrespective of their absolute locations. The approach was tested in application to tracking data from two Bundesliga games of the 2018/2019 season. It enabled detection of interesting and meaningful general patterns of team behaviors in three classes of situations defined by football experts. The experts found the approach and the underlying concepts worth implementing in tools for football analysts.