Network Design and Improvement Hartmut Noltemeier and Hans-Christoph Wirth Department of Computer Science, University of W¨rzburg u Am Hubland, 97074 W¨rzburg, Germany u E-mail: {noltemei, wirth}@informatik.uni-wuerzburg.de and Sven Oliver Krumke Konrad Zuse Zentrum Takustrasse 7, 14195 Berlin-Dahlem, Germany E-mail: krumke@zib.de Inspired by the fact that many combinatorial optimization problems arising in practice are NP-hard, the design of e cient approximation algorithms has been a major research topic for the last years. Since we can not expect to solve any NP-hard problem in polynomial time, it is meaningful to compromise optimality of a solution and settle for a su ciently good solution that can be computed e ciently in polynomial time. 1. APPROXIMATION ALGORITHMS A polynomial running time algorithm is called an -approximation algorithm for a (minimization) problem, if for any instance of the problem, it produces a solution that is at most times the optimal solution. The factor is then called performance, approximation ratio or relative error of the algorithm. It should be noted that is not required to be a constant but may be a function of the input size. An approximation scheme contains for each xed > 0 an algorithm A with performance 1 +
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Network design and improvement
Noltemeier, H.; Wirth, H.-C.; Krumke, S. O.
Follow ACM Computing Surveys (CSUR)
, Volume 31 (3es)
Association for Computing Machinery – Sep 1, 1999
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