On the L2 L 2 -discrepancy
For a family of subsets S S of a finite set V V , a coloring ?:V?{-1,1} ? : V ? { - 1 , 1 } , and Sj?S S j ? S , let ?(Sj)=?v?Sj?(v) ? ( S j ) = ? v ? S j ? ( v ) . We consider the problem to minimize ?j?(Sj)2 ? j ? ( S j ) 2 and we call the problem L2 L 2 -discrepancy problem. We show that the problem is NP-complete, and we also provide an upper bound for the L2 L 2 -discrepancy.
l2 l 2 -discrepancy l2 l 2 l2 l 2 l 2 hypergraph np-completeness