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Introduction

Theoretical foundations - an ultra-quick recall

• All items in the dataset are called Links (aka Arcs), and are expected to represent some oriented connection joining two Nodes.
  Example: in the above figure Link L3 connects Nodes N2 and N5.
• So all Links are always expected to explicitly reference a Start-Node (aka Node-From) and an End-Node (aka Node-To).
  • Links are always oriented, and their natural direction is From-To:
    • in an unidirectional Network each Link is an one-way connection.
      If the connection is available in the opposite direction a second Link must be explicitly declared.
      Example: Link X1 goes from Node A to Node B, and Link X2 goes from Node B to Node A.
    • in a bidirectional Network all Links are assumed to establish a connection in both directions.
      Definiting an one-way connection requires an appropriate attribute to be set (see below).
  • The Start- and End-Node could eventually be the same, and in this case we'll have a self-closed Link.
  • Network's Links can eventually define a linear Geometry (LINESTRING) going from the Start-Node to the End-Node, but this is an optional feature, not a mandatory requirement.
  • What is absolutely mandatory is that each Link must explicitly reference its Nodes.
• A Network supporting Geometries is a Spatial Network; otherwise a Network lacking any Geometry is a Logical Network.
  • In a Spatial Network all Links must have a corresponding Geometry.
  • In a Logical Network all Links are strictly forbidden to have any Geometry.
  • In a Spatial Network both the StartPoint and EndPoint of each Link's LINESTRING are always expected to exactly coincide with the corresponding Nodes.
• In a Spatial Network all references to the same Node by different Links must be an exact match.
  Example: Node N5 is shared by Links L3, L6, L7, L9 and L10, so all their corresponding LINESTRINGS are expected to have the corresponding extremity (Start- or End-, depending on the orientation) points that must exactly match the other.
  A topological inconsistency exists if any of these conditions are not satisfied, which leads to an invalid Network.
• In a Spatial Network two
• Accordingly to the above premises, Nodes are never expected to be explicitly declared in a separate Table.
  Just a single Table declaring all Links is required in order to fully define a topologically valid Network.
  All the Nodes can then be easily extracted from the Links' definitions and the coordinates for each Node can be directly set by extracting the extreme Point of the corresponding Linestrings.
  If any mismatch is detected this surely means that the Network is invalid.
• A Link may legitimately self-intersect itself (e.g. forming a loop), as shown in the above figure by Link L15 (orange spot).
• Two Links may legitimately intersect where no Node exists, as exemplified on the above figure by Links L4 and L7 (green spot).
  This usually happens when one of the two Links overpasses the other, or where some technical restriction exists (e.g. two insulated wires in an Electrical Network).
• Links aren't strictly required to be associated with any specific attribute, but the following attributes are almost universally supported:
  • a name identifying the Link.
    Examples: the road toponym in a road network, or the river name in an hydrographic network.
  • one (or even more) appropriate cost value(s).
    Example: the time required to traverse the Link (may be distinguished between pedestrians, bicycles, cars, lorries and so on).
  • a pair of boolean flags (from-to and to-from) are intendend to specify if the Link can be traversed on both directions or just in one (one-way).

Logical conclusions

• Hydrographic Networks.
• Gas / Water / Oil Networks.
• Electrical Networks.
• Telecomunication Networks.
• Social or Economical Networks representing relationships between individuals or companies.
• Epidemiological Networks representing the propagation of infective diseases between individuals or groups.

The Dijkstra's algorithm

• Any Node-to-Node connection identified by Dijkstra's is certainly ensured to be optimal.
  In other words, no connetction presenting a lower cost can conceptually exist.
• When Dijsjtra's fails to identify a solution this surely means that no solution is possible.

The A* algorithm

Creating a VirtualRouting Table

SELECT CreateRouting('byfoot_data', 'byfoot', 'roads_vw', 'node_from', 'nodeto', 'geom', NULL);

SELECT CreateRouting_GetLastError();
------------------------------------
ToNode Column "nodeto" is not defined in the Input Table

SELECT CreateRouting('byfoot_data', 'byfoot', 'roads_vw', 'node_from', 'node_to', 'geom', NULL);
-------------
1

SELECT CreateRouting_GetLastError();
------------------------------------
NULL

1. byfoot_data: the name of the Network Binary Data to be created.
2. byfoot: the name of the VirtualRouting Table to be created.
3. roads_vw: the name of the Spatial Table or Spatial View representing the underlying Network.
   Note: in this case we actually used a Spatial View.
4. node_from: name of the column (in the above Table or View) expected to contain node-from values.
5. node_to: name of the column (in the above Table or View) expected to contain node-to values.
6. geom: name of the column (in the above Table or View) expected to contain Linestrings.
   We could have legitimately passed a NULL value for this argument in the case of a Logical Network or if we weren't interested to get a Geometry representing any Routing solution.
7. NULL: name of the column (in the above Table or View) expected to contain cost values.
   In this case we have passed a NULL value, and consequently the cost of each Link will be assumed to be represented by the geometric length of the corresponding Linestring.
   Note #1: in the case of Networks based on any long/lat (aka geographic) Reference System the geometry length of all Linestrings will be precisely measured on the ellipsoid by applying the most accurate geodesic formulae and will be consequently expressed in meters.
   Note #2: the geom-column and cost-column arguments are never allowed to be NULL at the same time.

CREATE VIRTUAL TABLE test_network USING VirtualNetwork('some_data_table');

CREATE VIRTUAL TABLE test_routing USING VirtualRouting('some_data_table');

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