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