417 research outputs found
A Simple Linear Time Algorithm for Computing a 1-Median on Cactus Graphs
We address the problem of finding a 1-median on a cactus graph. The problem has already been solved in linear time by the algorithms of Burkard and Krarup (1998), and Lan and Wang (2000). These algorithms are complicated and need efforts. Hence, we develop in this paper a simpler algorithm. First, we construct a condition for a cycle that contains a 1-median or for a vertex that is indeed a 1-median of the cactus. Based on this condition, we localize the search for deriving a 1-median on the underlying cactus. Complexity analysis shows that the approach runs in linear time
High Energy Scattering in the Quasi-Potential Approach
Asymptotic behavior of the scattering amplitude for two scalar particles by
scalar, vector and tensor exchanges at high energy and fixed momentum transfers
is reconsidered in quantum field theory. In the framework of the
quasi-potential approach and the modified perturbation theory a systematic
scheme of finding the leading eikonal scattering amplitudes and its corrections
are developed and constructed.The connection between the solutions obtained by
quasi-potential and functional approaches is also discussed.The first
correction to leading eikonal amplitude is found. Keywords: Eikonal scattering
theory, Quantum gravity.Comment: 18 pages. arXiv admin note: substantial text overlap with
arXiv:0804.343
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