Geoscience Reference

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Fig. 6
Graph of the ratio of least risk on shortest path length to the shortest path length

A comparison of the lengths of the least risk and shortest paths for one set of

paths from a single source to every other vertex in the data set is shown in Fig.
6
.

The figure provides a scatter plot of the normalized least risk path length (the ratio

of least risk to shortest path lengths), plotted against shortest path length. In this

example, more than 98 % of the least risk paths are less than 50 % longer than the

corresponding shortest path.

Most paths are (almost) similar in length to its shortest path equivalent. Often

only a small change in path choice can be found with a difference of only a couple of

nodes compared to the shortest path. On the other hand, the strongly correlated stripes

going from top left to bottom right in the graph exhibit blocks of correlated paths with

very similar path sequences throughout their entire route. These occur because many

adjacent nodes are required to take similar edges to reach their destination. This can

also be seen in Fig.
5
. The nodes within the dashed rectangle all take the same route

for both their least risk and shortest path, resulting in connected ratios in Fig.
6
.

4.2 Analysis of Indoor Least Risk Paths Compared

to the Results in Outdoor Space

In this section, several of the data obtained before will be compared with the

results obtained by the calculations of least risk paths by Grum (
2005
) and sim-

plest paths by Duckham and Kulik (
2003
). We mainly want to investigate whether