The summary of experimental results of Ekillion will be illustrated as follows.
Table 1 displays all JR train paths for four key regions of metropolis suburbs in Japan represented in a graph data structure, and the corresponding graph structure information on number of nodes (number of stations), edges (number of station spacing) and total distance.
In this report, the results of the graph are shown in two formats, namely “All Stations in the Rail Network” which refers to the actual train route map in graph structure, and “Transfer Stations Network” which excludes 2nd degree node (intermediate stations that do not have connections between trains).
Table 2 shows the degree distribution of nodes (station). 1st degree refers to the last station (It does not necessarily correspond to the so-called terminal station, but instead refers to the termination of segment between metropolis suburbs.)
Region | Railroad Network (all stations) |
Railroad Network (interchange stations only) |
||||
Nodes | Edges | Total Distance | Nodes | Edges | Total Distance | |
Osaka | 355 | 364 | 941.0 km | 26 | 34 | 924.3 km |
Tokyo | 623 | 653 | 2,055.6 km | 72 | 101 | 2,037.9 km |
Fukuoka | 128 | 131 | 323.0 km | 19 | 22 | 323.0 km |
Niigata | 58 | 59 | 174.2 km | 7 | 7 | 159.0 km |
Region | number of n-th degree stations | 1st Degree Stations | Max Degree Stations | ||||
1 | 2 | 3 | 4 | 5 | |||
Osaka | 7 | 329 | 13 | 6 | 0 | JR-Namba, Wadamisaki, Sonobe, Sakurajima, Higashi-Hagoromo, Kansai-Kuko(Kansai Airport), Banshu-Ako | Kyoto, Osaka, Amagasaki, Kizu, Tennoji, Kyobashi (4th degree) |
Tokyo | 18 | 551 | 34 | 16 | 4 | Iwaki, Kuroiso, Umi-Shibaura, Okawa, Ogimachi, Kurihama, Nirasaki, Choshi, Narita-Kuko(Narita Airport) and others | Nishi-funabashi, Haijima, Akabane, Omiya (5th degree) |
Fukuoka | 8 | 109 | 8 | 3 | 0 | Hakata-minami, Mojiko, Tosu, Yukuhashi, Wakamatsu, Imayama, Saitozaki, Umi | Orio, Kashii, Chojabaru (4th degree) |
Niigata | 3 | 51 | 3 | 1 | 0 | Gosen, Nagaoka, Yahiko | Niitsu (4th degree) |
Taking into consideration roundtrip routes from one station to another, let’s explore the maximum possible routes between two stations.
Table 3 shows the result of “Transfer Stations Network”, and Table 4 shows “All Stations in Railroad network”.
The intermediate stations are excluded from the “Transfer Stations Network”. For instance, Osaka Station and Kyoto Station are treated as neighbor stations.
Name of s-t stations | Number of Routes | Longest Distance (km) | Stations | Search for number of s-t stations | Processing Time (sec) | Time/pair | |
Osaka | Kyoto – Osaka | 103 | 514.8 | 16 | 34 | 1.49 | 0.043 |
Tokyo | Abiko – Narita | 9,427,117 | 976.4 | 52 | 101 | 15.07 | 0.149 |
Fukuoka | Keisen – Shin-Iizuka | 9 | 157.5 | 11 | 22 | 0.94 | 0.043 |
Niigata | Higashi-Sanjo – Yoshida | 3 | 108.5 | 5 | 7 | 0.37 | 0.053 |
Name of s-t stations | Number of Routes | Longest Distance (km) | Stations | Search for number of s-t stations | Processing Time (sec) | Time/pair | |
Osaka | Higashi-Yodogawa – Shin-Osaka | 103 | 556.9 | 208 | 364 | 23.55 | 0.065 |
Tokyo | Fusa – Kinoshita | 9,427,117 | 1,007.4 | 331 | 653 | 2715 | 4.16 |
Fukuoka | Fukkodai-mae – Kyusandai-mae | 9 | 163.4 | 66 | 131 | 6.45 | 0.049 |
Niigata | Tagami – Yashiroda | 3 | 121.0 | 41 | 59 | 2.57 | 0.043 |
* If the number of routes is equal, the route with maximum distance between the two stations is displayed.
* Execution environment: amazon AWS m3.2xlarge (8 cores, 26 ECUs, 30 GB memory)
Taking into consideration roundtrip routes from one station to another station, let’s explore the maximum number of possible routes between two stations.
In the previous session, “Search for Adjacent Stations” is restricted to adjacent stations. However this section search for all possible combinations of starting and ending stations, and explores all possible routes between stations in the metroplis suburbs without the previous restriction.
Table 5 shows the result of “Transfer stations network”, and Table 6 shows the results of “All Stations in the Railroad Network”.
Name of s-t stations | Number of Routes | Longest Distance (km) | Stations | Search for number of s-t stations | Processing Time (sec) | Time/pair | |
Osaka | Banshu-Ako – Ohmi-Shiotsu | 392 | 653.4 | 20 | 325 | 5.73 | 0.018 |
Tokyo | Isogo – Kazusa-Kameyama | 26,440,720 | 1,121.1 | 52 | 2,556 | 143.8 | 0.0056 |
Fukuoka | Imayama – Hakata-Minami | 14 | 200.0 | 11 | 171 | 2.82 | 0.016 |
Niigata | Higashi-Sanjo – Shibata | 4 | 87.7 | 5 | 21 | 0.32 | 0.015 |
Name of s-t stations | Number of Routes | Longest Distance (km) | Stations | Search for number of s-t stations | Processing Time | Time/pair | |
Osaka | Ritto – Tsukaguchi | 392 | 743.1 | 283 | 62,790 | 29.6 min | 0.028 |
Tokyo | Hongodai – Higashi-Jujo | 28,328,716 | 1,078.0 | 360 | 339,076 | – | – |
Fukuoka | Harumachi – Higashi-Mizumaki | 16 | 200.3 | 81 | 8,125 | 2.5 min | 0.019 |
Niigata | Echigo-Ishiyama – Nagaoka | 4 | 134.1 | 46 | 1,653 | 0.5 min | 0.018 |
* If the number of routes is equal, the route with maximum distance between the two stations is displayed.
* Execution environment: amazon AWS m3.2xlarge (8 cores, 26 ECUs, 30 GB memory)
* The processing time results are not available for Tokyo in Table 6 as the experiments are executed in a different environment.
Taking into consideration roundtrip routes from one station to another station, let’s explore the longest possible route between two stations.
Table 7 shows the results restricted to adjacent stations. Table 8 shows the results of including all stations in the search.
Name of s-t Stations | Routes | Longest Distance (km) | Stations | |
Osaka | JR-Kawachi-Eiwa – JR-Shuntokumichi | 71 | 557.0 | 208 |
Tokyo | Nishi-Nippori – Nippori | 4,789,007 | 1,016.8 | 340 |
Fukuoka | Hakata – Yoshizuka | 7 | 163.4 | 66 |
Niigata | Tagami – Yashiroda | 3 | 121.0 | 41 |
Name of s-t Stations | Routes | Longest Distance (km) | Stations | |
Osaka | JR-Namba – Tsukaguchi | 210 | 743.5 | 286 |
Tokyo | Iwaki – Nirasaki | 6,632,867 | 1,201.3 | 379 |
Fukuoka | Imayama – Mizumaki | 10 | 210.2 | 85 |
Niigata | Kita-Sanjo – Nagaoka | 3 | 142.2 | 48 |