**6. Conclusions**

In this paper, a novel exact algorithm to the general linearly constrained zero-one quadratic programming problem with *k*-diagonal matrix is proposed. The algorithm is designed by analyzing the property of matrix *Q* and then combining the famous basic algorithm and dynamic programming method. The complexity of the algorithm is analyzed and shows that it is polynomially solvable when *m* is fixed. The experimental results also illustrate the feasibility and efficiency of the algorithm. Designing efficient algorithm to this special class of problem 01*CQP* not only provides useful

information for designing efficient algorithms for other special classes but also can provide hints and facilitate the derivation of efficient relaxations for the general problems. And finally, the phasor measurement units placement problem is used to demonstrate that the algorithm has wide potential applications in decision-making real-life problems.

**Author Contributions:** S.G. put forward ideas and algorithms. S.G. and X.C simulated the results and wrote important parts of the article. X.C. formatted the whole paper, and summarized the results in tables. All authors have read and agreed to the published version of the manuscript.

**Funding:** The work described in the paper was supported by the National Science Foundation of China under Grants 61876105 and 61503233.

**Conflicts of Interest:** The authors declare no conflict of interest.
