7 research outputs found
Engineering an Approximation Scheme for Traveling Salesman in Planar Graphs
We present an implementation of a linear-time approximation scheme for the traveling salesman problem on planar graphs with edge weights. We observe that the theoretical algorithm involves constants that are too large for practical use. Our implementation, which is not subject to the theoretical algorithm\u27s guarantee, can quickly find good tours in very large planar graphs
On a strong form of Oliver’s p-group conjecture.
We introduce a stronger and more tractable form of Olivers p-group conjecture, and derive a reformulation in terms of the modular representation theory of a quotient group. The Sylow p-subgroups of the symmetric group Sn and of the general linear group satisfy both the strong conjecture and its reformulation
Weak closure and Oliver's p-group conjecture
To date almost all verifications of Oliver's p-group conjecture have
proceeded by verifying a stronger conjecture about weakly closed quadratic
subgroups. We construct a group of order 3^n for n = 49 which refutes the
weakly closed conjecture but satisfies Oliver's conjecture.Comment: 9 page
On Oliver's p-group conjecture ::II.
Let be an odd prime and a finite -group. B.~Oliver's conjecture arises from an open problem in the theory of -local finite groups and says that a certain characteristic subgroup of always contains the Thompson subgroup. In previous work the first two authors and M.~Lilienthal recast Oliver's conjecture as a statement about the representation theory of the factor group . We now verify the conjecture for a wide variety of groups~
Approximating connectivity domination in weighted bounded-genus graphs
International audienc