Approximation Algorithms
نویسنده
چکیده
Many of the optimization problems we would like to solve are NP hard There are several ways of coping with this apparent hardness For most problems there are straightforward exhaustive search algorithms and one could try to speed up such an algorithm Techniques which can be used include divide and conquer or the re ned branch and bound which allows to eliminate part of the search tree by computing at every node bounds on the optimum value dynamic programming which sometimes leads to pseudo polynomial algorithms cutting plane algorithms in which one tries to re ne a linear programming relaxation to better match the convex hull of integer solutions randomization etc Instead of trying to obtain an optimum solution we could also settle for a suboptimal solution The latter approach refers to heuristic or rule of thumb methods The most widely used such methods involve some sort of local search of the problem space yielding a locally optimal solution In fact heuristic methods can also be applied to polynomially solvable problems for which existing algorithms are not e cient enough A n algorithm or even a linear time algorithm with a constant of although e cient from a complexity point of view will probably never get implemented because of its inherent ine ciency The drawback with heuristic algorithms is that it is di cult to compare them Which is better which is worse For this purpose several kinds of analyses have been introduced
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تاریخ انتشار 1994