Shortest Path Algorithms

Samar D. Kenkre

Tarun Bhatia

Yash J. Nagpal

3rd Year B.Tech(Civil)

APPLICATIONS OF GIS

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Topology in GIS A GIS topology is a set of rules and behaviours that model how

points, lines and polygons share coincident geometry.

When a map is stretched or distorted, some properties (topological properties) don’t change. Eg. Adjacencies, Relationships such as “is contained in”, “is contained in”, spatial features, etc.

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Topology in GIS

Topology enables connectivity and contiguity analysis, thereby making Shortest path algorithms run consistently and accurately.

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Courtesy: Dr. Amba Shetty, NITK Surathkal

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What are shortest path problems? In graph theory, the shortest path problem is the problem of

finding a path between two vertices (or nodes) such that the sum of the weights of its constituent edges is minimized.

An example is finding the quickest way to get from one location to another on a road map; in this case, the vertices represent locations and the edges represent segments of road and are weighted by the time needed to travel that segment.

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What are shortest path problems? The problem is also sometimes called the single-pair shortest

path problem, to distinguish it from the following generalizations:

The single-source shortest path problem, in which we have to find shortest paths from a source vertex v to all other vertices in the graph.

The single-destination shortest path problem, in which we have to find shortest paths from all vertices in the graph to a single destination vertex v. This can be reduced to the single-source shortest path problem by reversing the edges in the graph.

The all-pairs shortest path problem, in which we have to find shortest paths between every pair of vertices v, v' in the graph.

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Single source shortest path problem The problem of finding shortest paths from a source vertex v to all

other vertices in the graph

Different Algorithms used: Dijktra’s Algorithm

Bellman-Ford Algo

J C Green Algo

Pertubation Theory

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Dijkstra’s Algorithm Edsger Wybe Dijkstra

May 11,1930 – August 6,2002

Dutch computer Scientist, Received the Turing Award in 1972, highest achievement in the field of Computer Science

Known for his many essays on programming and contributions to Graph Theory

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Running time

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Single source variable destination

Single Source variable destination type

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Applications

The closest facility solver measures the cost of traveling between incidents and facilities and determines which are nearest to one other. When finding closest facilities, you can specify how many to find and whether the direction of travel is toward or away from them. Eg. Ambulances and hospitals

1) CLOSEST FACILITY ANALYSIS

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Most Scenic path

Developed at MIT

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Case StudyFinding a Reliable Route between two points in Houston, TX in a Transportation Network using

GIS.

Road classification- Houston, TX

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References

http://wiki.gis.com/wiki/index.php/Shortest_path_problem

http://resources.arcgis.com

“Introduction to GIS”, Dr. Amba Shetty, NITK Surathkal

Zhao Na, “An Improved Algorithm of the Shortest Path Search Problem in GIS Field”, 2012 International Conference on Communication, Electronics and Automation Engineering, pp 1035-1039.