APPARATUS AND METHOD FOR GENERATING A SHORTEST-PATH TREE IN A GRAPH
First Claim
1. A method for causing a computer to execute a process comprising:
- generating, for each of vertices in a graph represented by the vertices and edges connecting the vertices, a first shortest-path tree rooted at a first root vertex that is equal to the each vertex in the graph, the first shortest-path tree representing shortest paths from the first root vertex to vertices, a path between two vertices being a sequence of edges connecting a sequence of adjacent vertices through which the two vertices are connected to each other, a length of the path being a number of edges included in the path, a shortest path between the two vertices being a path whose length is smallest among all paths between the two vertices, a distance between the two vertices being a length of the shortest path between the two vertices, whereinthe generating a vertex in the first shortest path tree whose distance from the first root vertex is a natural number of N is performed based on searching for one or more child vertices of a vertex within a second shortest-path tree rooted at a second root vertex adjacent to the first root vertex whose distance from the first root vertex is N−
1, and the vertex for searching is included in both the first shortest-path tree and the second shortest-path tree.
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Abstract
An apparatus generates, for each of vertices in a graph represented by the vertices and edges connecting the vertices, a first shortest-path tree rooted at a first root vertex equal to the each vertex, where the first shortest-path tree represents shortest paths from the first root vertex to vertices. The apparatus generates a vertex in the first shortest path tree whose distance from the first root vertex is a natural number of N, based on searching for one or more child vertices of a vertex within a second shortest-path tree rooted at a second root vertex adjacent to the first root vertex whose distance from the first root vertex is N−1, where the vertex for searching is included in both the first shortest-path tree and the second shortest-path tree.
18 Citations
18 Claims
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1. A method for causing a computer to execute a process comprising:
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generating, for each of vertices in a graph represented by the vertices and edges connecting the vertices, a first shortest-path tree rooted at a first root vertex that is equal to the each vertex in the graph, the first shortest-path tree representing shortest paths from the first root vertex to vertices, a path between two vertices being a sequence of edges connecting a sequence of adjacent vertices through which the two vertices are connected to each other, a length of the path being a number of edges included in the path, a shortest path between the two vertices being a path whose length is smallest among all paths between the two vertices, a distance between the two vertices being a length of the shortest path between the two vertices, wherein the generating a vertex in the first shortest path tree whose distance from the first root vertex is a natural number of N is performed based on searching for one or more child vertices of a vertex within a second shortest-path tree rooted at a second root vertex adjacent to the first root vertex whose distance from the first root vertex is N−
1, and the vertex for searching is included in both the first shortest-path tree and the second shortest-path tree. - View Dependent Claims (2, 3, 4, 5, 6)
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7. An apparatus comprising:
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a processor configured to generate, for each of vertices in a graph represented by the vertices and edges connecting the vertices, a first shortest-path tree rooted at a first root vertex that is equal to the each vertex in the graph, the first shortest-path tree representing shortest paths from the first root vertex to vertices, a path between two vertices being a sequence of edges connecting a sequence of adjacent vertices through which the two vertices are connected to each other, a length of the path being a number of edges included in the path, a shortest path between the two vertices being a path whose length is smallest among all paths between the two vertices, a distance between the two vertices being a length of the shortest path between the two vertices, wherein the generating a vertex in the first shortest path tree whose distance from the first root vertex is a natural number of N is performed based on searching for one or more child vertices of a vertex within a second shortest-path tree rooted at a second root vertex adjacent to the first root vertex whose distance from the first root vertex is N−
1, and the vertex for searching is included in both the first shortest-path tree and the second shortest-path tree; anda memory coupled to the processor, the memory being configured to store information on the shortest-path trees. - View Dependent Claims (8, 9, 10, 11, 12)
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13. A non-transitory, computer-readable recording medium having stored therein a program for causing a computer to execute a process comprising:
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generating, for each of vertices in a graph represented by the vertices and edges connecting the vertices, a first shortest-path tree rooted at a first root vertex that is equal to the each vertex in the graph, the first shortest-path tree representing shortest paths from the first root vertex to vertices, a path between two vertices being a sequence of edges connecting a sequence of adjacent vertices through which the two vertices are connected to each other, a length of the path being a number of edges included in the path, a shortest path between the two vertices being a path whose length is smallest among all paths between the two vertices, a distance between the two vertices being a length of the shortest path between the two vertices, wherein the generating a vertex in the first shortest path tree whose distance from the first root vertex is a natural number of N is performed based on searching for one or more child vertices of a vertex within a second shortest-path tree rooted at a second root vertex adjacent to the first root vertex whose distance from the first root vertex is N−
1, and the vertex for searching is included in both the first shortest-path tree and the second shortest-path tree. - View Dependent Claims (14, 15, 16, 17, 18)
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Specification