Heuristic for the Consecutive Block Minimization Algorithms And Results

Abstract

In this paper, we discuss a hard problem called Consecutive block minimization (CBM), it is defined as the problem of finding a permutation of the columns of binary matrix which minimizes the number of consecutives blocks. Some combinational problems can be modelled using binary matrices, we can verify whether these matrices hold the consecutive ones property, which implies existence of permutation of the columns of the matrix such that all non zoro elements can be placed as a block in every row.In this study, we propose a heuristic based on a reduction and approximation of the CBM to a particular version and instances, we propose two results, one called negative result, the other positive result.