The Set Covering and Other Problems: An Empiric Complexity Analysis Using the Minimum Ellipsoidal Width

This research aims to explain the intrinsic difficulty of Karp’s list twenty-one problems through use empirical complexity measures based on ellipsoidal width polyhedron generated by constraints relaxed linear programming problem. The variables used as are number nodes visited B&B and CPU time spent solving problems. measurements explanatory correspond Dikin ellipse eigenvalues within polyhedron. Other constraint clearance with respect analytical center ellipse. results these in terms particularly satisfactory. They show strong correlations, above 60%, most cases.