The last few years have seen a rapid growth in research on issues related to counting, both theoretical and applied. Among others, the fields of discrete optimization and more recently, computational convexity (the study of the computational and algorithmic. aspects of high-dimensional convex bodies, especially polytopes) have been important sources of new questions involving counting. Furthermore, major new results have been proved about. complexity classes based on counting.

This workshop was intended to bring together people from different communities who are interested in counting issues, and to facilitate (and further stimulate) communication amongst the researchers involved.

According to the concept of this conference, the participants belonged to different fields of theoretical computer science and discrete mathematics.

The meeting was attended by 22 participants who each gave a talk. Some of the lectures surveyed new developments in important subfields. others presented recent new results. The lengths of the talks varied between 30 and 60 minutes.

The topics that were discussed at the workshop reflected the wide range of the subject. Some of the lectures dealt with aspects of counting related to structural complexity theory, with complexity classes based on counting, and with counting issues in the theory of communication complexity. Others were devoted to randomized and approximate counting problems, while yet others mentioned algebraic aspects of the field. Another group of contributions focussed on graph theoretic counting problems, and certain complexity issues in enumerative combinatoric.s. Some other talks gave results on counting issues in integer programming, while counting (and uniqueness) issues in convexity was the subject of another group of lectures. Many of the problems discussed were motivated by practical applications.

In addition various open problems were stated which led to vivid discussions and numerous interactions.

The conference showed that even though the participants belonged to different fields that have quite different tool-boxes, approaches and ideas for solving their problems, there is a deep and close connection which is centered around the concept of counting.

Creative Commons BY 3.0 DE