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Distributed and Dynamic Graph Algorithms and Complexity

Periodic Reporting for period 2 - DisDyn (Distributed and Dynamic Graph Algorithms and Complexity)

Reporting period: 2018-08-01 to 2020-01-31

Graph data such as social networks are, like other modern big data, sheer in volume, come from a variety of sources, and evolve at a high velocity. To deal with such data, traditionally fast algorithms, i.e. those that can quickly process a static graph data on a single machine, are no longer considered sufficient. Instead, an algorithm must be distributed, so that it can handle graph data stored at multiple machines, and dynamic, so that it can handle rapid changes. Di?erent aspects of distributed and dynamic algorithms have long been studied by different subfields of computer science. Among the most important ones are:

* Communication rounds: The number of rounds needed for machines to communicate to process graph data distributively stored across machines. This is a central subject of study in the area of distributed algorithms.

* Update time: The time needed for a single machine to process updates (e.g. insertions and deletions of nodes and edges) in order to maintain some knowledge about the graph. This is the main subject in the area of dynamic algorithms.

The general goal of this project is to advance our understanding of these aspects of distributed and dynamic algorithms. The plan is to develop a systematic, unified, approach to study these algorithms by focusing on solving a few selected problems that are known to be hard against both distributed and dynamic algorithms.
* So far, the project has been carried out by two PhD students, two postdocs, and the PI. The team has achieved reached milestones. This leads to 13 articles published in the fields' flagship conferences, namely FOCS/STOC. In these articles algorithms are developed and analyzed mathematically. While analyzing these algorithms experimentally is not part of the project, it has been started.

* The PI has given survey talks to fellow computer scientists and students at many research institutions and events. These talks covered some dynamic algorithms and complexity studied in this project. Below are selected talks.

-- Course: The PI has lectured at 19th Max Planck Advanced Course on the Foundations of Computer Science in Saarbrücken, Germany.
-- Survey: The PI gave a survey talk at Highlights of Algorithms 2018 in Amsterdam, the Netherlands.

Other talks include conference talks at flagship conferences (e.g. FOCS/STOC 2017-present) and invited-only workshops (e.g. Shonan meeting (Japan), Dagstuhl workshops (Germany), and Bertinoro workshops (Italy))
* The project has led to much more understanding of dynamic and distributed algorithms, as originally expected in the proposal. This includes new distributed shortest paths and connectivity algorithms, and new dynamic shortest paths and connectivity algorithms.

* Beyond the proposal's expectation, the project has also led to more efficient algorithms in various settings. This include faster algorithms for vertex connectivity, a deterministic linear programming solver, a deterministic max-flow algorithm, and connectivity algorithms with efficient query complexity.

* Many of the above results made the first progress in decades (five decades in some case).