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Geometric Algorithms and Combinatorial Optimization (Paperback, 2nd ed. 1993. Softcover reprint of the original 2nd ed. 1993)
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Geometric Algorithms and Combinatorial Optimization (Paperback, 2nd ed. 1993. Softcover reprint of the original 2nd ed. 1993)
Series: Algorithms and Combinatorics, 2
Expected to ship within 10 - 15 working days
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Since the publication of the first edition of our book, geometric
algorithms and combinatorial optimization have kept growing at the
same fast pace as before. Nevertheless, we do not feel that the
ongoing research has made this book outdated. Rather, it seems that
many of the new results build on the models, algorithms, and
theorems presented here. For instance, the celebrated
Dyer-Frieze-Kannan algorithm for approximating the volume of a
convex body is based on the oracle model of convex bodies and uses
the ellipsoid method as a preprocessing technique. The polynomial
time equivalence of optimization, separation, and membership has
become a commonly employed tool in the study of the complexity of
combinatorial optimization problems and in the newly developing
field of computational convexity. Implementations of the basis
reduction algorithm can be found in various computer algebra
software systems. On the other hand, several of the open problems
discussed in the first edition are still unsolved. For example,
there are still no combinatorial polynomial time algorithms known
for minimizing a submodular function or finding a maximum clique in
a perfect graph. Moreover, despite the success of the interior
point methods for the solution of explicitly given linear programs
there is still no method known that solves implicitly given linear
programs, such as those described in this book, and that is both
practically and theoretically efficient. In particular, it is not
known how to adapt interior point methods to such linear programs.
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