Graph Golf

The Order/degree Problem Competition

Rankings and solutions 2017

Update 2017-07-24

Current rankings

General Graph Widest Improvement ranking

Rank Author Number of best solutions
1 Yong Zhang 3
1 Yinling Wang 3
1 Francis Lau 3
1 Xin Han 3
1 Vincent Chau 3
6 Ryuhei Mori 2
7 Teruaki Kitasuka 1
7 Takayuki Matsuzaki 1
7 Masahiro Iida 1

General Graph Deepest Improvement ranking

Rank Author ASPL gap
1 Ryuhei Mori 0.0
2 Masahiro Iida 0.037009803921568496
2 Takayuki Matsuzaki 0.037009803921568496
2 Teruaki Kitasuka 0.037009803921568496
5 thai9cdb 0.1948618054816862
6 Francis Lau 0.2949871405814033
7 Xin Han 0.2962566336015975
7 Yinling Wang 0.2962566336015975
7 Vincent Chau 0.2962566336015975
7 Yong Zhang 0.2962566336015975
11 hiro 0.4193548387096775
12 Yosuke Kikuchi 0.635294117647059
12 Tamami Okada 0.635294117647059

Grid Graph Widest Improvement ranking

Rank Author Number of best solutions
1 Nakano 18
2 Vincent Chau 1
2 Francis Lau 1
2 Xin Han 1
2 Yinling Wang 1
2 Yong Zhang 1
2 Masahiro Iida 1
2 Teruaki Kitasuka 1
2 Takayuki Matsuzaki 1

Grid Graph Deepest Improvement ranking

Rank Author ASPL gap
1 Takayuki Matsuzaki 0.0
1 Teruaki Kitasuka 0.0
1 Masahiro Iida 0.0
4 Yosuke Kikuchi 0.016666666666666607
5 Vincent Chau 0.5948164816481651
5 Yong Zhang 0.5948164816481651
5 Xin Han 0.5948164816481651
5 Yinling Wang 0.5948164816481651
5 Francis Lau 0.5948164816481651
10 Nakano 1.2724750275027503

Current best solutions

Order n Degree d Length r Diam. k ASPL l ASPL gap
list 32 5 3 2.03226 0.00000
list 256 18 3 1.95362 0.02420
list 576 30 2 1.94783 0.00000
list 1344 30 3 2.44723 0.13971
list 4896 24 4 2.94530 0.06788
list 9344 10 6 4.30815 0.29499
list 88128 12 7 4.91098 0.13021
list 98304 10 7 5.38272 0.22735
list 100000 32 5 3.71722 0.04554
list 100000 64 4 3.03472 0.07632
list 16 3 2 3 2.20000 0.00000
list 256 3 3 10 5.95631 0.36808
list 256 3 4 9 5.76366 0.17543
list 256 3 15 8 5.66835 0.08012
list 256 6 3 10 4.15668 1.05080
list 256 6 4 8 3.58609 0.48021
list 256 6 15 4 3.19084 0.08496
list 256 15 3 10 3.91250 1.85368
list 256 15 4 8 3.12206 1.06324
list 256 15 15 3 2.17972 0.12089
list 10000 3 6 34 15.59941 4.82443
list 10000 3 18 17 11.54243 0.76745
list 10000 3 33 16 11.26490 0.48993
list 10000 9 6 33 11.70118 7.30244
list 10000 9 18 12 5.35898 0.96024
list 10000 9 33 7 4.64071 0.24197
list 10000 28 6 33 11.73970 8.82091
list 10000 28 18 12 4.77906 1.86027
list 10000 28 33 7 3.51361 0.59482

Complete list of solutions

: Nominated

32 nodes, degree 5

Rank Author Diam. k ASPL l Diam. gap ASPL gap Info. Date (UTC) Week
1 Ryuhei Mori 3 2.03226 0 0.00000 2017-03-25 05:30:47 25
2 thai9cdb 3 2.10685 0 0.07460 2017-07-20 08:52:00 29
3 hiro 3 2.13105 0 0.09879 2017-07-06 02:39:32 27
4 (random) 4 2.28024 1 0.24798 2017-03-05 18:31:14 25
5 hiro 4 2.45161 1 0.41935 2017-06-19 16:06:26 25

5 solutions

256 nodes, degree 18

Rank Author Diam. k ASPL l Diam. gap ASPL gap Info. Date (UTC) Week
1 Takayuki Matsuzaki, Teruaki Kitasuka, Masahiro Iida 3 1.95362 1 0.02420 2017-07-14 07:46:50 28
2 Takayuki Matsuzaki, Teruaki Kitasuka, Masahiro Iida 3 1.96642 1 0.03701 2017-07-01 06:57:25 26
3 (random) 3 2.18808 1 0.25867 2017-03-05 18:31:14 25
4 thai9cdb 3 2.19789 1 0.26847 2017-07-20 08:55:20 29
5 Tamami Okada, Yosuke Kikuchi 4 2.56471 2 0.63529 2017-05-23 07:44:29 25

5 solutions

576 nodes, degree 30

Rank Author Diam. k ASPL l Diam. gap ASPL gap Info. Date (UTC) Week
1 Ryuhei Mori 2 1.94783 0 0.00000 2017-03-25 05:32:28 25
2 (random) 3 2.14106 1 0.19323 2017-03-05 18:31:14 25

2 solutions

1344 nodes, degree 30

Rank Author Diam. k ASPL l Diam. gap ASPL gap Info. Date (UTC) Week
1 Vincent Chau, Xin Han, Francis Lau, Yinling Wang, Yong Zhang 3 2.44723 0 0.13971 2017-07-23 12:03:53 29
2 Vincent Chau, Xin Han, Yinling Wang, Yong Zhang 3 2.45349 0 0.14597 2017-07-16 12:59:50 28
3 (random) 3 2.48257 0 0.17505 2017-03-05 18:31:14 25
4 thai9cdb 3 2.50238 0 0.19486 2017-07-20 09:11:53 29

4 solutions

4896 nodes, degree 24

Rank Author Diam. k ASPL l Diam. gap ASPL gap Info. Date (UTC) Week
1 Vincent Chau, Xin Han, Francis Lau, Yinling Wang, Yong Zhang 4 2.94530 1 0.06788 2017-07-23 12:03:53 29
2 Vincent Chau, Xin Han, Yinling Wang, Yong Zhang 4 2.94726 1 0.06983 2017-07-16 12:59:50 28
3 (random) 4 2.94896 1 0.07153 2017-03-05 18:31:14 25

3 solutions

9344 nodes, degree 10

Rank Author Diam. k ASPL l Diam. gap ASPL gap Info. Date (UTC) Week
1 Vincent Chau, Xin Han, Francis Lau, Yinling Wang, Yong Zhang 6 4.30815 1 0.29499 2017-07-23 12:03:53 29
2 Vincent Chau, Xin Han, Yinling Wang, Yong Zhang 6 4.30942 1 0.29626 2017-07-16 12:59:50 28
3 (random) 6 4.31101 1 0.29784 2017-03-05 18:31:14 25

3 solutions

88128 nodes, degree 12

Rank Author Diam. k ASPL l Diam. gap ASPL gap Info. Date (UTC) Week
1 (random) 7 4.91098 2 0.13021 2017-03-05 18:31:14 25

1 solutions

98304 nodes, degree 10

Rank Author Diam. k ASPL l Diam. gap ASPL gap Info. Date (UTC) Week
1 (random) 7 5.38272 1 0.22735 2017-03-05 18:31:14 25

1 solutions

100000 nodes, degree 32

Rank Author Diam. k ASPL l Diam. gap ASPL gap Info. Date (UTC) Week
1 (random) 5 3.71722 1 0.04554 2017-03-05 18:31:14 25

1 solutions

100000 nodes, degree 64

Rank Author Diam. k ASPL l Diam. gap ASPL gap Info. Date (UTC) Week
1 (random) 4 3.03472 1 0.07632 2017-03-05 18:31:14 25

1 solutions

16 nodes, degree 3, length 2

Rank Author Diam. k ASPL l Length r Diam. gap ASPL gap Info. Date (UTC) Week
1 Takayuki Matsuzaki, Teruaki Kitasuka, Masahiro Iida 3 2.20000 2 0 0.00000 2017-07-02 08:16:38 26
1 Nakano 3 2.20000 2 0 0.00000 2017-06-27 02:29:03 26
3 Yosuke Kikuchi 3 2.21667 2 0 0.01667 2017-04-14 09:02:21 25
4 (random) 9 3.79167 2 6 1.59167 2017-03-05 18:33:27 25

4 solutions

256 nodes, degree 3, length 3

Rank Author Diam. k ASPL l Length r Diam. gap ASPL gap Info. Date (UTC) Week
1 Nakano 10 5.95631 3 3 0.36808 2017-07-14 08:05:19 28
2 Nakano 10 5.96654 3 3 0.37831 2017-06-27 02:29:20 26
3 (random) 22 8.58333 3 15 2.99510 2017-03-05 18:33:27 25

3 solutions

256 nodes, degree 3, length 4

Rank Author Diam. k ASPL l Length r Diam. gap ASPL gap Info. Date (UTC) Week
1 Nakano 9 5.76366 4 2 0.17543 2017-07-14 08:05:12 28
2 Nakano 9 5.78627 4 2 0.19804 2017-06-27 02:29:33 26
3 (random) 18 7.89026 4 11 2.30202 2017-03-05 18:33:27 25

3 solutions

256 nodes, degree 3, length 15

Rank Author Diam. k ASPL l Length r Diam. gap ASPL gap Info. Date (UTC) Week
1 Nakano 8 5.66835 15 1 0.08012 2017-07-14 08:05:04 28
2 Nakano 8 5.68713 15 1 0.09890 2017-06-27 02:29:55 26
2 Nakano 8 5.68713 15 1 0.09890 2017-06-27 02:29:42 26
4 (random) 13 6.27417 15 6 0.68594 2017-03-05 18:33:27 25

4 solutions

256 nodes, degree 6, length 3

Rank Author Diam. k ASPL l Length r Diam. gap ASPL gap Info. Date (UTC) Week
1 Nakano 10 4.15668 3 6 1.05080 2017-07-14 08:04:56 28
2 Nakano 10 4.15864 3 6 1.05276 2017-06-27 02:30:14 26
3 (random) 13 5.31893 3 9 2.21305 2017-03-05 18:33:27 25

3 solutions

256 nodes, degree 6, length 4

Rank Author Diam. k ASPL l Length r Diam. gap ASPL gap Info. Date (UTC) Week
1 Nakano 8 3.58609 4 4 0.48021 2017-07-14 08:04:48 28
2 Nakano 8 3.59433 4 4 0.48845 2017-06-27 02:30:27 26
3 (random) 10 4.54951 4 6 1.44363 2017-03-05 18:33:27 25

3 solutions

256 nodes, degree 6, length 15

Rank Author Diam. k ASPL l Length r Diam. gap ASPL gap Info. Date (UTC) Week
1 Nakano 4 3.19084 15 0 0.08496 2017-07-14 08:04:41 28
2 Nakano 4 3.19694 15 0 0.09105 2017-06-27 02:30:37 26
3 (random) 5 3.39648 15 1 0.29059 2017-03-05 18:33:27 25

3 solutions

256 nodes, degree 15, length 3

Rank Author Diam. k ASPL l Length r Diam. gap ASPL gap Info. Date (UTC) Week
1 Nakano 10 3.91250 3 7 1.85368 2017-07-14 08:04:33 28
1 Nakano 10 3.91250 3 7 1.85368 2017-06-27 02:30:54 26
3 (random) 10 4.19871 3 7 2.13989 2017-03-05 18:33:27 25

3 solutions

256 nodes, degree 15, length 4

Rank Author Diam. k ASPL l Length r Diam. gap ASPL gap Info. Date (UTC) Week
1 Nakano 8 3.12206 4 5 1.06324 2017-07-14 08:04:25 28
2 Nakano 8 3.12322 4 5 1.06440 2017-06-27 02:31:06 26
3 (random) 8 3.46495 4 5 1.40613 2017-03-05 18:33:27 25

3 solutions

256 nodes, degree 15, length 15

Rank Author Diam. k ASPL l Length r Diam. gap ASPL gap Info. Date (UTC) Week
1 Nakano 3 2.17972 15 0 0.12089 2017-07-14 08:04:16 28
2 Nakano 3 2.19007 15 0 0.13125 2017-06-27 02:31:14 26
3 (random) 4 2.37362 15 1 0.31480 2017-03-05 18:33:27 25

3 solutions

10000 nodes, degree 3, length 6

Rank Author Diam. k ASPL l Length r Diam. gap ASPL gap Info. Date (UTC) Week
1 Nakano 34 15.59941 6 22 4.82443 2017-07-14 08:04:06 28
2 Nakano 35 16.32588 6 23 5.55090 2017-07-03 07:19:45 27
3 Nakano 48 20.88129 6 36 10.10632 2017-06-27 02:31:25 26
4 (random) 59 23.75336 6 47 12.97839 2017-03-05 18:33:27 25

4 solutions

10000 nodes, degree 3, length 18

Rank Author Diam. k ASPL l Length r Diam. gap ASPL gap Info. Date (UTC) Week
1 Nakano 17 11.54243 18 5 0.76745 2017-07-14 08:03:58 28
2 Nakano 18 11.66915 18 6 0.89417 2017-07-03 07:19:34 27
3 Nakano 22 12.56584 18 10 1.79086 2017-06-27 02:31:44 26
3 Nakano 22 12.56584 18 10 1.79086 2017-06-27 02:31:35 26
5 (random) 26 13.14730 18 14 2.37232 2017-03-05 18:33:27 25

5 solutions

10000 nodes, degree 3, length 33

Rank Author Diam. k ASPL l Length r Diam. gap ASPL gap Info. Date (UTC) Week
1 Nakano 16 11.26490 33 4 0.48993 2017-07-14 08:03:50 28
2 Nakano 16 11.27838 33 4 0.50341 2017-07-03 07:19:26 27
3 Nakano 17 11.51883 33 5 0.74385 2017-06-27 02:31:52 26
4 (random) 19 11.67654 33 7 0.90157 2017-03-05 18:33:27 25

4 solutions

10000 nodes, degree 9, length 6

Rank Author Diam. k ASPL l Length r Diam. gap ASPL gap Info. Date (UTC) Week
1 Nakano 33 11.70118 6 28 7.30244 2017-07-14 08:03:38 28
2 Nakano 33 12.12310 6 28 7.72436 2017-07-03 07:19:17 27
3 (random) 36 13.57024 6 31 9.17150 2017-03-05 18:33:27 25
4 Nakano 44 17.40128 6 39 13.00254 2017-06-27 02:32:03 26

4 solutions

10000 nodes, degree 9, length 18

Rank Author Diam. k ASPL l Length r Diam. gap ASPL gap Info. Date (UTC) Week
1 Nakano 12 5.35898 18 7 0.96024 2017-07-14 08:03:14 28
2 Nakano 12 5.65529 18 7 1.25655 2017-07-03 07:19:08 27
3 (random) 14 6.17511 18 9 1.77637 2017-03-05 18:33:27 25
4 Nakano 20 8.84187 18 15 4.44313 2017-06-27 02:32:10 26

4 solutions

10000 nodes, degree 9, length 33

Rank Author Diam. k ASPL l Length r Diam. gap ASPL gap Info. Date (UTC) Week
1 Nakano 7 4.64071 33 2 0.24197 2017-07-14 08:03:03 28
2 Nakano 7 4.72338 33 2 0.32464 2017-07-03 07:18:59 27
3 (random) 9 4.92380 33 4 0.52506 2017-03-05 18:33:27 25

3 solutions

10000 nodes, degree 28, length 6

Rank Author Diam. k ASPL l Length r Diam. gap ASPL gap Info. Date (UTC) Week
1 Nakano 33 11.73970 6 30 8.82091 2017-07-14 08:02:51 28
2 (random) 34 11.82560 6 31 8.90681 2017-03-05 18:33:27 25
3 Nakano 34 12.56342 6 31 9.64462 2017-07-03 07:18:50 27

3 solutions

10000 nodes, degree 28, length 18

Rank Author Diam. k ASPL l Length r Diam. gap ASPL gap Info. Date (UTC) Week
1 Nakano 12 4.77906 18 9 1.86027 2017-07-14 08:02:26 28
2 (random) 12 4.82148 18 9 1.90269 2017-03-05 18:33:27 25
3 Nakano 13 5.41412 18 10 2.49533 2017-07-03 07:18:39 27

3 solutions

10000 nodes, degree 28, length 33

Rank Author Diam. k ASPL l Length r Diam. gap ASPL gap Info. Date (UTC) Week
1 Vincent Chau, Xin Han, Francis Lau, Yinling Wang, Yong Zhang 7 3.51361 33 4 0.59482 2017-07-23 12:03:53 29
2 (random) 7 3.53370 33 4 0.61491 2017-03-05 18:33:27 25
3 Nakano 8 4.19127 33 5 1.27248 2017-07-03 07:18:24 27

3 solutions

Other order/degree pairs

Author Order n Degree d Diam. k ASPL l Diam. gap ASPL gap Info. Date (UTC)
Ryuhei Mori 576 25 2 1.957 0 0.000 2017-03-25 05:32:28

1 solutions