tcga workshop keynote presentationwebdocs.cs.ualberta.ca/~hayward/talks/hex.sol10.pdf · tcga...
TRANSCRIPT
![Page 1: TCGA workshop keynote presentationwebdocs.cs.ualberta.ca/~hayward/talks/hex.sol10.pdf · TCGA workshop keynote presentation pawlewicz + hayward@ualberta.ca computing UAlberta 2013](https://reader036.vdocuments.net/reader036/viewer/2022063007/5fb975cf52899f7f145dcccd/html5/thumbnails/1.jpg)
hexknowledge
search10x10
solving 10x10 hexTCGA workshop keynote presentation
pawlewicz + [email protected]
computing UAlberta
2013 june 29
pawlewicz + [email protected] solving 10x10 hex
![Page 2: TCGA workshop keynote presentationwebdocs.cs.ualberta.ca/~hayward/talks/hex.sol10.pdf · TCGA workshop keynote presentation pawlewicz + hayward@ualberta.ca computing UAlberta 2013](https://reader036.vdocuments.net/reader036/viewer/2022063007/5fb975cf52899f7f145dcccd/html5/thumbnails/2.jpg)
hexknowledge
search10x10
thank you
invitation Prof Mark Kayll UMontana
solving 10×10 Hex joint with Jakub Pawlewicz
builds on work with B Arneson, P Henderson
machine Martin Muller
photo courtesy MIT Museum, MIT, Cambridge MA
Natural Sciences and Engineering Research Council of Canada
pawlewicz + [email protected] solving 10x10 hex
![Page 3: TCGA workshop keynote presentationwebdocs.cs.ualberta.ca/~hayward/talks/hex.sol10.pdf · TCGA workshop keynote presentation pawlewicz + hayward@ualberta.ca computing UAlberta 2013](https://reader036.vdocuments.net/reader036/viewer/2022063007/5fb975cf52899f7f145dcccd/html5/thumbnails/3.jpg)
hexknowledge
search10x10
1 hex
2 knowledge
3 search
4 10x10
pawlewicz + [email protected] solving 10x10 hex
![Page 4: TCGA workshop keynote presentationwebdocs.cs.ualberta.ca/~hayward/talks/hex.sol10.pdf · TCGA workshop keynote presentation pawlewicz + hayward@ualberta.ca computing UAlberta 2013](https://reader036.vdocuments.net/reader036/viewer/2022063007/5fb975cf52899f7f145dcccd/html5/thumbnails/4.jpg)
hexknowledge
search10x10
propertiesShannon machineprovably hardhumanscomputers
1942 hex
rules
2 players, alternate moves
win: connect your two sides
pawlewicz + [email protected] solving 10x10 hex
![Page 5: TCGA workshop keynote presentationwebdocs.cs.ualberta.ca/~hayward/talks/hex.sol10.pdf · TCGA workshop keynote presentation pawlewicz + hayward@ualberta.ca computing UAlberta 2013](https://reader036.vdocuments.net/reader036/viewer/2022063007/5fb975cf52899f7f145dcccd/html5/thumbnails/5.jpg)
hexknowledge
search10x10
propertiesShannon machineprovably hardhumanscomputers
1942 hex
rules
2 players, alternate moves
win: connect your two sides
pawlewicz + [email protected] solving 10x10 hex
![Page 6: TCGA workshop keynote presentationwebdocs.cs.ualberta.ca/~hayward/talks/hex.sol10.pdf · TCGA workshop keynote presentation pawlewicz + hayward@ualberta.ca computing UAlberta 2013](https://reader036.vdocuments.net/reader036/viewer/2022063007/5fb975cf52899f7f145dcccd/html5/thumbnails/6.jpg)
hexknowledge
search10x10
propertiesShannon machineprovably hardhumanscomputers
n x n Hex: 1st-player win
proof
lemma: extra X-cell ok for player X
lemma: no draws
suppose P2 has win strategy S2
then P1 can move anywhere, forget move, and follow S2
thus P1 has win strategy, contradiction 2
pawlewicz + [email protected] solving 10x10 hex
![Page 7: TCGA workshop keynote presentationwebdocs.cs.ualberta.ca/~hayward/talks/hex.sol10.pdf · TCGA workshop keynote presentation pawlewicz + hayward@ualberta.ca computing UAlberta 2013](https://reader036.vdocuments.net/reader036/viewer/2022063007/5fb975cf52899f7f145dcccd/html5/thumbnails/7.jpg)
hexknowledge
search10x10
propertiesShannon machineprovably hardhumanscomputers
no-draw
pawlewicz + [email protected] solving 10x10 hex
![Page 8: TCGA workshop keynote presentationwebdocs.cs.ualberta.ca/~hayward/talks/hex.sol10.pdf · TCGA workshop keynote presentation pawlewicz + hayward@ualberta.ca computing UAlberta 2013](https://reader036.vdocuments.net/reader036/viewer/2022063007/5fb975cf52899f7f145dcccd/html5/thumbnails/8.jpg)
hexknowledge
search10x10
propertiesShannon machineprovably hardhumanscomputers
no-draw
pawlewicz + [email protected] solving 10x10 hex
![Page 9: TCGA workshop keynote presentationwebdocs.cs.ualberta.ca/~hayward/talks/hex.sol10.pdf · TCGA workshop keynote presentation pawlewicz + hayward@ualberta.ca computing UAlberta 2013](https://reader036.vdocuments.net/reader036/viewer/2022063007/5fb975cf52899f7f145dcccd/html5/thumbnails/9.jpg)
hexknowledge
search10x10
propertiesShannon machineprovably hardhumanscomputers
n x n+1 Hex: longer-side win
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
pawlewicz + [email protected] solving 10x10 hex
![Page 10: TCGA workshop keynote presentationwebdocs.cs.ualberta.ca/~hayward/talks/hex.sol10.pdf · TCGA workshop keynote presentation pawlewicz + hayward@ualberta.ca computing UAlberta 2013](https://reader036.vdocuments.net/reader036/viewer/2022063007/5fb975cf52899f7f145dcccd/html5/thumbnails/10.jpg)
hexknowledge
search10x10
propertiesShannon machineprovably hardhumanscomputers
n x n+1 Hex: longer-side win
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
A
B
C
D
E
F
G
H
I
J
K
L
M
N
O
P
Q
R
S
T
U
pawlewicz + [email protected] solving 10x10 hex
![Page 11: TCGA workshop keynote presentationwebdocs.cs.ualberta.ca/~hayward/talks/hex.sol10.pdf · TCGA workshop keynote presentation pawlewicz + hayward@ualberta.ca computing UAlberta 2013](https://reader036.vdocuments.net/reader036/viewer/2022063007/5fb975cf52899f7f145dcccd/html5/thumbnails/11.jpg)
hexknowledge
search10x10
propertiesShannon machineprovably hardhumanscomputers
1951 Shannon machine
pawlewicz + [email protected] solving 10x10 hex
![Page 12: TCGA workshop keynote presentationwebdocs.cs.ualberta.ca/~hayward/talks/hex.sol10.pdf · TCGA workshop keynote presentation pawlewicz + hayward@ualberta.ca computing UAlberta 2013](https://reader036.vdocuments.net/reader036/viewer/2022063007/5fb975cf52899f7f145dcccd/html5/thumbnails/12.jpg)
hexknowledge
search10x10
propertiesShannon machineprovably hardhumanscomputers
1951 Shannon machine
play on any graph
two marked vertices
black move: ‘short’ any vertex (make nbrs clique)
white move: ‘cut’ any vertex (delete)
black wins iff two marked vertices are shorted (connected)
generalizes Hex
pawlewicz + [email protected] solving 10x10 hex
![Page 13: TCGA workshop keynote presentationwebdocs.cs.ualberta.ca/~hayward/talks/hex.sol10.pdf · TCGA workshop keynote presentation pawlewicz + hayward@ualberta.ca computing UAlberta 2013](https://reader036.vdocuments.net/reader036/viewer/2022063007/5fb975cf52899f7f145dcccd/html5/thumbnails/13.jpg)
hexknowledge
search10x10
propertiesShannon machineprovably hardhumanscomputers
1951 Shannon machine
pawlewicz + [email protected] solving 10x10 hex
![Page 14: TCGA workshop keynote presentationwebdocs.cs.ualberta.ca/~hayward/talks/hex.sol10.pdf · TCGA workshop keynote presentation pawlewicz + hayward@ualberta.ca computing UAlberta 2013](https://reader036.vdocuments.net/reader036/viewer/2022063007/5fb975cf52899f7f145dcccd/html5/thumbnails/14.jpg)
hexknowledge
search10x10
propertiesShannon machineprovably hardhumanscomputers
1951 Shannon machine
T
T
pawlewicz + [email protected] solving 10x10 hex
![Page 15: TCGA workshop keynote presentationwebdocs.cs.ualberta.ca/~hayward/talks/hex.sol10.pdf · TCGA workshop keynote presentation pawlewicz + hayward@ualberta.ca computing UAlberta 2013](https://reader036.vdocuments.net/reader036/viewer/2022063007/5fb975cf52899f7f145dcccd/html5/thumbnails/15.jpg)
hexknowledge
search10x10
propertiesShannon machineprovably hardhumanscomputers
1951 Shannon machine
T
T
pawlewicz + [email protected] solving 10x10 hex
![Page 16: TCGA workshop keynote presentationwebdocs.cs.ualberta.ca/~hayward/talks/hex.sol10.pdf · TCGA workshop keynote presentation pawlewicz + hayward@ualberta.ca computing UAlberta 2013](https://reader036.vdocuments.net/reader036/viewer/2022063007/5fb975cf52899f7f145dcccd/html5/thumbnails/16.jpg)
hexknowledge
search10x10
propertiesShannon machineprovably hardhumanscomputers
provably hard
1975 Even & Tarjan Shannon v-switching: PS-c
1981 Stefan Reisch Hex: PS-c
2000 Clay Math Inst P vs NP: $1 000 000
pawlewicz + [email protected] solving 10x10 hex
![Page 17: TCGA workshop keynote presentationwebdocs.cs.ualberta.ca/~hayward/talks/hex.sol10.pdf · TCGA workshop keynote presentation pawlewicz + hayward@ualberta.ca computing UAlberta 2013](https://reader036.vdocuments.net/reader036/viewer/2022063007/5fb975cf52899f7f145dcccd/html5/thumbnails/17.jpg)
hexknowledge
search10x10
propertiesShannon machineprovably hardhumanscomputers
humans
solved openings
2001 Yang 17/49 7x7
2002 Yang 8x8
2003 Yang 9x9
2004 Noshita 7x7
2005 Noshita 8x8
2006 Mishima 8x8
pawlewicz + [email protected] solving 10x10 hex
![Page 18: TCGA workshop keynote presentationwebdocs.cs.ualberta.ca/~hayward/talks/hex.sol10.pdf · TCGA workshop keynote presentation pawlewicz + hayward@ualberta.ca computing UAlberta 2013](https://reader036.vdocuments.net/reader036/viewer/2022063007/5fb975cf52899f7f145dcccd/html5/thumbnails/18.jpg)
hexknowledge
search10x10
propertiesShannon machineprovably hardhumanscomputers
computers
solved openings
1995 Enderton 6x62000 van Rijswijck 6x62003 H Bjo Joh Kan Po vRij 5d 7x72007 Rasmussen et al. 7x72009 Arneson H Henderson 4d 8x82010 A H H 25d some 9x92012 Pawlewicz H 110d x 24 thread 9x92013 Pawlewicz H 63d x 24 thread centre 10x10
pawlewicz + [email protected] solving 10x10 hex
![Page 19: TCGA workshop keynote presentationwebdocs.cs.ualberta.ca/~hayward/talks/hex.sol10.pdf · TCGA workshop keynote presentation pawlewicz + hayward@ualberta.ca computing UAlberta 2013](https://reader036.vdocuments.net/reader036/viewer/2022063007/5fb975cf52899f7f145dcccd/html5/thumbnails/19.jpg)
hexknowledge
search10x10
propertiesShannon machineprovably hardhumanscomputers
computers
pawlewicz + [email protected] solving 10x10 hex
![Page 20: TCGA workshop keynote presentationwebdocs.cs.ualberta.ca/~hayward/talks/hex.sol10.pdf · TCGA workshop keynote presentation pawlewicz + hayward@ualberta.ca computing UAlberta 2013](https://reader036.vdocuments.net/reader036/viewer/2022063007/5fb975cf52899f7f145dcccd/html5/thumbnails/20.jpg)
hexknowledge
search10x10
propertiesShannon machineprovably hardhumanscomputers
computers
pawlewicz + [email protected] solving 10x10 hex
![Page 21: TCGA workshop keynote presentationwebdocs.cs.ualberta.ca/~hayward/talks/hex.sol10.pdf · TCGA workshop keynote presentation pawlewicz + hayward@ualberta.ca computing UAlberta 2013](https://reader036.vdocuments.net/reader036/viewer/2022063007/5fb975cf52899f7f145dcccd/html5/thumbnails/21.jpg)
hexknowledge
search10x10
propertiesShannon machineprovably hardhumanscomputers
computers
pawlewicz + [email protected] solving 10x10 hex
![Page 22: TCGA workshop keynote presentationwebdocs.cs.ualberta.ca/~hayward/talks/hex.sol10.pdf · TCGA workshop keynote presentation pawlewicz + hayward@ualberta.ca computing UAlberta 2013](https://reader036.vdocuments.net/reader036/viewer/2022063007/5fb975cf52899f7f145dcccd/html5/thumbnails/22.jpg)
hexknowledge
search10x10
propertiesShannon machineprovably hardhumanscomputers
computers
pawlewicz + [email protected] solving 10x10 hex
![Page 23: TCGA workshop keynote presentationwebdocs.cs.ualberta.ca/~hayward/talks/hex.sol10.pdf · TCGA workshop keynote presentation pawlewicz + hayward@ualberta.ca computing UAlberta 2013](https://reader036.vdocuments.net/reader036/viewer/2022063007/5fb975cf52899f7f145dcccd/html5/thumbnails/23.jpg)
hexknowledge
search10x10
propertiesShannon machineprovably hardhumanscomputers
computers
pawlewicz + [email protected] solving 10x10 hex
![Page 24: TCGA workshop keynote presentationwebdocs.cs.ualberta.ca/~hayward/talks/hex.sol10.pdf · TCGA workshop keynote presentation pawlewicz + hayward@ualberta.ca computing UAlberta 2013](https://reader036.vdocuments.net/reader036/viewer/2022063007/5fb975cf52899f7f145dcccd/html5/thumbnails/24.jpg)
hexknowledge
search10x10
propertiesShannon machineprovably hardhumanscomputers
computers
pawlewicz + [email protected] solving 10x10 hex
![Page 25: TCGA workshop keynote presentationwebdocs.cs.ualberta.ca/~hayward/talks/hex.sol10.pdf · TCGA workshop keynote presentation pawlewicz + hayward@ualberta.ca computing UAlberta 2013](https://reader036.vdocuments.net/reader036/viewer/2022063007/5fb975cf52899f7f145dcccd/html5/thumbnails/25.jpg)
hexknowledge
search10x10
propertiesShannon machineprovably hardhumanscomputers
computers
pawlewicz + [email protected] solving 10x10 hex
![Page 26: TCGA workshop keynote presentationwebdocs.cs.ualberta.ca/~hayward/talks/hex.sol10.pdf · TCGA workshop keynote presentation pawlewicz + hayward@ualberta.ca computing UAlberta 2013](https://reader036.vdocuments.net/reader036/viewer/2022063007/5fb975cf52899f7f145dcccd/html5/thumbnails/26.jpg)
hexknowledge
search10x10
propertiesShannon machineprovably hardhumanscomputers
computers
pawlewicz + [email protected] solving 10x10 hex
![Page 27: TCGA workshop keynote presentationwebdocs.cs.ualberta.ca/~hayward/talks/hex.sol10.pdf · TCGA workshop keynote presentation pawlewicz + hayward@ualberta.ca computing UAlberta 2013](https://reader036.vdocuments.net/reader036/viewer/2022063007/5fb975cf52899f7f145dcccd/html5/thumbnails/27.jpg)
hexknowledge
search10x10
propertiesShannon machineprovably hardhumanscomputers
computers
pawlewicz + [email protected] solving 10x10 hex
![Page 28: TCGA workshop keynote presentationwebdocs.cs.ualberta.ca/~hayward/talks/hex.sol10.pdf · TCGA workshop keynote presentation pawlewicz + hayward@ualberta.ca computing UAlberta 2013](https://reader036.vdocuments.net/reader036/viewer/2022063007/5fb975cf52899f7f145dcccd/html5/thumbnails/28.jpg)
hexknowledge
search10x10
virtual connectionsinferior cells
knowledge
virtual connections: combining rules, mustplay
inferior cells: dead, captured, etc.
pawlewicz + [email protected] solving 10x10 hex
![Page 29: TCGA workshop keynote presentationwebdocs.cs.ualberta.ca/~hayward/talks/hex.sol10.pdf · TCGA workshop keynote presentation pawlewicz + hayward@ualberta.ca computing UAlberta 2013](https://reader036.vdocuments.net/reader036/viewer/2022063007/5fb975cf52899f7f145dcccd/html5/thumbnails/29.jpg)
hexknowledge
search10x10
virtual connectionsinferior cells
a virtual connection
pawlewicz + [email protected] solving 10x10 hex
![Page 30: TCGA workshop keynote presentationwebdocs.cs.ualberta.ca/~hayward/talks/hex.sol10.pdf · TCGA workshop keynote presentation pawlewicz + hayward@ualberta.ca computing UAlberta 2013](https://reader036.vdocuments.net/reader036/viewer/2022063007/5fb975cf52899f7f145dcccd/html5/thumbnails/30.jpg)
hexknowledge
search10x10
virtual connectionsinferior cells
a virtual connection
pawlewicz + [email protected] solving 10x10 hex
![Page 31: TCGA workshop keynote presentationwebdocs.cs.ualberta.ca/~hayward/talks/hex.sol10.pdf · TCGA workshop keynote presentation pawlewicz + hayward@ualberta.ca computing UAlberta 2013](https://reader036.vdocuments.net/reader036/viewer/2022063007/5fb975cf52899f7f145dcccd/html5/thumbnails/31.jpg)
hexknowledge
search10x10
virtual connectionsinferior cells
combining rule: and (full)
pawlewicz + [email protected] solving 10x10 hex
![Page 32: TCGA workshop keynote presentationwebdocs.cs.ualberta.ca/~hayward/talks/hex.sol10.pdf · TCGA workshop keynote presentation pawlewicz + hayward@ualberta.ca computing UAlberta 2013](https://reader036.vdocuments.net/reader036/viewer/2022063007/5fb975cf52899f7f145dcccd/html5/thumbnails/32.jpg)
hexknowledge
search10x10
virtual connectionsinferior cells
combining rule: and (full)
pawlewicz + [email protected] solving 10x10 hex
![Page 33: TCGA workshop keynote presentationwebdocs.cs.ualberta.ca/~hayward/talks/hex.sol10.pdf · TCGA workshop keynote presentation pawlewicz + hayward@ualberta.ca computing UAlberta 2013](https://reader036.vdocuments.net/reader036/viewer/2022063007/5fb975cf52899f7f145dcccd/html5/thumbnails/33.jpg)
hexknowledge
search10x10
virtual connectionsinferior cells
combining rule: and (full)
pawlewicz + [email protected] solving 10x10 hex
![Page 34: TCGA workshop keynote presentationwebdocs.cs.ualberta.ca/~hayward/talks/hex.sol10.pdf · TCGA workshop keynote presentation pawlewicz + hayward@ualberta.ca computing UAlberta 2013](https://reader036.vdocuments.net/reader036/viewer/2022063007/5fb975cf52899f7f145dcccd/html5/thumbnails/34.jpg)
hexknowledge
search10x10
virtual connectionsinferior cells
combining rule: and (full)
pawlewicz + [email protected] solving 10x10 hex
![Page 35: TCGA workshop keynote presentationwebdocs.cs.ualberta.ca/~hayward/talks/hex.sol10.pdf · TCGA workshop keynote presentation pawlewicz + hayward@ualberta.ca computing UAlberta 2013](https://reader036.vdocuments.net/reader036/viewer/2022063007/5fb975cf52899f7f145dcccd/html5/thumbnails/35.jpg)
hexknowledge
search10x10
virtual connectionsinferior cells
combining rule: and (full)
pawlewicz + [email protected] solving 10x10 hex
![Page 36: TCGA workshop keynote presentationwebdocs.cs.ualberta.ca/~hayward/talks/hex.sol10.pdf · TCGA workshop keynote presentation pawlewicz + hayward@ualberta.ca computing UAlberta 2013](https://reader036.vdocuments.net/reader036/viewer/2022063007/5fb975cf52899f7f145dcccd/html5/thumbnails/36.jpg)
hexknowledge
search10x10
virtual connectionsinferior cells
combining rule: and (full)
pawlewicz + [email protected] solving 10x10 hex
![Page 37: TCGA workshop keynote presentationwebdocs.cs.ualberta.ca/~hayward/talks/hex.sol10.pdf · TCGA workshop keynote presentation pawlewicz + hayward@ualberta.ca computing UAlberta 2013](https://reader036.vdocuments.net/reader036/viewer/2022063007/5fb975cf52899f7f145dcccd/html5/thumbnails/37.jpg)
hexknowledge
search10x10
virtual connectionsinferior cells
combining rule: and (semi)
pawlewicz + [email protected] solving 10x10 hex
![Page 38: TCGA workshop keynote presentationwebdocs.cs.ualberta.ca/~hayward/talks/hex.sol10.pdf · TCGA workshop keynote presentation pawlewicz + hayward@ualberta.ca computing UAlberta 2013](https://reader036.vdocuments.net/reader036/viewer/2022063007/5fb975cf52899f7f145dcccd/html5/thumbnails/38.jpg)
hexknowledge
search10x10
virtual connectionsinferior cells
combining rule: and (semi)
pawlewicz + [email protected] solving 10x10 hex
![Page 39: TCGA workshop keynote presentationwebdocs.cs.ualberta.ca/~hayward/talks/hex.sol10.pdf · TCGA workshop keynote presentation pawlewicz + hayward@ualberta.ca computing UAlberta 2013](https://reader036.vdocuments.net/reader036/viewer/2022063007/5fb975cf52899f7f145dcccd/html5/thumbnails/39.jpg)
hexknowledge
search10x10
virtual connectionsinferior cells
combining rule: and (semi)
pawlewicz + [email protected] solving 10x10 hex
![Page 40: TCGA workshop keynote presentationwebdocs.cs.ualberta.ca/~hayward/talks/hex.sol10.pdf · TCGA workshop keynote presentation pawlewicz + hayward@ualberta.ca computing UAlberta 2013](https://reader036.vdocuments.net/reader036/viewer/2022063007/5fb975cf52899f7f145dcccd/html5/thumbnails/40.jpg)
hexknowledge
search10x10
virtual connectionsinferior cells
combining rule: or
pawlewicz + [email protected] solving 10x10 hex
![Page 41: TCGA workshop keynote presentationwebdocs.cs.ualberta.ca/~hayward/talks/hex.sol10.pdf · TCGA workshop keynote presentation pawlewicz + hayward@ualberta.ca computing UAlberta 2013](https://reader036.vdocuments.net/reader036/viewer/2022063007/5fb975cf52899f7f145dcccd/html5/thumbnails/41.jpg)
hexknowledge
search10x10
virtual connectionsinferior cells
combining rule: or
pawlewicz + [email protected] solving 10x10 hex
![Page 42: TCGA workshop keynote presentationwebdocs.cs.ualberta.ca/~hayward/talks/hex.sol10.pdf · TCGA workshop keynote presentation pawlewicz + hayward@ualberta.ca computing UAlberta 2013](https://reader036.vdocuments.net/reader036/viewer/2022063007/5fb975cf52899f7f145dcccd/html5/thumbnails/42.jpg)
hexknowledge
search10x10
virtual connectionsinferior cells
combining rule: or
pawlewicz + [email protected] solving 10x10 hex
![Page 43: TCGA workshop keynote presentationwebdocs.cs.ualberta.ca/~hayward/talks/hex.sol10.pdf · TCGA workshop keynote presentation pawlewicz + hayward@ualberta.ca computing UAlberta 2013](https://reader036.vdocuments.net/reader036/viewer/2022063007/5fb975cf52899f7f145dcccd/html5/thumbnails/43.jpg)
hexknowledge
search10x10
virtual connectionsinferior cells
combining rule: or
pawlewicz + [email protected] solving 10x10 hex
![Page 44: TCGA workshop keynote presentationwebdocs.cs.ualberta.ca/~hayward/talks/hex.sol10.pdf · TCGA workshop keynote presentation pawlewicz + hayward@ualberta.ca computing UAlberta 2013](https://reader036.vdocuments.net/reader036/viewer/2022063007/5fb975cf52899f7f145dcccd/html5/thumbnails/44.jpg)
hexknowledge
search10x10
virtual connectionsinferior cells
where must white play?
pawlewicz + [email protected] solving 10x10 hex
![Page 45: TCGA workshop keynote presentationwebdocs.cs.ualberta.ca/~hayward/talks/hex.sol10.pdf · TCGA workshop keynote presentation pawlewicz + hayward@ualberta.ca computing UAlberta 2013](https://reader036.vdocuments.net/reader036/viewer/2022063007/5fb975cf52899f7f145dcccd/html5/thumbnails/45.jpg)
hexknowledge
search10x10
virtual connectionsinferior cells
where must white play?
pawlewicz + [email protected] solving 10x10 hex
![Page 46: TCGA workshop keynote presentationwebdocs.cs.ualberta.ca/~hayward/talks/hex.sol10.pdf · TCGA workshop keynote presentation pawlewicz + hayward@ualberta.ca computing UAlberta 2013](https://reader036.vdocuments.net/reader036/viewer/2022063007/5fb975cf52899f7f145dcccd/html5/thumbnails/46.jpg)
hexknowledge
search10x10
virtual connectionsinferior cells
where must white play?
pawlewicz + [email protected] solving 10x10 hex
![Page 47: TCGA workshop keynote presentationwebdocs.cs.ualberta.ca/~hayward/talks/hex.sol10.pdf · TCGA workshop keynote presentation pawlewicz + hayward@ualberta.ca computing UAlberta 2013](https://reader036.vdocuments.net/reader036/viewer/2022063007/5fb975cf52899f7f145dcccd/html5/thumbnails/47.jpg)
hexknowledge
search10x10
virtual connectionsinferior cells
where must white play?
pawlewicz + [email protected] solving 10x10 hex
![Page 48: TCGA workshop keynote presentationwebdocs.cs.ualberta.ca/~hayward/talks/hex.sol10.pdf · TCGA workshop keynote presentation pawlewicz + hayward@ualberta.ca computing UAlberta 2013](https://reader036.vdocuments.net/reader036/viewer/2022063007/5fb975cf52899f7f145dcccd/html5/thumbnails/48.jpg)
hexknowledge
search10x10
virtual connectionsinferior cells
dead
pawlewicz + [email protected] solving 10x10 hex
![Page 49: TCGA workshop keynote presentationwebdocs.cs.ualberta.ca/~hayward/talks/hex.sol10.pdf · TCGA workshop keynote presentation pawlewicz + hayward@ualberta.ca computing UAlberta 2013](https://reader036.vdocuments.net/reader036/viewer/2022063007/5fb975cf52899f7f145dcccd/html5/thumbnails/49.jpg)
hexknowledge
search10x10
virtual connectionsinferior cells
black-dominated (dot superior)
pawlewicz + [email protected] solving 10x10 hex
![Page 50: TCGA workshop keynote presentationwebdocs.cs.ualberta.ca/~hayward/talks/hex.sol10.pdf · TCGA workshop keynote presentation pawlewicz + hayward@ualberta.ca computing UAlberta 2013](https://reader036.vdocuments.net/reader036/viewer/2022063007/5fb975cf52899f7f145dcccd/html5/thumbnails/50.jpg)
hexknowledge
search10x10
virtual connectionsinferior cells
black-captured
pawlewicz + [email protected] solving 10x10 hex
![Page 51: TCGA workshop keynote presentationwebdocs.cs.ualberta.ca/~hayward/talks/hex.sol10.pdf · TCGA workshop keynote presentation pawlewicz + hayward@ualberta.ca computing UAlberta 2013](https://reader036.vdocuments.net/reader036/viewer/2022063007/5fb975cf52899f7f145dcccd/html5/thumbnails/51.jpg)
hexknowledge
search10x10
virtual connectionsinferior cells
black-dominated (dot superior)
pawlewicz + [email protected] solving 10x10 hex
![Page 52: TCGA workshop keynote presentationwebdocs.cs.ualberta.ca/~hayward/talks/hex.sol10.pdf · TCGA workshop keynote presentation pawlewicz + hayward@ualberta.ca computing UAlberta 2013](https://reader036.vdocuments.net/reader036/viewer/2022063007/5fb975cf52899f7f145dcccd/html5/thumbnails/52.jpg)
hexknowledge
search10x10
virtual connectionsinferior cells
black-capture-reversible (to white dot)
pawlewicz + [email protected] solving 10x10 hex
![Page 53: TCGA workshop keynote presentationwebdocs.cs.ualberta.ca/~hayward/talks/hex.sol10.pdf · TCGA workshop keynote presentation pawlewicz + hayward@ualberta.ca computing UAlberta 2013](https://reader036.vdocuments.net/reader036/viewer/2022063007/5fb975cf52899f7f145dcccd/html5/thumbnails/53.jpg)
hexknowledge
search10x10
virtual connectionsinferior cells
black fill decomposition
pawlewicz + [email protected] solving 10x10 hex
![Page 54: TCGA workshop keynote presentationwebdocs.cs.ualberta.ca/~hayward/talks/hex.sol10.pdf · TCGA workshop keynote presentation pawlewicz + hayward@ualberta.ca computing UAlberta 2013](https://reader036.vdocuments.net/reader036/viewer/2022063007/5fb975cf52899f7f145dcccd/html5/thumbnails/54.jpg)
hexknowledge
search10x10
virtual connectionsinferior cells
star decomposition
pawlewicz + [email protected] solving 10x10 hex
![Page 55: TCGA workshop keynote presentationwebdocs.cs.ualberta.ca/~hayward/talks/hex.sol10.pdf · TCGA workshop keynote presentation pawlewicz + hayward@ualberta.ca computing UAlberta 2013](https://reader036.vdocuments.net/reader036/viewer/2022063007/5fb975cf52899f7f145dcccd/html5/thumbnails/55.jpg)
hexknowledge
search10x10
virtual connectionsinferior cells
black star decomp domination
pawlewicz + [email protected] solving 10x10 hex
![Page 56: TCGA workshop keynote presentationwebdocs.cs.ualberta.ca/~hayward/talks/hex.sol10.pdf · TCGA workshop keynote presentation pawlewicz + hayward@ualberta.ca computing UAlberta 2013](https://reader036.vdocuments.net/reader036/viewer/2022063007/5fb975cf52899f7f145dcccd/html5/thumbnails/56.jpg)
hexknowledge
search10x10
virtual connectionsinferior cells
modify H-search
and/or combining rules + capture
+ =
pawlewicz + [email protected] solving 10x10 hex
![Page 57: TCGA workshop keynote presentationwebdocs.cs.ualberta.ca/~hayward/talks/hex.sol10.pdf · TCGA workshop keynote presentation pawlewicz + hayward@ualberta.ca computing UAlberta 2013](https://reader036.vdocuments.net/reader036/viewer/2022063007/5fb975cf52899f7f145dcccd/html5/thumbnails/57.jpg)
hexknowledge
search10x10
pnsdfpnsfdfpns
proof number search negamax p,d values3,5
1,4
1,3
3,1
1,3
1,1 1,1 1,1
1,1 1,1 1,1
2,3
2,2
1,3
1,1 1,1 1,1
1,2
1,1 1,1
1,3
1,1 1,1 1,1
2,4
1,2
1,4
1,2
1,1 1,1
1,1 1,2
1,1 1,1
1,1
1,1
1,2
1,1 1,1
2,2
1,3
1,1 1,2
1,1 1,1
1,1
1,2
1,1 1,1
1,1
pawlewicz + [email protected] solving 10x10 hex
![Page 58: TCGA workshop keynote presentationwebdocs.cs.ualberta.ca/~hayward/talks/hex.sol10.pdf · TCGA workshop keynote presentation pawlewicz + hayward@ualberta.ca computing UAlberta 2013](https://reader036.vdocuments.net/reader036/viewer/2022063007/5fb975cf52899f7f145dcccd/html5/thumbnails/58.jpg)
hexknowledge
search10x10
pnsdfpnsfdfpns
proof number search2,5
1,4
1,3
3,1
1,3
1,1 1,1 1,1
1,1 1,1 1,1
2,2
1,2
1,3
1,1 1,1 1,1
1,1
0,∞ 1,1
1,3
1,1 1,1 1,1
2,4
1,2
1,4
1,2
1,1 1,1
1,1 1,2
1,1 1,1
1,1
1,1
1,2
1,1 1,1
2,2
1,3
1,1 1,2
1,1 1,1
1,1
1,2
1,1 1,1
1,1
pawlewicz + [email protected] solving 10x10 hex
![Page 59: TCGA workshop keynote presentationwebdocs.cs.ualberta.ca/~hayward/talks/hex.sol10.pdf · TCGA workshop keynote presentation pawlewicz + hayward@ualberta.ca computing UAlberta 2013](https://reader036.vdocuments.net/reader036/viewer/2022063007/5fb975cf52899f7f145dcccd/html5/thumbnails/59.jpg)
hexknowledge
search10x10
pnsdfpnsfdfpns
proof number search3,4
1,4
1,3
3,1
1,3
1,1 1,1 1,1
1,1 1,1 1,1
1,3
2,1
1,3
1,1 1,1 1,1
0,2
∞,0 1,1
1,3
1,1 1,1 1,1
2,4
1,2
1,4
1,2
1,1 1,1
1,1 1,2
1,1 1,1
1,1
1,1
1,2
1,1 1,1
2,2
1,3
1,1 1,2
1,1 1,1
1,1
1,2
1,1 1,1
1,1
pawlewicz + [email protected] solving 10x10 hex
![Page 60: TCGA workshop keynote presentationwebdocs.cs.ualberta.ca/~hayward/talks/hex.sol10.pdf · TCGA workshop keynote presentation pawlewicz + hayward@ualberta.ca computing UAlberta 2013](https://reader036.vdocuments.net/reader036/viewer/2022063007/5fb975cf52899f7f145dcccd/html5/thumbnails/60.jpg)
hexknowledge
search10x10
pnsdfpnsfdfpns
F-DFPNS
PNS Allis et al
pawlewicz + [email protected] solving 10x10 hex
![Page 61: TCGA workshop keynote presentationwebdocs.cs.ualberta.ca/~hayward/talks/hex.sol10.pdf · TCGA workshop keynote presentation pawlewicz + hayward@ualberta.ca computing UAlberta 2013](https://reader036.vdocuments.net/reader036/viewer/2022063007/5fb975cf52899f7f145dcccd/html5/thumbnails/61.jpg)
hexknowledge
search10x10
pnsdfpnsfdfpns
F-DFPNS
PNS Allis et al
DFPNS Nagai
pawlewicz + [email protected] solving 10x10 hex
![Page 62: TCGA workshop keynote presentationwebdocs.cs.ualberta.ca/~hayward/talks/hex.sol10.pdf · TCGA workshop keynote presentation pawlewicz + hayward@ualberta.ca computing UAlberta 2013](https://reader036.vdocuments.net/reader036/viewer/2022063007/5fb975cf52899f7f145dcccd/html5/thumbnails/62.jpg)
hexknowledge
search10x10
pnsdfpnsfdfpns
F-DFPNS
PNS Allis et al
DFPNS Nagai
DFPNS in Hex ?
pawlewicz + [email protected] solving 10x10 hex
![Page 63: TCGA workshop keynote presentationwebdocs.cs.ualberta.ca/~hayward/talks/hex.sol10.pdf · TCGA workshop keynote presentation pawlewicz + hayward@ualberta.ca computing UAlberta 2013](https://reader036.vdocuments.net/reader036/viewer/2022063007/5fb975cf52899f7f145dcccd/html5/thumbnails/63.jpg)
hexknowledge
search10x10
pnsdfpnsfdfpns
F-DFPNS
PNS Allis et al
DFPNS Nagai
DFPNS in Hex ?
. . . requires non-incremental H-search :(
pawlewicz + [email protected] solving 10x10 hex
![Page 64: TCGA workshop keynote presentationwebdocs.cs.ualberta.ca/~hayward/talks/hex.sol10.pdf · TCGA workshop keynote presentation pawlewicz + hayward@ualberta.ca computing UAlberta 2013](https://reader036.vdocuments.net/reader036/viewer/2022063007/5fb975cf52899f7f145dcccd/html5/thumbnails/64.jpg)
hexknowledge
search10x10
pnsdfpnsfdfpns
F-DFPNS
PNS Allis et al
DFPNS Nagai
DFPNS in Hex ?
. . . requires non-incremental H-search :(
. . . uniform branching factor :(
pawlewicz + [email protected] solving 10x10 hex
![Page 65: TCGA workshop keynote presentationwebdocs.cs.ualberta.ca/~hayward/talks/hex.sol10.pdf · TCGA workshop keynote presentation pawlewicz + hayward@ualberta.ca computing UAlberta 2013](https://reader036.vdocuments.net/reader036/viewer/2022063007/5fb975cf52899f7f145dcccd/html5/thumbnails/65.jpg)
hexknowledge
search10x10
pnsdfpnsfdfpns
F-DFPNS
PNS Allis et al
DFPNS Nagai
DFPNS in Hex ?
. . . requires non-incremental H-search :(
. . . uniform branching factor :(
idea: move ordering + DFPNS = F-DFPNS
pawlewicz + [email protected] solving 10x10 hex
![Page 66: TCGA workshop keynote presentationwebdocs.cs.ualberta.ca/~hayward/talks/hex.sol10.pdf · TCGA workshop keynote presentation pawlewicz + hayward@ualberta.ca computing UAlberta 2013](https://reader036.vdocuments.net/reader036/viewer/2022063007/5fb975cf52899f7f145dcccd/html5/thumbnails/66.jpg)
hexknowledge
search10x10
pnsdfpnsfdfpns
F-DFPNS (1)
expand node
consider first b + ⌈f × 6⌉ = 4 (of 6) live children
b
b b b b b b
pawlewicz + [email protected] solving 10x10 hex
![Page 67: TCGA workshop keynote presentationwebdocs.cs.ualberta.ca/~hayward/talks/hex.sol10.pdf · TCGA workshop keynote presentation pawlewicz + hayward@ualberta.ca computing UAlberta 2013](https://reader036.vdocuments.net/reader036/viewer/2022063007/5fb975cf52899f7f145dcccd/html5/thumbnails/67.jpg)
hexknowledge
search10x10
pnsdfpnsfdfpns
F-DFPNS (2)
discover move 3 loses
consider first b + ⌈f × 5⌉ = 4 (of 5) live children
b
b b ⊗ b b b
pawlewicz + [email protected] solving 10x10 hex
![Page 68: TCGA workshop keynote presentationwebdocs.cs.ualberta.ca/~hayward/talks/hex.sol10.pdf · TCGA workshop keynote presentation pawlewicz + hayward@ualberta.ca computing UAlberta 2013](https://reader036.vdocuments.net/reader036/viewer/2022063007/5fb975cf52899f7f145dcccd/html5/thumbnails/68.jpg)
hexknowledge
search10x10
pnsdfpnsfdfpns
F-DFPNS (3)
discover move 5 loses
consider first b + ⌈f × 4⌉ = 3 (of 4) live children
b
b b ⊗ b ⊗ b
pawlewicz + [email protected] solving 10x10 hex
![Page 69: TCGA workshop keynote presentationwebdocs.cs.ualberta.ca/~hayward/talks/hex.sol10.pdf · TCGA workshop keynote presentation pawlewicz + hayward@ualberta.ca computing UAlberta 2013](https://reader036.vdocuments.net/reader036/viewer/2022063007/5fb975cf52899f7f145dcccd/html5/thumbnails/69.jpg)
hexknowledge
search10x10
pnsdfpnsfdfpns
F-DFPNS (4)
discover move 2 wins, so . . .
. . . root solved without exploring 6th move
⊕
b ⊕ ⊗ b ⊗ b
pawlewicz + [email protected] solving 10x10 hex
![Page 70: TCGA workshop keynote presentationwebdocs.cs.ualberta.ca/~hayward/talks/hex.sol10.pdf · TCGA workshop keynote presentation pawlewicz + hayward@ualberta.ca computing UAlberta 2013](https://reader036.vdocuments.net/reader036/viewer/2022063007/5fb975cf52899f7f145dcccd/html5/thumbnails/70.jpg)
hexknowledge
search10x10
Pawlewicz: stronger VC enginePawlewicz: SPDFPNS
solving 10x10
stronger VC computations
scalable parallel DFPN S
pawlewicz + [email protected] solving 10x10 hex
![Page 71: TCGA workshop keynote presentationwebdocs.cs.ualberta.ca/~hayward/talks/hex.sol10.pdf · TCGA workshop keynote presentation pawlewicz + hayward@ualberta.ca computing UAlberta 2013](https://reader036.vdocuments.net/reader036/viewer/2022063007/5fb975cf52899f7f145dcccd/html5/thumbnails/71.jpg)
hexknowledge
search10x10
Pawlewicz: stronger VC enginePawlewicz: SPDFPNS
Pawlewicz: stronger VC computations
faster and/or-rule VC computation
limit form of new VCs, so never redundant
find fewer VCs, but solve 2 to 10 times faster
pawlewicz + [email protected] solving 10x10 hex
![Page 72: TCGA workshop keynote presentationwebdocs.cs.ualberta.ca/~hayward/talks/hex.sol10.pdf · TCGA workshop keynote presentation pawlewicz + hayward@ualberta.ca computing UAlberta 2013](https://reader036.vdocuments.net/reader036/viewer/2022063007/5fb975cf52899f7f145dcccd/html5/thumbnails/72.jpg)
hexknowledge
search10x10
Pawlewicz: stronger VC enginePawlewicz: SPDFPNS
example: vcs to side
pawlewicz + [email protected] solving 10x10 hex
![Page 73: TCGA workshop keynote presentationwebdocs.cs.ualberta.ca/~hayward/talks/hex.sol10.pdf · TCGA workshop keynote presentation pawlewicz + hayward@ualberta.ca computing UAlberta 2013](https://reader036.vdocuments.net/reader036/viewer/2022063007/5fb975cf52899f7f145dcccd/html5/thumbnails/73.jpg)
hexknowledge
search10x10
Pawlewicz: stronger VC enginePawlewicz: SPDFPNS
example: semis
pawlewicz + [email protected] solving 10x10 hex
![Page 74: TCGA workshop keynote presentationwebdocs.cs.ualberta.ca/~hayward/talks/hex.sol10.pdf · TCGA workshop keynote presentation pawlewicz + hayward@ualberta.ca computing UAlberta 2013](https://reader036.vdocuments.net/reader036/viewer/2022063007/5fb975cf52899f7f145dcccd/html5/thumbnails/74.jpg)
hexknowledge
search10x10
Pawlewicz: stronger VC enginePawlewicz: SPDFPNS
example: semis
pawlewicz + [email protected] solving 10x10 hex
![Page 75: TCGA workshop keynote presentationwebdocs.cs.ualberta.ca/~hayward/talks/hex.sol10.pdf · TCGA workshop keynote presentation pawlewicz + hayward@ualberta.ca computing UAlberta 2013](https://reader036.vdocuments.net/reader036/viewer/2022063007/5fb975cf52899f7f145dcccd/html5/thumbnails/75.jpg)
hexknowledge
search10x10
Pawlewicz: stronger VC enginePawlewicz: SPDFPNS
example: semis
pawlewicz + [email protected] solving 10x10 hex
![Page 76: TCGA workshop keynote presentationwebdocs.cs.ualberta.ca/~hayward/talks/hex.sol10.pdf · TCGA workshop keynote presentation pawlewicz + hayward@ualberta.ca computing UAlberta 2013](https://reader036.vdocuments.net/reader036/viewer/2022063007/5fb975cf52899f7f145dcccd/html5/thumbnails/76.jpg)
hexknowledge
search10x10
Pawlewicz: stronger VC enginePawlewicz: SPDFPNS
example: semis
pawlewicz + [email protected] solving 10x10 hex
![Page 77: TCGA workshop keynote presentationwebdocs.cs.ualberta.ca/~hayward/talks/hex.sol10.pdf · TCGA workshop keynote presentation pawlewicz + hayward@ualberta.ca computing UAlberta 2013](https://reader036.vdocuments.net/reader036/viewer/2022063007/5fb975cf52899f7f145dcccd/html5/thumbnails/77.jpg)
hexknowledge
search10x10
Pawlewicz: stronger VC enginePawlewicz: SPDFPNS
greedy union semis to get full
pawlewicz + [email protected] solving 10x10 hex
![Page 78: TCGA workshop keynote presentationwebdocs.cs.ualberta.ca/~hayward/talks/hex.sol10.pdf · TCGA workshop keynote presentation pawlewicz + hayward@ualberta.ca computing UAlberta 2013](https://reader036.vdocuments.net/reader036/viewer/2022063007/5fb975cf52899f7f145dcccd/html5/thumbnails/78.jpg)
hexknowledge
search10x10
Pawlewicz: stronger VC enginePawlewicz: SPDFPNS
block cell to get another vc
pawlewicz + [email protected] solving 10x10 hex
![Page 79: TCGA workshop keynote presentationwebdocs.cs.ualberta.ca/~hayward/talks/hex.sol10.pdf · TCGA workshop keynote presentation pawlewicz + hayward@ualberta.ca computing UAlberta 2013](https://reader036.vdocuments.net/reader036/viewer/2022063007/5fb975cf52899f7f145dcccd/html5/thumbnails/79.jpg)
hexknowledge
search10x10
Pawlewicz: stronger VC enginePawlewicz: SPDFPNS
block cell to get another vc
pawlewicz + [email protected] solving 10x10 hex
![Page 80: TCGA workshop keynote presentationwebdocs.cs.ualberta.ca/~hayward/talks/hex.sol10.pdf · TCGA workshop keynote presentation pawlewicz + hayward@ualberta.ca computing UAlberta 2013](https://reader036.vdocuments.net/reader036/viewer/2022063007/5fb975cf52899f7f145dcccd/html5/thumbnails/80.jpg)
hexknowledge
search10x10
Pawlewicz: stronger VC enginePawlewicz: SPDFPNS
block cell to get another vc
pawlewicz + [email protected] solving 10x10 hex
![Page 81: TCGA workshop keynote presentationwebdocs.cs.ualberta.ca/~hayward/talks/hex.sol10.pdf · TCGA workshop keynote presentation pawlewicz + hayward@ualberta.ca computing UAlberta 2013](https://reader036.vdocuments.net/reader036/viewer/2022063007/5fb975cf52899f7f145dcccd/html5/thumbnails/81.jpg)
hexknowledge
search10x10
Pawlewicz: stronger VC enginePawlewicz: SPDFPNS
block cell to get another vc
pawlewicz + [email protected] solving 10x10 hex
![Page 82: TCGA workshop keynote presentationwebdocs.cs.ualberta.ca/~hayward/talks/hex.sol10.pdf · TCGA workshop keynote presentation pawlewicz + hayward@ualberta.ca computing UAlberta 2013](https://reader036.vdocuments.net/reader036/viewer/2022063007/5fb975cf52899f7f145dcccd/html5/thumbnails/82.jpg)
hexknowledge
search10x10
Pawlewicz: stronger VC enginePawlewicz: SPDFPNS
Pawlewicz: scalable parallel DFPNS
parallel PNS: keep tree in memory? e.g. I-Chen Wu connect6
Hex: leaf computations fast, so tree too big
how to assign jobs to processors?
jobs too long: computation redundantjobs too short: too much client/server trafficsolution: MaxWorkPerJob
pawlewicz + [email protected] solving 10x10 hex
![Page 83: TCGA workshop keynote presentationwebdocs.cs.ualberta.ca/~hayward/talks/hex.sol10.pdf · TCGA workshop keynote presentation pawlewicz + hayward@ualberta.ca computing UAlberta 2013](https://reader036.vdocuments.net/reader036/viewer/2022063007/5fb975cf52899f7f145dcccd/html5/thumbnails/83.jpg)
hexknowledge
search10x10
Pawlewicz: stronger VC enginePawlewicz: SPDFPNS
SP DFPN S features
1+ε variant of DFPN
advanced TT resolution: upon collision, search next k (say 4)cells for empty location; if none found, overwrite location withsmallest work job
once node computation assigned to leaf, use virtual win/lossso new threads go elsewhere
. . . so compute virtual (dis)proof numbers
shared TT: many-read / 1-write locks
tune MaxWorkPerJob
for Hex: use Focussed DFPN S
pawlewicz + [email protected] solving 10x10 hex
![Page 84: TCGA workshop keynote presentationwebdocs.cs.ualberta.ca/~hayward/talks/hex.sol10.pdf · TCGA workshop keynote presentation pawlewicz + hayward@ualberta.ca computing UAlberta 2013](https://reader036.vdocuments.net/reader036/viewer/2022063007/5fb975cf52899f7f145dcccd/html5/thumbnails/84.jpg)
hexknowledge
search10x10
Pawlewicz: stronger VC enginePawlewicz: SPDFPNS
SP DFPN S performance
speedup test: 8 hardest 8x8 openings, 8 11x11 positions
speedup performance: 11.8 on 16 threads (.74)
solved all 9x9 openings
solved centre 10x10 opening
pawlewicz + [email protected] solving 10x10 hex
![Page 85: TCGA workshop keynote presentationwebdocs.cs.ualberta.ca/~hayward/talks/hex.sol10.pdf · TCGA workshop keynote presentation pawlewicz + hayward@ualberta.ca computing UAlberta 2013](https://reader036.vdocuments.net/reader036/viewer/2022063007/5fb975cf52899f7f145dcccd/html5/thumbnails/85.jpg)
hexknowledge
search10x10
Pawlewicz: stronger VC enginePawlewicz: SPDFPNS
SP DFPN S performance
pawlewicz + [email protected] solving 10x10 hex
![Page 86: TCGA workshop keynote presentationwebdocs.cs.ualberta.ca/~hayward/talks/hex.sol10.pdf · TCGA workshop keynote presentation pawlewicz + hayward@ualberta.ca computing UAlberta 2013](https://reader036.vdocuments.net/reader036/viewer/2022063007/5fb975cf52899f7f145dcccd/html5/thumbnails/86.jpg)
hexknowledge
search10x10
Pawlewicz: stronger VC enginePawlewicz: SPDFPNS
SP DFPN S performance
a
a
b
b
c
c
d
d
e
e
f
f
g
g
h
h
i
i
j
j
1 1
2 2
3 3
4 4
5 5
6 6
7 7
8 8
9 9
10 10
1
2 3
4
5
6
7
8
9
10
11
12
13
14
15
1617
1819
20
21
22 23
24
25
26 27
28 29
30
31
pawlewicz + [email protected] solving 10x10 hex
![Page 87: TCGA workshop keynote presentationwebdocs.cs.ualberta.ca/~hayward/talks/hex.sol10.pdf · TCGA workshop keynote presentation pawlewicz + hayward@ualberta.ca computing UAlberta 2013](https://reader036.vdocuments.net/reader036/viewer/2022063007/5fb975cf52899f7f145dcccd/html5/thumbnails/87.jpg)
hexknowledge
search10x10
Pawlewicz: stronger VC enginePawlewicz: SPDFPNS
SP DFPN S performance
opening #threads time winner
a2 8/24 68d09:40:18 blacka3 8 80d08:37:34 whitea4 8 33d14:06:03 blacka5 8 65d04:14:52 blacka6 24 110d14:35:06 blacka7 24 4d08:56:03 whitea8 24 6d14:21:30 black
pawlewicz + [email protected] solving 10x10 hex
![Page 88: TCGA workshop keynote presentationwebdocs.cs.ualberta.ca/~hayward/talks/hex.sol10.pdf · TCGA workshop keynote presentation pawlewicz + hayward@ualberta.ca computing UAlberta 2013](https://reader036.vdocuments.net/reader036/viewer/2022063007/5fb975cf52899f7f145dcccd/html5/thumbnails/88.jpg)
hexknowledge
search10x10
Pawlewicz: stronger VC enginePawlewicz: SPDFPNS
SP DFPN S performance
opening #threads time winner
b2 8 53d15:18:21 blackb4 8 29d23:53:14 blackb6 8 1d21:52:28 blackb7 8 4d17:19:13 blackc2 24 1d08:42:57 blacki1 24 6d00:51:25 black
10x10:f5 24 63d20:44:30 black
pawlewicz + [email protected] solving 10x10 hex
![Page 89: TCGA workshop keynote presentationwebdocs.cs.ualberta.ca/~hayward/talks/hex.sol10.pdf · TCGA workshop keynote presentation pawlewicz + hayward@ualberta.ca computing UAlberta 2013](https://reader036.vdocuments.net/reader036/viewer/2022063007/5fb975cf52899f7f145dcccd/html5/thumbnails/89.jpg)
hexknowledge
search10x10
Pawlewicz: stronger VC enginePawlewicz: SPDFPNS
how long until 11x11 ?
states (approx) center cell: solver fn calls
2x2 9.0 e 0 0
3x3 5.5 e 1 0
4x4 7.6 e 5 0
5x5 4.0 e 9 0
6x6 4.0 e 14 2
7x7 1.5 e 20 68
8x8 1.0 e 27 19 554
9x9 2.7 e 34 912 352
10x10 1.2 e 43 5 821 097 789
11x11 2.2 e 52 ??? ??? ??? ??? ???
pawlewicz + [email protected] solving 10x10 hex
![Page 90: TCGA workshop keynote presentationwebdocs.cs.ualberta.ca/~hayward/talks/hex.sol10.pdf · TCGA workshop keynote presentation pawlewicz + hayward@ualberta.ca computing UAlberta 2013](https://reader036.vdocuments.net/reader036/viewer/2022063007/5fb975cf52899f7f145dcccd/html5/thumbnails/90.jpg)
hexknowledge
search10x10
Pawlewicz: stronger VC enginePawlewicz: SPDFPNS
thank you
invitation Prof Mark Kayll UMontana
solving 10×10 Hex joint with Jakub Pawlewicz
builds on work with B Arneson, P Henderson
machine Martin Muller
photo courtesy MIT Museum, MIT, Cambridge MA
Natural Sciences and Engineering Research Council of Canada
pawlewicz + [email protected] solving 10x10 hex