Example Of Set Covering Problem

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Example of set covering problem. 22 03 2017 given a universe u of n elements a collection of subsets of u say s s 1 s 2 s m where every subset s i has an associated cost. Set cover problem chapter 2 1 12 what is the set cover problem. Since our contruction takes polynomial time and we have shown that set cover is in np we can conclude that set cover is np complete. Each element of universe u is contained in either of the subsets of set s.

As a specific example of the set cover problem consider the instance f a b b c a c. Note that showing that a general instance of set cover can be solved. The set cover problem is a classical question in combinatorics computer science operations research and complexity theory it is one of karp s 21 np complete problems shown to be np complete in 1972. Set cover problem set 1 greedy approximate algorithm last updated.

Set covering problems have been studied extensively in various applications and comprehensive review articles on existing work in this field can for example be found in 12 18 2 23. For each of several doctors available for on call duty the additional. Decision version of the set covering problem. Consider that there are 10 simple points are in the universe u and each of the point is contained in subsets as shown in the figure below.

Given a set of elements called the universe and. In the set covering problem a set of finite capacity is given which is also called the universe u of n elements. During interviews be ready to describe situations you ve encountered in previous roles the processes you followed to address problems the skills you applied and the results of your actions. Set covering problem a hospital er needs to keep doctors on call so that a qualified individual is available to perform every medical procedure that might be required there is an ocial list of such procedures.

You must select a minimum number of any size set of these sets so that the sets you have picked contain all the elements that are contained in any of the sets in the input wikipedia additionally you want to minimize the cost of the sets. Thus the optimal value of the objective function of the corresponding 0 1 integer program is 2 the number of sets in the optimal covers. It is a problem whose study has led to the development of fundamental techniques for the entire field of approximation algorithms.