- Strong generating sets of vertex cover algebras

H. de Vere Cole and E. Russell

An analogue of the Schreier-Sims algorithm for strong generating sets (SGS) of permutation groups is developed for graded vertex cover algebras (GVCA). It is shown how to transform instances of certain classical cover problems into a form suitable for the SGS-GVCA algorithm, opening up the possibility of distributed attacks against previously indecomposable search spaces.

I plan to invite interested parties to join a "sudoku@home" distributed project, probably using BOINC.

Any volunteers to lend some CPU cycles

fyi, here's an example of one of the "certificates" generated by the code, in this case being an SGS proving the non-existence of a 16 in grids mapping to vertex cover A1 component 2009:

- Code: Select all
`47596.32861385247992874356135412789678269514.......257846239715537416982291578.34`

6239.1.7874.....695.....421...18.95228539471.17952684....2196....267.134816435.97

394.615.857.8423.92.8953.716.318.79282743961.1596278.4985.16.4773.59.186416278.53

83.74152.49.8523.12.1963.783.529.61768241793.....362.4764.29.5352.37.196913685.42

82.......37.....684.....7216.417.98278263914.1594286.3943.16.5726.59.314517384.96

63.94157.71.8523699.576.4215.817.93236942871.1273956.4496.17.5327.58.196851639247

27.84156.41.9523789.5763.21...19......243519.15928764....5289....831......1674.32