Solving large instances of the quadratic cost of partition problem on dense graphs by data correcting algorithms

The Data-Correcting Algorithm (DCA) corrects the data of a hard problem instance in such a way that we obtain an instance of a well solvable special case. For a given prescribed accuracy of the solution, the DCA uses a branch and bound scheme to make sure that the solution of the corrected instance satisfies this given prescribed accuracy. We describe the "hardness" of randomly generated instances of the Quadratic Cost Partition Problem (QCP) by the density of the corresponding graphs as well as by the cardinality of an optimal solution of the QCP. We study the behaviour of the DCAs through the number of search levels of the so called Preliminary Preservation Al-gorithm and average computational times. We report average computational times of the DCA for instances of dense graphs with the number of vertices up to 500 which can be solved on a standard PC within 10 minutes.