Geoscience Reference
In-Depth Information
Table 1
Summary of the entire dataset
Total cost difference (m)
Length difference (m)
Risk value difference (m)
−
4.48
Average
11.13
15.61
Min
0.00
−
74.63
0.00
Max
135.48
0.00
145.73
Table 2
Classification of
path lengths
Length increase
Number of paths
Percentage of total paths
Equal path lengths
160,984
46.64
0-5 %
87,681
25.40
5-10 %
50,773
14.71
10-25 %
41,196
11.94
25-50 %
4,363
1.26
>50 %
159
0.05
Total
345,156
100.00
lost by taking a slightly longer route. Given the definition of least risk paths, we
put forward the following hypotheses. First, the length of a path described by the
least risk path algorithm is expected to be equal or longer than its equivalent short-
est path. As such, it provides a measure of detour a wayfinder would need to take
when using a path that is less easy to get lost on. Second, the risk values of the
shortest path will be equal or larger than for the least risk path. The least risk path
algorithm will more likely calculate routes with fewer intersections, away from the
major corridors where many choices appear. It will also take longer edges while
the shortest path will go for the most direct option ignoring the complexity of the
individual intersections. Third, the total risk value for the shortest path will be
equal or higher than for the least risk paths as this is the minimization criterion for
the least risk algorithm. Above aspects are analysed in the following paragraphs by
comparing paths calculated by the least risk path algorithm and those calculated
by the Dijkstra shortest path algorithm. These results aim to provide an indica-
tion of the balance struck by the different algorithms between the desire for direct
routes versus less risky routes.
Table
1
shows that on average, the difference in path length for least risk paths
is around 4.5 m with a decrease in risk value of 15.6 m. The values comparing the
Dijkstra algorithm with the least risk path algorithm (total risk value minimiza-
tion) align with the hypothesis stated before, with an increase in risk values for
shortest paths and an increase in length values for least risk paths.
Over the entire dataset, a least risk path indoor is on average 4 % longer than its
respective shortest path (using both the calculations of Duckham and Kulik (
2003
)
as well as those from Jiang and Liu (
2011
)). Although 53 % of least risk paths are
longer than their equivalent shortest paths, the majority (almost 99 %) of the paths
are less than a quarter longer (see Table
2
). This indicates that even though half of
all the paths seem to deviate from the shortest path to obtain a theoretically less risky
route (otherwise their lengths would be equal), those deviations are mostly limited
