Abstract: A method of path routing in a multilayered structure including layers and one or more links formed between adjacent layers includes identifying path connection elements included in each layer of a multilayered structure with layers that can have at least one links between adjacent layers, generating, for each layer of the multilayered structure, an embedded frame including the path connection elements identified in each layer of the multilayered structure, generating a topological frame including an outer boundary enclosing one or more punctures formed by the links among the plurality of path connection elements included in the embedded frame and one or more local path points arranged on a boundary of each of the one or more punctures, and generating a circular frame including a single circular closed curve by merging the boundary of each of the one or more punctures and the outer boundary of the topological frame.

Abstract: A method for path routing according to an embodiment of the present disclosure may include selecting a first start point and a first end point with which path routing is performed in a circular frame generated by connecting all points included in one or more start point sets included in a layer, one or more end point sets paired with the start point set, and one or more edge point pair sets to one closed curve, generating a connectivity graph by connecting edge points included in one or more nodes corresponding to segments obtained by dividing the circular frame into one or more regions, and connecting the first start point and the first end point based on a cost for connecting the first start point and the first end point calculated using the connectivity graph.

Abstract: A method for path routing according to an embodiment of the present disclosure may include selecting a first start point and a first end point with which path routing is performed in a circular frame generated by connecting all points included in one or more start point sets included in a layer, one or more end point sets paired with the start point set, and one or more edge point pair sets to one closed curve, generating a connectivity graph by connecting edge points included in one or more nodes corresponding to segments obtained by dividing the circular frame into one or more regions, and connecting the first start point and the first end point based on a cost for connecting the first start point and the first end point calculated using the connectivity graph.

Abstract: A method of path routing in a multilayered structure including layers and one or more links formed between adjacent layers includes identifying path connection elements included in each layer of a multilayered structure with layers that can have at least one links between adjacent layers, generating, for each layer of the multilayered structure, an embedded frame including the path connection elements identified in each layer of the multilayered structure, generating a topological frame including an outer boundary enclosing one or more punctures formed by the links among the plurality of path connection elements included in the embedded frame and one or more local path points arranged on a boundary of each of the one or more punctures, and generating a circular frame including a single circular closed curve by merging the boundary of each of the one or more punctures and the outer boundary of the topological frame.