This document discusses shortest path algorithms in GIS. It defines shortest path problems as finding the lowest cost path between two nodes in a graph. Topology in GIS allows accurate connectivity and contiguity analysis to run shortest path algorithms. Common shortest path problems include single-source, single-destination, and all-pairs variants. Dijkstra's algorithm is described for solving the single-source shortest path problem from a starting node to all others. Applications include finding closest facilities like hospitals and determining scenic routes between locations. An example case study finds reliable transportation routes in Houston, TX using a GIS network.

1. Shortest Path Algorithms
Samar D. Kenkre
Tarun Bhatia
Yash J. Nagpal
3rd Year B.Tech(Civil)
APPLICATIONS OF GIS

2. 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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3. Topology in GIS
 Topology enables connectivity and contiguity analysis, thereby making
Shortest path algorithms run consistently and accurately.
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4. Courtesy: Dr. Amba Shetty, NITK Surathkal
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5. 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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6. 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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7. 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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8. 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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10. Running time
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11. Single source variable destination
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Single Source variable destination type

12. 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
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1) CLOSEST FACILITY ANALYSIS

13. Most Scenic path
 Developed at MIT
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14. Case Study
Finding a Reliable Route between two points in
Houston, TX in a Transportation Network using GIS.
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Road classification-
Houston, TX

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17. 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.
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