Public Defense

In his dissertation Joachim Spoerhase considers competitive location problems where two competing providers place their facilities sequentially and users can decide between the competitors. He assumes that both competitors act non-cooperatively and aim at maximizing their own benefits. He investigates the complexity and approximability of such problems on graphs, in particular on simple graph classes such as trees and paths. He also develops fast algorithms for single competitive location problems where each provider places a single facility.

In addition to this, he investigates voting location.  Voting location problems aim at identifying locations that meet social criteria. The provider wants to satisfy the users (customers) of the facility to be opened. In general, there is no location that is favored by all users. Therefore, a satisfactory compromise has to be found. To this end, criteria arising from voting theory are considered. The solution of the location problem is understood as the winner of a virtual election among the users of the facilities, in which the potential locations play the role of the candidates and the users represent the voters. Competitive and voting location problems turn out to be closely related.