Theoretical aspects and algorithms for architectural design and communication in current networks

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The mathematical structure inherent in problems originated in design and administration of sensor networks has made them central to the theoretical computer science community as they utilize different techniques from areas like graph theory, computational geometry, design theory, and algebraic combinatorics. My goal is to build on my expertise and to answer some of the emerging questions in the area of ad-hoc and sensor networks: I propose to study and better understand the potential of geometric information in computation. The classical theory of graph algorithms was developed for offline models and is not sufficient for many modern applications where we are dealing with huge networks and we have only access to some local part of it at a time. It is more and more apparent that geometric information is useful to handle these settings.