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GRAPHALGAPP Report Summary

Project ID: 340506
Funded under: FP7-IDEAS-ERC
Country: Austria

Mid-Term Report Summary - GRAPHALGAPP (Challenges in Graph Algorithms with Applications)

A graph is a model of a binary relation between elements in a set. For example, every member of a social network can be an element and two members are related if they are friends in the social network. The goal of the project is to develop new algorithmic techniques that analyze properties of graphs, for example, that find sets of elements that are highly-related. As real-life graphs frequently change, we specifically investigate the area of dynamic graph algorithms where the goal is to quickly update a graph after it was (slightly) modified.
We have developed new dynamic graph algorithms for various fundamental graph properties such as shortest paths, reachability, matching, minimum cut, and set cover that are faster than any previously known algorithms and we have also shown that for a large set of graph properties (under reasonable assumptions) no very efficient algorithm can exists.

We then applied these algorithmic and proof techniques to problems in computer verification. Computer verification is the sub-field of computer science that develops algorithms that find mistakes in computer software or hardware. We developed faster algorithms for various verification problems and also separated various problems in computer verification in regard to how efficiently they can be solved. Specifically, we showed that (a) certain problems can be solved strictly faster on graphs than on a more refined model called Markov Decision Process and (b) the well-known problems of Streett and Rabin problems cannot be solved with the same time complexity. The latter fact is surprising as these two problems are closely related.

We also developed algorithms for other fields of applications, namely new online matching algorithms which are relevant for the ads assignment problem in online advertisement and a new approximation algorithm for a problem arising in conservation biology.
We presented and published all our results in suitable conferences.

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