Mathematical model of interest matchmaking in electronic social networks

Social activities in electronic networks play an increasingly important role in our every-day lives. We are exchanging important information via electronic mails, wikis, web-based forums, or blogs, and meet new friends or business contacts in Internet communities and social network services. Parallel to this growing socialization of the World Wide Web, the requirements on the electronic services become more ambitious. Huge data quantities have to be processed, user-friendly interfaces are to be designed, and more and more sophisticated computations must be implemented to o er complex solutions. This paper studies a special aspect of social network services, the matchmaking problem. In essence it asks, given a search pro le, for advertising pro les matching it best. This problem is in principle well-known in Grid computing, where computational tasks are seeking for appropriate resources such as CPU time and memory space on di erent computers. In electronic social networks, however, the problem is more general because not only speci ed attribute ranges are to be compared but more or less vaguely describable interests. The aim of this paper is to formulate a mathematical model for the problem of matchmaking of attribute ranges and elds of interests in electronic social networks. It tackles the following fundamental questions. How can an appropriate system and its data structure be designed? How is the mathematical formulation of a matching problem as an optimization problem? In particular, what is its search space, what is its objective function? Whereas the idea to use a fuzzy function to calculate the matching degree of two numerical ranges may suggest itself, how could a function calculating a matching degree of two elds of interest look like? One of the central results of this paper is the proposal of a precise de nition of such a function computing this matching degree and the presentation of a concrete example. The paper is organized as follows. After a de nition of electronic social networks is given in the next section,