Research Interests: Summary
نویسندگان
چکیده
My current research interests are in structural and algorithmic graph theory – a field connecting pure mathematics with theoretical computer science. I am particularly interested in studying ways to cope with (hard) optimization problems on graphs. In these problems, it is often desirable to find a particular substructure of a graph that is optimal with respect to some criteria. A general framework for these problems is: Given a graph, find a subset of its vertices (or edges) of minimum or maximum cardinality (or weight), subject to some specified constraints (requirements). For example, the maximum independent set problem asks for a maximum subset of pairwise non-adjacent vertices in a given graph. See [28] for a general introduction to graph theory, and [7] for an algorithmic point of view. Most graph optimization problems are computationally intractable; they are among the many NP-hard problems (the monograph by Garey and Johnson [8] is a classic reference for basics of computational complexity). There are several ways of dealing with an NP-hard problem. Since solving such a problem to optimality is believed to be prohibitive in terms of computational time, we can instead try to develop approximation algorithms, which allow us to obtain approximate solutions in reasonable time. Also, even though a problem may be hard in general, it is sometimes possible to find restrictions on the input instances under which the problem can be solved efficiently, i.e., in polynomial time. Of course, what’s interesting here is to identify cases for which polynomialtime solutions require new algorithmic ideas. Most of my research is devoted to these and related issues.
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