1. 1 An Efficient Algorithm for Eyespace Classification in Go Author: Peter Drake, Niku Schreiner Brett Tomlin, Loring Veenstra Presented by: Xiaozhen Niu

2. 2 Outline Introduction Eyespace Simple and Improved Canonical Form Whole Board Evaluation Summary Limitations

3. 3 Introduction Eye evaluation is important for life and death problem Goal: create a database for eyespace classifications

4. 4 Life and Death Definitions: Alive: even if the attacker plays first, the defender can ensure alive Dead: even if the defender plays first, the defender can not ensure alive Unsettled: neither alive or dead

5. 5 Example Group A: alive, B: dead, C: alive, D: unsettled

6. 6 Eyespace Relevant features of an eyespace: Size Shape Which points within the space, if any, are occupied by friendly or enemy stones Which points within the space, if any, are on edge or corner points

7. 7 Size True: Size 1 or 2 are dead Size 3 is unsettled Assumption: Any eyespace of size 7 or more is alive

8. 8 Shapes Shapes of eyespaces from size 1 to 6

9. 9 Graph Representation Adjacency matrix representation:

10. 10 Simple and Improved Canonical Form Simple canonical form: consider all possible numberings of the vertices, and choose the one that produces the lexicographically largest adjacency matrix

11. 11 Drawbacks N! ways of numbering a graph with N vertices Not enough information (internal stones, edge of the board…) Different shapes really need different representations?

12. 12 Example Group A, B and C are different, however they should have the same representation!

13. 13 Improved Canonical Form Adding 7 label bits at the each row: Stone (2 bits): 00 for black, 01 for white, 10 for empty Edginess (2 bits): 01 on edge, 00 not on edge, 10 at corner Neighboring (3 bits): how many neighbors it has?

14. 14 Whole Board Evaluation How to determine eyespaces? Use a simple heuristic: if a contiguous group partitions the board to one or more disjoint regions, all of them except the largest one are eyespaces

15. 15 Eyespaces of a Group If there is a viable (unsettle or alive) enemy group inside one of the partition regions, that region does not count as eyespace

16. 16 Example A: dead, B: unsettled C: alive D: unsettled Therefore E is alive

17. 17 Summary An accurate eyespace representation Can be used in static evaluation or during the search Compared to Cazenave’s approach, slower but more powerful, offering more information (internal stones, edges and corners)

18. 18 Limitations Only handles eyespace of one group!!! Surrounding information is important!

19. 19 Another Example Capture racing! W: 27 liberties B: 15 liberties But…