class SSShortestPath extends AnyRef
The SSShortestPath class is used to solve shortest path problems for graphs
stored in matrices. It solves the Single-Source Shortest Path 'SSSP' problem
for directed graphs (both digraphs and multi-digraphs). The SSShortestPath
companion object is used to form a matrix from an MGraph.
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The edge cost/distance (must be non-negative) can be stored in either a dense
or sparse matrix. Dijkstra's Algorithm is used.
- See also
en.wikipedia.org/wiki/Dijkstra%27s_algorithm ---------------------------------------------------------------------------- For multi-digraphs, each multi-edge between a pair vertices has it own edge weight (
TLabel=VectorDin this case). The minimum is taking when forming the corresponding matrix.thescipub.com/PDF/jcssp.2013.377.382.pdf ----------------------------------------------------------------------------
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- new SSShortestPath(c: MatriD, s: Int)
- c
the cost/distance matrix, where a value of zero implies no connection. If the actual distance is zero, use a very small number instead.
- s
the single-source vertex
Type Members
- case class Item(id: Int, dd: Double) extends Ordered[Item] with Product with Serializable
The
Iteminner case class has two fields, vertex id and distance from vertex s (the source) as well as a compare method based on distance.The
Iteminner case class has two fields, vertex id and distance from vertex s (the source) as well as a compare method based on distance.- id
the id of the vertex
- dd
the vertex's distance from vertex s
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- def spath(): (VectoD, VectorI)
Determine the shortest path from vertex 's' to each vertex 'j' returning the vector 'd' giving the distance from 's' to all other vertices and the vector 'p' of predecessor vertices.
Determine the shortest path from vertex 's' to each vertex 'j' returning the vector 'd' giving the distance from 's' to all other vertices and the vector 'p' of predecessor vertices. The path from 's' to each vertex can be deduced from the 'p' vector.
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