Computational complexity of the minimal committee problem and adjacent problems
Michael Khachay · Pattern Recognition and Image Analysis · 2006
The computational complexity of two important special cases of the minimal committee problem (MC), viz., the problem on the minimal committee of finite sets (MCFS) and the problem on the minimal committee of a system of linear algebraic inequalities (MCLE), is studied. Both problems are shown to be NP -hard. Separately, some adjacent problems of integer optimization are shown to be intractable. The efficient approximability threshold is estimated for the MCFS problem, the estimates being allied to the results known for the set cover problem. The intractable and polynomially solvable subclasses of the MCLE problem are given. The problem of the minimal affine separation committee (MASC) is considered in conclusion; the results obtained earlier for the MCLE problem are shown to be valid for this problem as well.