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Graphs are commonly used as a basic modeling tool in areas such as project management, production scheduling, line balancing, business process reengineering, and software visualization. An important problem in the area of graph drawing is to minimize arc crossings in a multi-layer hierarchical digraph. Existing solution methods for this problem are based on simple ordering rules for single layers that may lead to inferior drawings. This paper first introduces an extensive review of relevantdoi:10.1016/s0305-0548(96)00083-4 fatcat:i3xydmtc2vgi3g6mhxvt7wbuzy