Searching and Routing in Discrete and Continuous Domains (15w5084)


(Carleton University)

(University of Manitoba)

(Université Libre de Bruxelles)

Ian Munro (University of Waterloo)


The Casa Matemática Oaxaca (CMO) will host the "Searching and Routing in Discrete and Continuous Domains" workshop from October 11th to October 16th, 2015.

Everyday life technology strongly depends on networks. By network, we mean a set of points (vertices), together with a set of connections (edges) between these points. For instance, the road map of Canada is a network where each city is a vertex and each road between two cities is an edge. The many emails we send every day also need networks to travel. We could also mention social networks like Facebook, as well as many other situations where individuals or industries rely
on networks. A typical query in a network is to establish a connection between two given vertices (cities, servers, etc.) or to find the location of a vertex for which we only have partial information. The ultimate goal is to perform these tasks at the lowest possible cost. Depending on the context, the cost function can be price, distance, time, reliability, etc.

In some other situations, we are looking for a target in a continuous environment, where there is no proper road to follow. For instance, a helicopter of the Canadian Coast Guard is looking for a boat lost at sea with dead communication and orientation devices. Or it could be a hiker lost in the woods without map and without GPS, desperately looking for his way home. In these scenarios, there is no network, but there is someone looking for a target at unknown position with only partial information.

In this workshop, we study both the problems from the discrete setting (networks) and the continuous setting. We want to use the techniques from the discrete setting to solve problems in the continuous setting and vice versa.

The Casa Matemática Oaxaca (CMO) in Mexico, and the Banff International Research Station for Mathematical Innovation and Discovery (BIRS) in Banff, are collaborative Canada-US-Mexico ventures that provide an environment for creative interaction as well as the exchange of ideas, knowledge, and methods within the Mathematical Sciences, with related disciplines and with industry.

The research station in Banff is supported by Canada's Natural Science and Engineering Research Council (NSERC), the U.S. National Science Foundation (NSF), Alberta's Advanced Education and Technology, and Mexico's Consejo Nacional de Ciencia y Tecnología (CONACYT). The research station in Oaxaca is funded by CONACYT.