1963–64 Beşiktaş J.K. season

Prune and search is a method of solving optimization problems suggested by Nimrod Megiddo in 1983.

The basic idea of the method is a recursive procedure in which at each step the input size is reduced ("pruned") by a constant factor 0 < p < 1. As such, it is a form of decrease and conquer algorithm, where at each step the decrease is by a constant factor. Let n be the input size, T(n) be the time complexity of the whole prune-and-search algorithm, S(n) is the time complexity of the pruning step, then T(n) obeys the following recurrence relation:

$T(n)=S(n)+T(n(1-p)),$

which has the solution T(n) = O(S(n)), since summing a geometric series only multiplies by a constant factor, namely $1/(1-(1-p))=1/p.$

In particular, Megiddo himself used this approach in his linear time algorithm for the linear programming problem when the dimension is fixed and for the minimal enclosing sphere problem for a set of points in space.

References

43 year old Petroleum Engineer Harry from Deep River, usually spends time with hobbies and interests like renting movies, property developers in singapore new condominium and vehicle racing. Constantly enjoys going to destinations like Camino Real de Tierra Adentro.