43,427 research outputs found
Algorithms for the minimum sum coloring problem: a review
The Minimum Sum Coloring Problem (MSCP) is a variant of the well-known vertex
coloring problem which has a number of AI related applications. Due to its
theoretical and practical relevance, MSCP attracts increasing attention. The
only existing review on the problem dates back to 2004 and mainly covers the
history of MSCP and theoretical developments on specific graphs. In recent
years, the field has witnessed significant progresses on approximation
algorithms and practical solution algorithms. The purpose of this review is to
provide a comprehensive inspection of the most recent and representative MSCP
algorithms. To be informative, we identify the general framework followed by
practical solution algorithms and the key ingredients that make them
successful. By classifying the main search strategies and putting forward the
critical elements of the reviewed methods, we wish to encourage future
development of more powerful methods and motivate new applications
Extension Of Bertrand's Theorem And Factorization Of The Radial Schr\"odinger Equation
The Bertrand's theorem is extended, i.e. closed orbits still may exist for
other central potentials than the power law Coulomb potential and isotropic
harmonic oscillator. It is shown that for the combined potential
(), when (and only when) is the Coulomb
potential or isotropic harmonic oscillator, closed orbits still exist for
suitable angular momentum. The correspondence between the closeness of
classical orbits and the existence of raising and lowering operators derived
from the factorization of the radial Schr\"odinger equation is investigated.Comment: 4 pages, 1 figug
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