CONNECT · Combinatorics of Networks and Computation

Combinatorics of Networks and Computation

Networks are a fundamental part of modern society; they can be the byproduct of the interaction of agents spread worldwide; they might be the vast communication and transportation networks we have built during the past century; and they appear in the most unexpected forms. In the Combinatorics of Networks and Computation (CONNECT) project we study the fundamental properties of networks. We use tools from diverse areas of Mathematics and Computer Science to obtain new insights into these fascinating objects. The consortium involves researchers and graduate students of 14 universities from Austria, Belgium, Canada, Chile, Czech Republic, Italy, Mexico, and Spain. The activities of the project are divided into 5 work packages. Geometric Networks(WP1) Many networks have a geometric component; their nodes might have geographical location or the links between two nodes might be straight line segments. Work package 1 studies how these geometric constrains affect the properties of networks. Randomness and Imprecise Knowledge in Networks(WP2) Randomness and uncertainty are facts of life. In the case of networks, the location of a node in a network might be random; or our information on a real life network might be uncertain. Work package 2 studies how networks behave under uncertainty and randomness assumptions; we also design algorithms to deal with this uncertainty. Restricted Orientation Geometry(WP3) Manufacturing imposes geometric restrictions. For example, in a circuit each link is often laid out in one of two possible orientations. Work package 3 studies how geometric restrictions affect the properties of networks. Graph-based algorithms for UAVs and for Musical Information Retrieval(WP4) Graph-Based Models have been considered in many application areas. For instance, consider in the robotic area a search problem in which a cooperating team of agents is searching for a target in a bounded region. Typically, the approach is to reduce the continuous problem to an optimization on a finite graph and the paths are computed on this graph. In WP4, the goal is to take advance of our expertise in graph theory and algorithms in graphs for the design of efficient algorithms for two application areas, Aerial Robotics (AR) and MIR (Musical Information Retrieval). Dissemination and Gender Equality Promotion(WP5) We believe that social outreach is a crucial part of the scientific endeavor. We seek to make our results accessible to a wider audience. It is of particular interest to promote gender equality in Mathematics. Women continue to be underrepresented in the field of mathematical research. In this work package we take specific actions to address this issue.

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