775 research outputs found
New and simple algorithms for stable flow problems
Stable flows generalize the well-known concept of stable matchings to markets
in which transactions may involve several agents, forwarding flow from one to
another. An instance of the problem consists of a capacitated directed network,
in which vertices express their preferences over their incident edges. A
network flow is stable if there is no group of vertices that all could benefit
from rerouting the flow along a walk.
Fleiner established that a stable flow always exists by reducing it to the
stable allocation problem. We present an augmenting-path algorithm for
computing a stable flow, the first algorithm that achieves polynomial running
time for this problem without using stable allocation as a black-box
subroutine. We further consider the problem of finding a stable flow such that
the flow value on every edge is within a given interval. For this problem, we
present an elegant graph transformation and based on this, we devise a simple
and fast algorithm, which also can be used to find a solution to the stable
marriage problem with forced and forbidden edges.
Finally, we study the stable multicommodity flow model introduced by
Kir\'{a}ly and Pap. The original model is highly involved and allows for
commodity-dependent preference lists at the vertices and commodity-specific
edge capacities. We present several graph-based reductions that show
equivalence to a significantly simpler model. We further show that it is
NP-complete to decide whether an integral solution exists
Proxy-SU(3) symmetry in the shell model basis
The proxy-SU(3) symmetry has been proposed for spin-orbit like nuclear shells
using the asymptotic deformed oscillator basis for the single particle
orbitals, in which the restoration of the symmetry of the harmonic oscillator
shells is achieved by a change of the number of quanta in the z-direction by
one unit for the intruder parity orbitals. The same definition suffices within
the cartesian basis of the Elliott SU(3) model. Through a mapping of the
cartesian Elliott basis onto the spherical shell model basis, we translate the
proxy-SU(3) approximation into spherical coordinates, proving, that in the
spherical shell model basis the proxy-SU(3) approximation corresponds to the
replacement of the intruder parity orbitals by their de Shalit--Goldhaber
partners. Furthermore it is shown, that the proxy-SU(3) approximation in the
cartesian Elliott basis is equivalent to a unitary transformation in the
z-coordinate, leaving the x-y plane intact, a result which in the asymptotic
deformed oscillator coordinates implies, that the z-projections of angular
momenta and spin remain unchanged. The present work offers a microscopic
justification of the proxy-SU(3) approximation and in addition paves the way,
for taking advantage of the proxy-SU(3) symmetry in shell model calculations.Comment: 15 pages, 7 tables, 1 figur
Clusterization in the shape isomers of the 56Ni nucleus
The interrelation of the quadrupole deformation and clusterization is investigated in the example of the 56Ni nucleus. The shape isomers, including superdeformed and hyperdeformed states, are obtained as stability regions of the quasidynamical U(3) symmetry based on a Nilsson calculation. Their possible binary clusterizations are investigated by considering both the consequences of the Pauli exclusion principle and the energetic preference
- …