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Table 2 Time of shortest path search with Dijkstra’s and A* algorithms in two original graphs ( G 1 , G 2 ) and time of shortest path search in four reduced graphs with the proposed approach

From: Algorithm for shortest path search in Geographic Information Systems by using reduced graphs

Graph

Algorithm

NVa

Time (seconds)

Optimal path

G 1

Dijkstra

41810

0.6160

yes

 

A* (h=0)

 

0.4938

yes

 

A* (h=Euclidean distance)

 

0.0200

no

G r 1.1

Algorithm 3 (MDijkstra)

250

0.0036

yes

G r 1.2

Algorithm 3 (MDijkstra)

1826

0.0265

yes

G 2

Dijkstra

149756

3.0249

yes

 

A* (h=0)

 

2.2108

yes

 

A* (h=Euclidean distance)

 

0.1011

no

G r 2.1

Algorithm 3 (MDijkstra)

765

0.0193

yes

G r 2.2

Algorithm 3 (MDijkstra)

2617

0.0722

yes

  1. aNumber of vertices of the graph.