Search Minimum of Maximums. Help Needed!

From: A. Carkaci (carkaci_at_yahoo.com)
Date: 05/24/04 

Date: 24 May 2004 14:23:16 -0700

I have a set, which consist of real numbers, say
S={x1,x2,x3,x4}

and a list of some subsets of the S, say
L={S_1,S_2,S_3,...S_N} where 1<=N<=2^|S| (|S| is the cardinality)

For example;
     S1={x1,x2,x3}
     S2={x2,x3}
     S3={x2}
     S4={x1,x4}

My aim is the search of the minimum of the maximum values in the L,
mathematically speaking, i am searching the following

        min ( max S_1, max S_2, max S_3,..., max S_N )

For the above example it becomes
        min ( max(x1,x2,x3), max(x2,x3), max(x2), max(x1,x4) )

How can I compute the above function efficently ? Direct
implementation of the above function is not computationaly efficient.