Directed Graph Library

by GRASS Development Team


The Directed Graph Library or DGLib (Micarelli 2002) provides functionality for vector network analysis. This library released under GPL is hosted by the GRASS project (in the CVS server). As stand-alone library it may also be used by other software project.

A graph is a system of logical connections between a collection of objects called vertices. Graphs are usually represented by a picture, so that each vertex is shown as a point, with the connections shown as line segments. These vertices are also commonly referred to as nodes, edges referred to as arcs. A directed graph (digraph) consists of a finite set of vertices, and a finite set of edges, where an edge is an ordered pair of vertices. A directed graph has the property that edges have a direction, this is the reason for defining an edge as an ordered pair of vertices often referred to as the head and the tail of the edge.

The original design idea behind DGLib was to support middle sized graphs in RAM with a near-static structure that doesn't need to be dynamically modified by the user program; ability to read graphs from input streams and process them with no needle to rebuild internal trees. A representation has been defined, where graph data is stored in 32bit word arrays and each element pointer is converted to a relative offset. This representation is serializable from/to input/output streams and allows fast load-and-use processing. Graphs need to be de-serialized in order to be edited. In further refactorings the library has evolved to support dynamic changes and state-independent algorithm (algorithms can be run on both serializable or editable graphs).

DGLib defines a serializable graph as being in FLAT state and a editable graph as being in TREE state. The implementation makes intensive use of libavl ( AVL data structures to support TREE state.

So far DGLib defines three different graph versions, version 1 supports directed graph with a weak concept of the edge, it can support many applications where one doesn't need to know about the input edges of a node (in-degree) and where there is no requirement to directly retrieve edges by their identifier but only by head/tail combinations. Version 2 adds in-degree support and a true edge addressing, yet supporting directed graph. Version 3 uses the same internal representation of version 2 but activates code branches to support undirected graphs.

The DGLib user can control a number of static features and can attach a arbitrary amount of data to each node (node-attributes) and each edge (edge-attributes). Attributes are not considered to be part of the graph structure and can be edited also when the graph is in FLAT state.

Graph traversal in neither recursive nor hook (callback) based, but built on the use of traversers for nodes and edges. By default, traversal is ordered by node and edge identifiers but can optionally be ordered by other means. For example, it is often useful to visit edges on a weight order} basis (greedy algorithm), this is possible via prioritizers that are activated by setting specific graph options.

Both preemptive (blocking) and non-preemptive (non-blocking/multiplexed) I/O is supported, although GRASS does not actually use graph storage it may be easily required by any other library user. Thread safety is so far ensured by a data separation design that keeps all application context states into stack containers, whose life cycle is controlled by the user program. Each graph is a separate container and two or more graphs never conflict. In addition algorithms (ie. shortest path) can safely share the same graph, while concurrent editing on the same graph is unsafe.

As DGLib is under development, only a bunch of polynomial time algorithms have been implemented, and the basic structure is being stressed to be a mature core to possibly time wasting computations. Current algorithms are: shortest path, depth spanning, and minimum spanning. Spanning algorithms silently behave as arborescenses when applied to directed graphs. A clip callback function, optionally supplied by the user, comes called by the library while traversing the graph in order to alter default algorithm behavior (i.e. user can control access to specific graph segments while computing shortest path).

The Directed Graph Library library provides functionality to assign costs to lines and/or nodes. That means that costs can be accumulated while traveling along polylines. The user can assign individual costs to all lines and/or nodes of a vector map and later calculate shortest path connections based on the accumulated costs. Applications are transport analysis, connectivity and more.

Text based on:

R. Blazek, M. Neteler, and R. Micarelli. The new GRASS 5.1 vector architecture. In Open source GIS - GRASS users conference 2002, Trento, Italy, 11-13 September 2002. University of Trento, Italy, 2002.

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Last change: $Date: 2008-11-27 16:55:48 +0100 (Thu, 27 Nov 2008) $