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| 1 | - Implement algorithm in haskell, split over single steps | ||
| 2 | - During presentation show steps working on examples of the problem (one solves during step 1, one fails during step 1, one that requires multiple rotations to be eliminated), within `ghci` | ||
| 3 | - For most important proofs (tbd) show applicable step in haskell code with sketch of proof | ||
| 4 | |||
| 5 | |||
| 6 | # Tables | ||
| 7 | - Definition: Tables, embedded tables, embedded pairs, embedded matchings | ||
| 8 | - Definition: stable tables | ||
| 9 | - Matchings embedded in stable tables are stable (4.2.4 ii) | ||
| 10 | - Stable tables are determined by all first OR all last entries (4.2.4 iii) | ||
| 11 | - No pair absent from a stable table can block any of it's embedded matchings (4.2.4 i) | ||
| 12 | |||
| 13 | # Phase 1 | ||
| 14 | - Removal of pairs from tables | ||
| 15 | - Engagement | ||
| 16 | - Present algorithm and demonstrate | ||
| 17 | - Phase 1 has no effect on the embeddedness of stable pairs (4.2.3 i) | ||
| 18 | - Phase 1 stabilizes a table, when it doesn't fail (4.2.2 + 4.2.3 ii) | ||
| 19 | - Phase 1 results in the largest stable table (4.2.4 iv) | ||
| 20 | |||
| 21 | # Rotations | ||
| 22 | - Definition: rotation, exposure of rotations in stable tables | ||
| 23 | - Directed graphs & tails | ||
| 24 | - (Rotations exposed in a stable T are either identical or disjunct (4.2.5)) | ||
| 25 | |||
| 26 | # Phase 2 | ||
| 27 | - Stable tables that are not already matchings expose at least one rotation and how to find it (4.2.6) | ||
| 28 | - Elimination of rotations from stable tables | ||
| 29 | - ignores non-elements of rotation (4.2.7 iii) | ||
| 30 | - results in table consistent with rotation (4.2.7 i, ii) | ||
| 31 | - Thus: produce stable subtables (4.2.8) | ||
| 32 | - Subtables that don't agree with an exposed rotation have at least that rotation removed entirely (4.2.9) | ||
| 33 | - Any subtable can be created by removing a series of exposed rotations (Cor 4.2.2) | ||
| 34 | - Removal of rotations preserve matchings (Thm 4.2.1) | ||
| 35 | - Present derived algorithm and demonstrate | ||