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arangodb/js/common/modules/@arangodb/graph/algorithms-common.js

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/*jshint strict: false */
////////////////////////////////////////////////////////////////////////////////
/// @brief Graph functionality
///
/// @file
///
/// DISCLAIMER
///
/// Copyright 2010-2012 triagens GmbH, Cologne, Germany
///
/// Licensed under the Apache License, Version 2.0 (the "License");
/// you may not use this file except in compliance with the License.
/// You may obtain a copy of the License at
///
/// http://www.apache.org/licenses/LICENSE-2.0
///
/// Unless required by applicable law or agreed to in writing, software
/// distributed under the License is distributed on an "AS IS" BASIS,
/// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
/// See the License for the specific language governing permissions and
/// limitations under the License.
///
/// Copyright holder is triAGENS GmbH, Cologne, Germany
///
/// @author Dr. Frank Celler, Lucas Dohmen
/// @author Copyright 2011-2012, triAGENS GmbH, Cologne, Germany
////////////////////////////////////////////////////////////////////////////////
var graph = require("@arangodb/graph-blueprint");
var Graph = graph.Graph;
var Vertex = graph.Vertex;
// -----------------------------------------------------------------------------
// --SECTION-- module "@arangodb/graph-blueprint"
// -----------------------------------------------------------------------------
function unite (l, r) {
return r.concat(l.filter(function (element) {
return (r.indexOf(element) === -1);
}));
}
function intersect (l, r) {
return l.filter(function (element) {
return (r.indexOf(element) > -1);
});
}
function removeLastOccurrenceOf (l, element) {
return l.splice(l.lastIndexOf(element), 1);
}
// -----------------------------------------------------------------------------
// --SECTION-- VERTEX
// -----------------------------------------------------------------------------
// -----------------------------------------------------------------------------
// --SECTION-- public functions
// -----------------------------------------------------------------------------
////////////////////////////////////////////////////////////////////////////////
/// @brief return the number of common neighbors
///
/// @FUN{@FA{vertex}.commonNeighborsWith(@FA{target_vertex}, @FA{options})}
///
////////////////////////////////////////////////////////////////////////////////
Vertex.prototype.commonNeighborsWith = function (target_vertex, options) {
var neighbor_set_one,
neighbor_set_two,
id_only,
common_neighbors,
all_neighbors,
return_value;
options = options || {};
id_only = function (neighbor) {
return neighbor.id;
};
if (typeof(target_vertex) !== 'object') {
throw "<target_vertex> must be a vertex object";
}
neighbor_set_one = this.getNeighbors(options).map(id_only);
neighbor_set_two = target_vertex.getNeighbors(options).map(id_only);
common_neighbors = intersect(neighbor_set_one, neighbor_set_two);
if ((options.listed !== undefined) && (options.listed === true)) {
return_value = common_neighbors;
}
else if ((options.normalized !== undefined) && (options.normalized === true)) {
all_neighbors = unite(neighbor_set_one, neighbor_set_two);
return_value = (common_neighbors.length / all_neighbors.length);
}
else {
return_value = common_neighbors.length;
}
return return_value;
};
////////////////////////////////////////////////////////////////////////////////
/// @brief return the number of common properties
///
/// @FUN{@FA{vertex}.commonPropertiesWith(@FA{target_vertex}, @FA{options})}
///
////////////////////////////////////////////////////////////////////////////////
Vertex.prototype.commonPropertiesWith = function (other_vertex, options) {
var property_names,
shared_properties = [],
this_vertex = this,
return_value;
options = options || {};
property_names = unite(this_vertex.getPropertyKeys(), other_vertex.getPropertyKeys());
property_names.forEach(function (property) {
if (this_vertex.getProperty(property) === other_vertex.getProperty(property)) {
shared_properties.push(property);
}
});
if ((options.listed !== undefined) && (options.listed === true)) {
return_value = shared_properties;
} else if ((options.normalized !== undefined) && (options.normalized === true)) {
return_value = shared_properties.length / property_names.length;
} else {
return_value = shared_properties.length;
}
return return_value;
};
////////////////////////////////////////////////////////////////////////////////
/// @brief find the shortest path to a certain vertex, return the ID
///
/// @FUN{@FA{vertex}.pathTo(@FA{target_vertex}, @FA{options})}
///
////////////////////////////////////////////////////////////////////////////////
Vertex.prototype.pathTo = function (target_vertex, options) {
if (typeof(target_vertex) !== 'object') {
throw "<target_vertex> must be an object";
}
var predecessors = target_vertex.determinePredecessors(this, options || {});
return (predecessors ? target_vertex.pathesForTree(predecessors) : []);
};
////////////////////////////////////////////////////////////////////////////////
/// @brief find the shortest path and return the number of edges to the target vertex
///
/// @FUN{@FA{vertex}.distanceTo(@FA{target_vertex}, @FA{options})}
///
////////////////////////////////////////////////////////////////////////////////
Vertex.prototype.distanceTo = function (target_vertex, options) {
var predecessors = target_vertex.determinePredecessors(this, options || {}),
current_vertex_id = target_vertex.getId(),
count = 0;
while (predecessors[current_vertex_id] !== undefined) {
current_vertex_id = predecessors[current_vertex_id][0];
count += 1;
}
if (current_vertex_id !== this.getId()) {
count = Infinity;
}
return count;
};
////////////////////////////////////////////////////////////////////////////////
/// @brief determine all the pathes to this node from source
///
/// @FUN{@FA{vertex}.determinePredecessors(@FA{source}, @FA{options})}
///
////////////////////////////////////////////////////////////////////////////////
Vertex.prototype.determinePredecessors = function (source, options) {
var graph = this._graph, // Graph
determined_list = [], // [ID]
predecessors, // { ID => [ID] }
source_id = source.getId(), // ID
todo_list = [source_id], // [ID]
distances = {}, // { ID => Number }
current_vertex, // Vertex
current_vertex_id, // ID
return_value = false; // { ID => [ID]}
distances[source_id] = 0;
if (options.cached) {
predecessors = graph.getCachedPredecessors(this, source);
}
if (!predecessors) {
predecessors = {};
while (todo_list.length > 0) {
current_vertex_id = this._getShortestDistance(todo_list, distances);
current_vertex = this._graph.getVertex(current_vertex_id);
if (current_vertex_id === this.getId()) {
return_value = predecessors;
break;
} else {
removeLastOccurrenceOf(todo_list, current_vertex_id);
determined_list.push(current_vertex_id);
todo_list = unite(todo_list, current_vertex._processNeighbors(
determined_list,
distances,
predecessors,
options
));
}
}
graph.setCachedPredecessors(this, source, predecessors);
}
return return_value;
};
////////////////////////////////////////////////////////////////////////////////
/// @brief Helper function for determinePredecessors (changes distance and predecessors
///
/// @FUN{@FA{vertex}._processNeighbors(@FA{determined}, @FA{distances}, @FA{predecessors})}
///
////////////////////////////////////////////////////////////////////////////////
Vertex.prototype._processNeighbors = function (determined_list, distances, predecessors, options) {
var i,
current_neighbor_id,
current_distance,
raw_neighborlist,
compared_distance,
current_weight,
not_determined_neighbors = [];
raw_neighborlist = this.getNeighbors(options);
for (i = 0; i < raw_neighborlist.length; i += 1) {
current_neighbor_id = raw_neighborlist[i].id;
if (determined_list.lastIndexOf(current_neighbor_id) === -1) {
current_weight = raw_neighborlist[i].weight;
current_distance = distances[this.getId()] + current_weight;
not_determined_neighbors.push(current_neighbor_id);
compared_distance = distances[current_neighbor_id];
if ((compared_distance === undefined) || (compared_distance > current_distance)) {
predecessors[current_neighbor_id] = [this.getId()];
distances[current_neighbor_id] = current_distance;
} else if (compared_distance === current_distance) {
predecessors[current_neighbor_id].push(this.getId());
}
}
}
return not_determined_neighbors;
};
////////////////////////////////////////////////////////////////////////////////
/// @brief Get all paths from root to leave vertices for a given tree
///
/// @FUN{@FA{vertex}.pathesForTree(@FA{tree}, @FA{path_to_here})}
///
////////////////////////////////////////////////////////////////////////////////
Vertex.prototype.pathesForTree = function (tree, path_to_here) {
var my_children = tree[this.getId()],
i,
my_child,
pathes = [];
path_to_here = path_to_here || [];
path_to_here = path_to_here.concat(this.getId());
if (my_children === undefined) {
pathes = [path_to_here.reverse()];
} else {
for (i = 0; i < my_children.length; i += 1) {
my_child = this._graph.getVertex(my_children[i]);
pathes = pathes.concat(my_child.pathesForTree(tree, path_to_here));
}
}
return pathes;
};
////////////////////////////////////////////////////////////////////////////////
/// @brief Get all neighbours for this vertex
///
/// @FUN{@FA{vertex}.getNeighbors(@FA{options})}
///
////////////////////////////////////////////////////////////////////////////////
Vertex.prototype.getNeighbors = function (options) {
var current_vertex,
target_array = [],
addNeighborToList;
if (! options) {
options = { };
}
var direction = options.direction || 'both',
labels = options.labels,
weight = options.weight,
weight_function = options.weight_function,
default_weight = options.default_weight || Infinity,
only = options.only;
addNeighborToList = function (current_edge, current_vertex) {
var neighbor_info, current_label = current_edge.getLabel();
if ((labels === undefined) || (labels.lastIndexOf(current_label) > -1)) {
neighbor_info = { id: current_vertex.getId() };
if (weight !== undefined) {
neighbor_info.weight = current_edge.getProperty(weight) || default_weight;
} else if (weight_function !== undefined) {
neighbor_info.weight = weight_function(current_edge);
} else {
neighbor_info.weight = 1;
}
if ((only === undefined) || (only(current_edge))) {
target_array.push(neighbor_info);
}
}
};
if ((direction === 'both') || (direction === 'outbound')) {
this.getOutEdges().forEach(function (current_edge) {
current_vertex = current_edge.getInVertex();
if (current_vertex !== null) {
addNeighborToList(current_edge, current_vertex);
}
});
}
if ((direction === 'both') || (direction === 'inbound')) {
this.getInEdges().forEach(function (current_edge) {
current_vertex = current_edge.getOutVertex();
if (current_vertex !== null) {
addNeighborToList(current_edge, current_vertex);
}
});
}
return target_array;
};
////////////////////////////////////////////////////////////////////////////////
/// @brief Get the shortest distance for a given list of vertices and
/// their distances
///
/// @FUN{@FA{vertex}._getShortestDistance(@FA{todo_list}, @FA{distances})}
///
////////////////////////////////////////////////////////////////////////////////
Vertex.prototype._getShortestDistance = function (todo_list, distances) {
var shortest_distance = Infinity,
vertex = null,
i,
distance;
for (i = 0; i < todo_list.length; i += 1) {
distance = distances[todo_list[i]];
if (distance < shortest_distance) {
shortest_distance = distance;
vertex = todo_list[i];
}
}
return vertex;
};
////////////////////////////////////////////////////////////////////////////////
/// @brief calculate a measurement
///
/// @FUN{@FA{vertex}.measurement(@FA{measurement})}
///
/// Calculates the eccentricity, betweenness or closeness of the vertex
///
////////////////////////////////////////////////////////////////////////////////
Vertex.prototype.measurement = function (measurement) {
var graph = this._graph,
source = this,
value;
if (measurement === "betweenness") {
value = graph.geodesics({
grouped: true,
threshold: true
}).reduce(function (count, geodesic_group) {
var included = geodesic_group.filter(function (geodesic) {
return geodesic.slice(1, -1).indexOf(source.getId()) > -1;
});
return (included ? count + (included.length / geodesic_group.length) : count);
}, 0);
} else if (measurement === "eccentricity") {
value = graph._vertices.toArray().reduce(function (calculated, target) {
var distance = source.distanceTo(graph.getVertex(target._id));
return Math.max(calculated, distance);
}, 0);
} else if (measurement === "closeness") {
value = graph._vertices.toArray().reduce(function (calculated, target) {
var distance = source.distanceTo(graph.getVertex(target._id));
return calculated + distance;
}, 0);
} else {
throw "Unknown Measurement '" + measurement + "'";
}
return value;
};
// -----------------------------------------------------------------------------
// --SECTION-- Graph
// -----------------------------------------------------------------------------
// -----------------------------------------------------------------------------
// --SECTION-- public methods
// -----------------------------------------------------------------------------
////////////////////////////////////////////////////////////////////////////////
/// @brief return all shortest paths
///
/// @FUN{@FA{graph}.geodesics(@FA{options})}
///
/// Return all shortest paths
/// An optional `options` JSON object can be specified to control the result.
/// `options` can have the following sub-attributes:
/// - `grouped`: if not specified or set to `false`, the result will be a flat
/// list. If set to `true`, the result will be a list containing list of
/// paths, grouped for each combination of source and target.
/// - `threshold`: if not specified, all paths will be returned. If `threshold`
/// is `true`, only paths with a minimum length of 3 will be returned
////////////////////////////////////////////////////////////////////////////////
Graph.prototype.geodesics = function (options) {
var sources = this._vertices.toArray(),
targets = sources.slice(),
geodesics = [],
graph = this,
vertexConstructor;
options = options || {};
vertexConstructor = function (raw_vertex) {
return graph.constructVertex(raw_vertex._id);
};
sources = sources.map(vertexConstructor);
targets = targets.map(vertexConstructor);
sources.forEach(function (source) {
targets = targets.slice(1);
targets.forEach(function (target) {
var pathes = source.pathTo(target);
if (pathes.length > 0 && (!options.threshold || pathes[0].length > 2)) {
if (options.grouped) {
geodesics.push(pathes);
} else {
geodesics = geodesics.concat(pathes);
}
}
});
});
return geodesics;
};
////////////////////////////////////////////////////////////////////////////////
/// @brief calculate a measurement
///
/// @FUN{@FA{graph}.measurement(@FA{measurement})}
///
/// Calculates the diameter or radius of a graph.
/// `measurement` can either be:
/// - `diameter`: to calculate the diameter
/// - `radius`: to calculate the radius
///
////////////////////////////////////////////////////////////////////////////////
Graph.prototype.measurement = function (measurement) {
var graph = this,
vertices = graph._vertices.toArray(),
start_value;
switch (measurement) {
case "diameter":
start_value = 0;
break;
case "radius":
start_value = Infinity;
break;
default:
throw "Unknown Measurement '" + measurement + "'";
}
return vertices.reduce(function (calculated, vertex) {
vertex = graph.getVertex(vertex._id);
switch (measurement) {
case "diameter":
calculated = Math.max(calculated, vertex.measurement("eccentricity"));
break;
case "radius":
calculated = Math.min(calculated, vertex.measurement("eccentricity"));
break;
}
return calculated;
}, start_value);
};
////////////////////////////////////////////////////////////////////////////////
/// @brief calculate a normalized measurement
///
/// @FUN{@FA{graph}.normalizedMeasurement(@FA{measurement})}
///
/// Calculates the normalized degree, closeness, betweenness or eccentricity
/// of all vertices in a graph
/// `measurement` can either be:
/// - `closeness`: to calculate the closeness
/// - `betweenness`: to calculate the betweenness
/// - `eccentricity`: to calculate the eccentricity
///
////////////////////////////////////////////////////////////////////////////////
Graph.prototype.normalizedMeasurement = function (measurement) {
var graph = this,
vertices = graph._vertices.toArray(),
vertex_map,
max = 0;
vertex_map = vertices.reduce(function (map, raw_vertex) {
var vertex = graph.constructVertex(raw_vertex._id),
measured;
switch(measurement) {
case "closeness":
measured = 1 / vertex.measurement("closeness");
break;
case "betweenness":
measured = vertex.measurement("betweenness");
break;
case "eccentricity":
measured = 1 / vertex.measurement("eccentricity");
break;
default:
throw "Unknown measurement";
}
if (measured > max) {
max = measured;
}
map[vertex.getId()] = measured;
return map;
}, {});
Object.keys(vertex_map).forEach(function(key) {
vertex_map[key] = vertex_map[key] / max;
});
return vertex_map;
};
// -----------------------------------------------------------------------------
// --SECTION-- END-OF-FILE
// -----------------------------------------------------------------------------
// Local Variables:
// mode: outline-minor
// outline-regexp: "^\\(/// @brief\\|/// @addtogroup\\|// --SECTION--\\|/// @page\\|/// @}\\)"
// End:
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