Polynomial time solvable algorithms to binary quadratic programming problems with Q being a tri-diagonal or five-diagonal matrix

In the field of signal processing, many problems can be formulated as optimization problems. And most of these optimization problem can be further described in a formal form, that is binary quadratic programming problem(BQP). However, solving the BQP is proved to be NP-hard. Due to this reason, many novel algorithms have been proposed in order to improve the efficiency to solve the BQP. In this paper, polynomial algorithms to binary quadratic programming problems with Q being a tri-diagonal or five-diagonal matrix is focused by taking advantage of the basic algorithm proposed in. The basic algorithm is firstly reviewed and then this algorithm is modified to solve binary quadratic programming problems with Q being a tri-diagonal. Furthermore, by improving this algorithm, an algorithm is proposed to solve binary quadratic programming problems with Q being a five-diagonal matrix.