The field of dynamic graph algorithms studies algorithms for processing graphs that are changing over time. Formally, the goal is to process an interleaved sequence of update and query operations, where an update operation changes the input graph (e.g. inserts/deletes an edge), while the query operation is problem-specific and asks for some property of the current graph – for example, an s-t path, or a minimum spanning tree. The field has evolved rapidly over the past decade, and this Dagstuhl Seminar will bring together leading researchers in dynamic algorithms and related areas of graph algorithms. Some specific goals for the seminar are outlined below.

• Because the field has grown so much in recent years, one of the main motivations for this seminar is to establish the main challenges that remain – both a list of specific open problems that continue to resist progress, as well as a discussion of more general limitations to our current upper and lower bound techniques. The seminar will also provide a venue for the community to actively shape the direction of the field going forward.
• Much of the recent progress in the field has stemmed from a new set of techniques, many of which originated in other areas of graph or approximation algorithms. One of the goals of this seminar is thus to discuss how recent developments in graph algorithms broadly construed can be applied to the dynamic setting in particular, and to disseminate some of the recent techniques that have already had tremendous success in this regard. To this end, we will organize several tutorials from top experts in the field.
• The experimental evaluation of dynamic graph algorithms is still in its infancy. There are no established data sets or even evaluation methodologies. This seminar aims to include the leading researchers in the area of algorithms engineering of dynamic graph algorithms to address and, hopefully, resolve these fundamental questions.

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Aaron Bernstein, Shiri Chechik, Sebastian Forster, and Tsvi Kopelowitz