Method of forming, searching, or generating quasi-minimum tree providing optimum network configuration, and information recording medium which stores program thereof
First Claim
1. A forming, searching, or generating method for forming, searching, or generating a quasi-minimum tree providing an optimum network configuration connecting Steiner points which are a plurality of vertexes defined by selecting vertexes and edges on an undirected graph which is a geometrical structure consisting of vertexes and weighted edges, wherein, in creating or searching a path for forming, searching or generating an optimum network configuration by selecting said vertexes and edges, a plurality of trees which do not share said vertexes and edges with one another are created or searched by connecting vertexes to one another beginning from those with which the distance, which provides the total sum of the weights for the edges included in a single path connecting between any two provisional points, is the shortest, while creating or searching a tree providing a path which includes no closed path and is tolerated to be branched;
- and then, said plurality of trees are connected to one another to provide a tree with which all of said plurality of vertexes defined, i.e., Steiner points are connected to one another, and the total sum of the weights for said edges included is at a quasi-minimum.
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Abstract
A method for forming, searching, or generating a quasi-minimum tree providing an optimum network configuration, which provides an approximate solution to the Steiner problem. This method is a method for forming, searching, or generating a quasi-minimum tree providing an optimum network configuration connecting Steiner points v1 to v5 which are a plurality of vertexes defined by selecting vertexes and edges on an undirected graph which is a geometrical structure consisting of vertexes and weighted edges, wherein, a plurality of trees which do not share said vertexes and edges with one another are created or searched by connecting vertexes to one another beginning from those with which the distance, which provides the total sum of the weights for the edges included in a single path connecting between any two provisional points, is the shortest, while creating or searching a tree providing a path which includes no closed path and is tolerated to be branched; and then, said plurality of trees are connected to one another to provide a tree (a quasi-minimum tree) with which all of said plurality of vertexes defined, v1 to v5, are connected to one another, and the total sum of the weights for said edges included is at a quasi-minimum.
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Citations
23 Claims
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1. A forming, searching, or generating method for forming, searching, or generating a quasi-minimum tree providing an optimum network configuration connecting Steiner points which are a plurality of vertexes defined by selecting vertexes and edges on an undirected graph which is a geometrical structure consisting of vertexes and weighted edges, wherein,
in creating or searching a path for forming, searching or generating an optimum network configuration by selecting said vertexes and edges, a plurality of trees which do not share said vertexes and edges with one another are created or searched by connecting vertexes to one another beginning from those with which the distance, which provides the total sum of the weights for the edges included in a single path connecting between any two provisional points, is the shortest, while creating or searching a tree providing a path which includes no closed path and is tolerated to be branched; - and then, said plurality of trees are connected to one another to provide a tree with which all of said plurality of vertexes defined, i.e., Steiner points are connected to one another, and the total sum of the weights for said edges included is at a quasi-minimum.
- View Dependent Claims (3, 4, 5, 6, 7, 8, 9, 10, 11)
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2. A forming, searching, or generating method for forming, searching, or generating a quasi-minimum tree providing an optimum network configuration connecting Steiner points which are a plurality of vertexes defined by selecting vertexes and edges on an undirected graph which is a geometrical structure consisting of vertexes and weighted edges, wherein,
in the course of forming or generating said quasi-minimum tree providing an optimum network configuration, a plurality of trees providing a path which includes no closed path and is tolerated to be branched are formed and generated at the same time, and the plurality of trees do not share said vertexes and edges with one another.
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12. A computer readable information recording medium which is used with a forming, searching, or generating method for forming, searching, or generating a quasi-minimum tree providing an optimum network configuration connecting Steiner points which are a plurality of vertexes defined by selecting vertexes and edges on an undirected graph which is a geometrical structure consisting of vertexes and weighted edges, wherein,
in creating or searching a path for forming, searching or generating an optimum network configuration by selecting said vertexes and edges, a plurality of trees which do not share said vertexes and edges with one another are created or searched by connecting vertexes to one another beginning from those with which the distance, which provides the total sum of the weights for the edges included in a single path connecting between any two provisional points, is the shortest, while creating or searching a tree providing a path which includes no closed path and is tolerated to be branched; - and then, said plurality of trees are connected to one another to provide a tree with which all of said plurality of vertexes defined, i.e., Steiner points are connected to one another, and the total sum of the weights for said edges included is at a quasi-minimum, wherein
a program for executing said formation, search, or generation of a quasi-minimum tree providing an optimum network configuration is recorded. - View Dependent Claims (14, 15, 16, 17, 18, 19, 20, 21, 22)
- and then, said plurality of trees are connected to one another to provide a tree with which all of said plurality of vertexes defined, i.e., Steiner points are connected to one another, and the total sum of the weights for said edges included is at a quasi-minimum, wherein
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13. A computer readable information recording medium which is used with a forming, searching, or generating method for forming, searching, or generating a quasi-minimum tree providing an optimum network configuration connecting Steiner points which are a plurality of vertexes defined by selecting vertexes and edges on an undirected graph which is a geometrical structure consisting of vertexes and weighted edges, wherein,
in the course of forming or generating said quasi-minimum tree providing an optimum network configuration, a plurality of trees providing a path which includes no closed path and is tolerated to be branched are formed and generated at the same time, and the plurality of trees do not share said vertexes and edges with one another, wherein a program for executing said formation, search, or generation of a quasi-minimum tree providing an optimum network configuration is recorded.
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23. A computer readable information recording medium which records a program for creating or searching a path for forming or generating a quasi-minimum tree providing an optimum network configuration connecting Steiner points which are a plurality of vertexes defined by selecting vertexes and edges on an undirected graph which is a geometrical structure consisting of vertexes and weighted edges, wherein,
in creating or searching a path for forming, searching or generating an optimum network configuration by selecting said vertexes and edges, the program causes the computer to execute processing comprising: -
a step for reading or inputting data of said undirected graph;
a step for reading or inputting data of said Steiner points;
a step for creating or searching a plurality of trees which do not share said vertexes and edges with one another by connecting vertexes to one another beginning from those with which the distance, which provides the total sum of the weights for the edges included in a single path connecting between any two provisional points, is the shortest, while creating or searching a tree providing a path which includes no closed path and is tolerated to be branched;
a step for connecting said plurality of trees to one another to provide a tree with which all of said plurality of vertexes defined are connected to one another, and the total sum of the weights for said edges included is at a quasi-minimum; and
a step for outputting the results of said respective steps.
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Specification