1,322 research outputs found
Approximation Algorithms for the Asymmetric Traveling Salesman Problem : Describing two recent methods
Full text linkThe paper provides a description of the two recent approximation algorithms
for the Asymmetric Traveling Salesman Problem, giving the intuitive description
of the works of Feige-Singh[1] and Asadpour et.al\ [2].\newline [1] improves
the previous approximation algorithm, by improving the constant
from 0.84 to 0.66 and modifying the work of Kaplan et. al\ [3] and also shows
an efficient reduction from ATSPP to ATSP. Combining both the results, they
finally establish an approximation ratio of for ATSPP,\ considering a small ,\ improving the
work of Chekuri and Pal.[4]\newline Asadpour et.al, in their seminal work\ [2],
gives an randomized algorithm for
the ATSP, by symmetrizing and modifying the solution of the Held-Karp
relaxation problem and then proving an exponential family distribution for
probabilistically constructing a maximum entropy spanning tree from a spanning
tree polytope and then finally defining the thin-ness property and transforming
a thin spanning tree into an Eulerian walk.\ The optimization methods used in\
[2] are quite elegant and the approximation ratio could further be improved, by
manipulating the thin-ness of the cuts.Comment: 12 page
Low Energy Dynamics of Monopoles in Supersymmetric Yang-Mills Theories with Hypermultiplets
Full text linkWe derive the low energy dynamics of monopoles and dyons in N=2
supersymmetric Yang-Mills theories with hypermultiplets in arbitrary
representations by utilizing a collective coordinate expansion. We consider the
most general case that Higgs fields both in the vector multiplet and in the
hypermultiplets have nonzero vacuum expectation values. The resulting theory is
a supersymmetric quantum mechanics which has been obtained by a nontrivial
dimensional reduction of two-dimensional (4,0) supersymmetric sigma models with
potentials.Comment: 17pages, LaTeX, minor changes, references added, version published in
JHE
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