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<h1>Introduction</h1>
Previous versions of SpatiaLite traditionally supported a <b>pure SQL routing module</b> that was named <a
Since version <b>5.0.0</b> a brand new <b>routing module</b> (more advanced and sophisticated) is available, that is called <b>VirtualRouting</b>.<br>
The now obsolete <b>VirtualNetwork</b> is still supported by version <b>5.0.0</b> so as to not cause an abrupt break to already existing applications, but will presumably be discontinued in future versions.<br>
Using <b>VirtualRouting</b> instead of <b>VirtualNetwirk</b> is warmly recommended for any new development.
<h2>Theoretical foundations - an ultra-quick recall</h2>
All <b>Routing algorithms</b> (<i>aka</i> <b>Shortest Path</b> algorithms) are based on the mathematics of the <a theory</a> or to be more precise: on <b>Weighted Graphs</b>.
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<img alt="network">
<br>
A topologically valid <b>Network</b> is a dataset that fulfills the following requirements:
<ul>
<li>All items in the dataset are called <b>Links</b> (<i>aka</i> <b>Arcs</b>), and are expected to represent some oriented connection joining two <b>Nodes</b>.<br>
<u>Example</u>: in the above figure Link <b>L3</b> connects Nodes <b>N2</b> and
<li>So all <b>Links</b> are always expected to explicitly reference a <b>Start-Node</b> (<i>aka</i> <b>Node-From</b>) and an <b>End-Node</b> (<i>aka</i> <b>Node-To</b>).
<ul>
<li>Links are always <b>oriented</b>, and their natural direction is <b>From-To</b>:
<ul>
<li>in an <b>unidirectional</b> Network each Link is an <b>one-way</b> connection.<br>
If the connection is available in the opposite direction a second Link must be explicitly declared.<br>
<u>Example</u>: Link <b>X1</b> goes from Node <b>A</b> to Node <b>B</b>, and Link <b>X2</b> goes from Node <b>B</b> to Node
<li>in a <b>bidirectional</b> Network all Links are assumed to establish a connection in both directions.<br>
Definiting an <b>one-way connection</b> requires an appropriate attribute to be set (see below).</li>

<li>The <b>Start-</b> and <b>End-Node</b> could eventually be the same, and in this case we'll have a <b>self-closed</b> Link.</li>
<li>Network's Links <b>can</b> eventually define a linear Geometry (<b>LINESTRING</b>) going from the <b>Start-Node</b> to the <b>End-Node</b>, but this is an optional feature, not a mandatory requirement.</li>
<li>What is absolutely mandatory is that each <b>Link</b> must explicitly reference its

<li>A Network supporting Geometries is a <b>Spatial Network</b>; otherwise a Network lacking any Geometry is a <b>Logical Network</b>.
<ul>
<li>In a <b>Spatial Network</b> all Links <b>must</b> have a corresponding Geometry.</li>
<li>In a <b>Logical Network</b> all Links <b>are strictly forbidden</b> to have any Geometry.</li>
<li>In a <b>Spatial Network</b> both the <b>StartPoint</b> and <b>EndPoint</b> of each Link's <b>LINESTRING</b> are always expected to exactly coincide with the corresponding

<li>In a <b>Spatial Network</b> all references to the same <b>Node</b> by different Links <b>must</b> be an exact match.<br>
<u>Example</u>: Node <b>N5</b> is shared by Links <b>L3</b>, <b>L6</b>, <b>L7</b>, <b>L9</b> and <b>L10</b>, so all their corresponding LINESTRINGS are expected to have the corresponding extremity (<b>Start-</b> or <b>End-</b>, depending on the orientation) points that must exactly match the other.<br>
A <b>topological inconsistency</b> exists if any of these conditions are not satisfied, which leads to an <b>invalid</b> Network.</li>
<li>In a <b>Spatial Network</b> two
<li>Accordingly to the above premises, <b>Nodes</b> are never expected to be explicitly declared in a separate Table.<br>
Just a single Table declaring all <b>Links</b> is required in order to fully define a topologically valid Network.<br>
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.<br>
If any mismatch is detected this surely means that the Network is invalid.</li>
<li>A <b>Link</b> may legitimately self-intersect itself (e.g. forming a loop), as shown in the above figure by Link <b>L15</b> (orange spot).</li>
<li>Two <b>Links</b> may legitimately intersect where no Node exists, as exemplified on the above figure by Links <b>L4</b> and <b>L7</b> (green spot).<br>
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).</li>
<li><b>Links</b> aren't strictly required to be associated with any specific attribute, but the following attributes are almost universally supported:
<ul>
<li>a <b>name</b> identifying the Link.<br>
<u>Examples</u>: the <i>road toponym</i> in a <b>road network</b>, or the <i>river name</i> in an <b>hydrographic
<li>one (or even more) appropriate <b>cost value</b>(s).<br>
<u>Example</u>: the <i>time</i> required to traverse the Link (may be distinguished between pedestrians, bicycles, cars, lorries and so on).</li>
<li>a pair of <b>boolean flags</b> (<b>from-to</b> and <b>to-from</b>) are intendend to specify if the Link can be traversed on both directions or just in one

</ul>
<h4>Logical conclusions</h4>
Any topologically valid <b>Network</b> (irrespective of whether it is a <b>Spatial</b> or <b>Logical</b> type) is a valid <b>Graph</b>.<br>
A Network allowing the support (direct or indirect) of some appropriate <b>cost value</b> is a valid <b>Weighted Graph</b>, and can consequently support <b>Routing algorithms</b>.<br>
All Routing algorithms are intended to identify the <b>Shortest Path</b> solution connecting two <b>Nodes</b> in a <b>weighted graph</b> (<i>aka</i> <b>Network</b>).<br><br>
the term <b><i>Shortest can be easily misunderstood.<br>
Due to historical reasons the most common application field for Routing algorithms is related to <b>Road Networks</b>, but also many other kinds of Networks exist:
<ul>
<li>Hydrographic Networks.</li>
<li>Gas / Water / Oil Networks.</li>
<li>Electrical Networks.</li>
<li>Telecomunication Networks.</li>
<li>Social or Economical Networks representing relationships between individuals or companies.</li>
<li>Epidemiological Networks representing the propagation of infective diseases between individuals or groups.</li>

<br>
In all the above cases we certainly have valid Networks supporting Routing algorithns, but not all of them can imply something like a <i>spatial distance</i> (<i>geometric length</i>) or a <i>travel time</i>.<br>
In the most general acception <b>costs</b> can be represented by any reasonable physical quantity.<br>
So a more generalized definition is assuming that Routing algorithms are intended to identify <b>lesser cost</b> solutions on a <b>weighted graph</b>.<br>
The exact interpretation of the involved <b>costs</b> (<i>aka</i> <b>weights</b>) strictly depends on the very specific nature of each Network.
<h3>The Dijkstra's algorithm</h3>
This well known <a isn't necessarily the fastest one, but it always ensures <b>full correctness</b>:
<ul>
<li>Any Node-to-Node connection identified by Dijkstra's is certainly ensured to be <b>optimal</b>.<br>
In other words, no connetction presenting a lower cost can conceptually exist.</li>
<li>When Dijsjtra's fails to identify a solution this surely means that no solution is possible.</li>
</ul>
<h3>The A* algorithm</h3>
Many alternative Routing algorithms have been invented during the years.<br>
All them are based on heuristic assumptions and are intended to be faster than Dijkstra's, but none of them can ensure <b>full correctness</b> as Dijkstra's does.<br>
The <a algorithm</a> applies a mild heuristic optimization, and can be a realistic alternative to Dijkstra's in many cases.<br><br>
<hr>
<h2>Creating a VirtualRouting Table</h2>
All VirtualRouting queries are based on some <b>VirtualRouting Table</b>, and in turn a VirtualRouting Table is based on some appropriate <b>Binary Data Table</b> supporting an efficient representation of the underlying Network.<br>
So we'll start first by creating such tables.<br><br>
The old and now superseded <b>VirtualNetwork</b> required using a separate CLI tool (<b>spatialite_network</b>) in order to properly initialize a VirtualNetwork Table and its companion Binary Data Table;
alternatively <b>spatialite_gui</b> supported a <b>GUI wizard</b> for the same task. Since version <b>5.0.0</b> now SpatiaLite direcly supports a specific <b>CreateRouting()</b> SQL function.
<verbatim>
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
</verbatim>
<u>Note</u>: this first query contains an intended error causing <b>CreateRouting()</b> to fail raising an exception.<br>
CreateRouting() can fail for multiple reasons, and by calling <b>CreateRouting_GetLastError()</b> you can easily identify the exact reason why the most recent call to CreateRouting() failed.<br>
<verbatim>
SELECT CreateRouting('byfoot_data', 'byfoot', 'roads_vw', 'node_from', 'node_to', 'geom', NULL);
-------------
1

SELECT CreateRouting_GetLastError();
------------------------------------
NULL
</verbatim>
This second attempt if finally succesful, and now CreateRouting() returns <b>1</b> (<i>aka</i> <b>TRUE</b>), and as you can easily check now the Database contains two new Tables: <b>byfoot</b> and <b>byfoot_data</b>.<br>
<u>Note</u>: after a succesfull call to CreateRouting() <b>CreateRouting_GetLastError()</b> will always return <b>NULL</b>.<br><br>
You've just used the <i>reduced form</i> of CreateRouting(); let's see in more depth all the arguments and their meaning:
<ol>
<li><i>byfoot_data</i>: the name of the Network Binary Data to be created.</li>
<li><i>byfoot</i>: the name of the VirtualRouting Table to be created.</li>
<li><i>roads_vw</i>: the name of the <b>Spatial Table</b> or <b>Spatial View</b> representing the underlying Network.<br>
<u>Note</u>: in this case we actually used a Spatial View.</li>
<li><i>node_from</i>: name of the column (in the above Table or View) expected to contain <b>node-from</b> values.</li>
<li><i>node_to</i>: name of the column (in the above Table or View) expected to contain <b>node-to</b> values.</li>
<li><i>geom</i>: name of the column (in the above Table or View) expected to contain <b>Linestrings</b>.<br>
We could have legitimately passed a <b>NULL</b> value for this argument in the case of a <b>Logical Network</b> or if we weren't interested to get a <b>Geometry</b> representing any Routing solution.</li>
<li><i>NULL</i>: name of the column (in the above Table or View) expected to contain <b>cost</b> values.<br>
In this case we have passed a <b>NULL</b> value, and consequently the <b>cost</b> of each Link will be assumed to be represented by the <b>geometric length</b> of the corresponding Linestring.<br>
<u>Note #1</u>: in the case of Networks based on any (<i>aka</i> <b>geographic</b>) Reference System the geometry length of all Linestrings will be precisely <b>measured on the ellipsoid</b> by applying the most accurate <b>geodesic formulae</b> and will be consequently expressed in <b>meters</b>.<br>
<u>Note #2</u>: the <b>geom-column</b> and <b>cost-column</b> arguments are never allowed to be <b>NULL</b> at the same time.</li>
</ol>
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<h3>Technical note</h3>
The internal encoding adopted by the <b>Binaray Data Table</b> is unchanged and is the same for both <b>VirtualNextwok</b> and <b>VirtualRouting</b>.<br>
You can safely base a <b>VirtualRouting Table</b> on any existing Binary Data
Table created by the <b>spatialite-network</b> CLI tool, exactly as you can base a <b>VirtualNetwork Table</b> on any Binary Data Table created by the <b>CreateRouting()</b> SQL function.
<verbatim>
CREATE VIRTUAL TABLE test_network USING VirtualNetwork('some_data_table');

CREATE VIRTUAL TABLE test_routing USING VirtualRouting('some_data_table');
</verbatim>
In order to do such a thing you just have to execute an appropriate <b>CREATE VIRTUAL TABLE</b> statement.
<h4>Warning</h4>
In the case of <b>Spatial Networks</b> based on any <b>geographic</b> Reference System (uing <b>longitudes</b> and <b>latitudes</b>) there is an important difference between Binary Data Tables created by the <b>spatialite_network</b> GUI tool and  Binary Data Tables created by the <b>CreateRouting</b> SQL function when the <b>cost</b> is implicitly based on the geometric length of the Link's Linestring:
<ul>
<li>the <b>spatialite_network</b> CLI tool (and the <b>GUI wizard</b> implemented by previous versions of <b>spatialite_gui</b>) compute the Linestring's length as an <b>angular distance</b> expressed in
<li>the <b>CreateRouting()</b> SQL function computes the Linestring's length as a <b>linear distance</b> expressed in <b>metres</b> by applying the most accurate <b>geodesic
</ul>


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