Algorithms for some combinatorial problems

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The main theme of my research is the study of algorithms for solving combinatorial problems.  Combinatorics is relevant in many areas of computer science including cryptography, communication networks and bio-informatics.  To focus my research,  I will investigate the following: 1) degree sequences for k-hypergraphs, and 2) multilevel cooperative search and combinatorial designs.   The study of degree sequences for k-hypergraphs is an important open problem in hypergraph theory.  Although many people have studied this problem, there is no known simple characterization of the polytope of valid degree sequences for k-hypergraphs.  Such a characterization would be a major breakthough.  I propose to study the polytope  of valid degree sequences of 3-hypergraphs using an a linear-time algorithm that I have recently discovered.  By applying the algorithm, I hope to find new information about this polytope. In the second project, I propose to investigate the application of the multilevel cooperative search strategy to optimization problems derived from combinatorial design theory.  This is a new approach to solving combinatorial design optimization problems, and it often performs better than meta-heuristic search techniques such as genetic algorithms, simulated annealing and tabu search.  Recently, I applied the multilevel cooperative search strategy to the covering design problem and noticed that it performed very well as was able to discover some new results with this search strategy.  I propose to investigate why the multilevel cooperative search works better than meta-heuristic searchs such as simulated annealing and tabu search, for certain covering design problem instances and hope to determine conditions under which this search method will perform well.  In addition, I would like to investigate the possibility of applying the multilevel cooperative search to other combinatorial design optimization problems, such as Latin squares, t-designs and lotto designs.