On the impact of initialisation strategies on Maximum Flow algorithm performance

Due to its theoretical and practical importance in network theory, designing effective algorithms for the Maximum Flow Problem (MFP) remains a focus of research efforts. Although worst-case performance analysis is the main tool for examining performance, empirical analysis across a wide variety of benchmark cases can identify scenarios where practical performance may contradict theoretical worse-case. In our previous work, we used Instance Space Analysis (ISA) to identify the practical strengths and weaknesses of four state-of-theart MFP algorithms, and identified that the arc/path finding strategies employed by the algorithms explain critical differences in the algorithms' behaviours. In this paper, we leverage these insights to propose two new initialisation strategies, which are an essential part of the arc/path finding strategy. To employ these new strategies on our previously studied four algorithms, we propose modifications that result in 15 new algorithmic variants. Using a comprehensive experimental setup and ISA, we examine the impact of these proposed initialisation strategies on performance, and discuss the conditions under which each initialisation strategy is expected to improve performance. One of the novel initialisation strategies is shown to improve the performance of MFP algorithms in many instances, making it promising for even further improvements of the algorithms.