Lattice Algorithms and Their Applications to Combinatorial  Optimization
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While integer programming problems are known to be hard (NP-hard) in            general, there is a great practical need to solve such problems.  In            the last decade or so, operations researchers have looked at integer            programming problems from a computational complexity viewpoint and a            polynomial time algorithm was devised for any fixed number of                   dimensions.  The approach involved solving a well-defined problem on            lattices and then applying the result to integer programs.  A lattice           is the set of all integer combinations of a finite set of linearly              independent vectors (the finite set of vectors is called a basis of the         lattice).  These results indicate that a better understanding of                lattices could yield important advances in solving combinatorial                optimization problems.  This research will concentrate on lattices and          has two main aims:  to devise more efficient algorithms for lattice             problems, and to apply these algorithms to solve integer programming            and other combinatorial optimization problems.
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