Exact algorithms for the Steiner tree problem

In this thesis, the exact algorithms for the Steiner tree problem have been investigated. The Dreyfus-Wagner algorithm is a well-known dynamic programming method for computing minimum Steiner trees in general weighted graphs in time O(3k), where k is the number of the terminals. Firstly, two exact algorithms for the Steiner tree problem will be presented. The first one improves the running time of algorithm to O(2.684k) by showing that the optimum Steiner tree T can be partitioned into T = T1 [ T2 [ T3 in a certain way such that each Ti is a minimum Steiner tree in a suitable contracted graph Gi with less than k 2 terminals. The second algorithm is in time O((2 + )k) for any > 0. Every rectilinear Steiner tree problem admits an optimal tree T which is composed of tree stars. Moreover, the currently fastest algorithm for the rectilinear Steiner tree problem proceeds by composing an optimum tree T from tree star components in the cheapest way. F¨oßmeier and Kaufmann showed that any problem instance with k terminals has a number of tree stars in between 1.32k and 1.38k. We also present additional conditions on tree stars which allow us to further reduce the number of candidate components building the optimum Steiner tree to O(1.337k)

WR 7a: a V Sagittae or a qWR star?

The star WR 7a, also known as SPH 2, has a spectrum that resembles that of V Sagittae stars although no O VI emission has been reported. The Temporal Variance Spectrum - TVS - analysis of our data shows weak but strongly variable emission of O VI lines which is below the noise level in the intensity spectrum. Contrary to what is seen in V Sagittae stars, optical photometric monitoring shows very little, if any, flickering. We found evidence of periodic variability. The most likely photometric period is P(phot) = 0.227(14) d, while radial velocities suggest a period of P(spec) = 0.204(13) d. One-day aliases of these periods can not be ruled out. We call attention to similarities with HD 45166 and DI Cru (= WR 46), where multiple periods are present. They may be associated to the binary motion or to non-radial oscillations. In contrast to a previous conclusion by Pereira et al. (1998), we show that WR 7a contains hydrogen. The spectrum of the primary star seems to be detectable as the N V 4604A absorption line is visible. If so, it means that the wind is optically thin in the continuum and that it is likely to be a helium main sequence star. Given the similarity to HD 45166, we suggests that WR 7a may be a qWR - quasi Wolf-Rayet - star. Its classification is WN4h/CE in the Smith et al. (1996) three dimensional classification system.Comment: 6 pages, 6 figures, preprint of an article accepted for publication in Monthly Notices of The Royal Astronomical Societ

Transient jets in V617 Sagittarii

Some of the luminous Compact Binary Supersoft X-Ray sources (CBSS) have shown indications of jets, also called satellites due to their appearance in the spectra. In V Sagittae (V Sge) stars, the galactic counterparts of the CBSS, such features have been reported only for WX Cen. If V Sge stars are indeed the analogs of CBSS, one may expect transient jet emission in other objects of this class. Spectroscopic observations of the V Sge star V617 Sgr have been made, both at high photometric state and at decline. We show that V617 Sgr presents Halpha satellites at high photometric state with velocities of +/-780 km/s. This feature confirms, once more, the CBSS nature of the V Sge stars, however the details of the spectral characteristics also suggest that the two groups of stars display some intrinsic spectroscopic differences, which are likely to be due to a selection effect related to chemical abundance.Comment: Four pages, accepted to be published as a Letter in A&

Large-mass neutron stars with hyperonization

Within a density-dependent relativistic mean-field model using in-medium meson-hadron coupling constants and meson masses, we explore effects of in-medium hyperon interactions on properties of neutron stars. It is found that the hyperonic constituents in large-mass neutron stars can not be simply ruled out, while the recently measured mass of the millisecond pulsar J1614-2230 can constrain significantly the in-medium hyperon interactions. Moreover, effects of nuclear symmetry energy on hyperonization in neutron stars are also discussed

Quark Matter in Neutron Stars: An apercu

The existence of deconfined quark matter in the superdense interior of neutron stars is a key question that has drawn considerable attention over the past few decades. Quark matter can comprise an arbitrary fraction of the star, from 0 for a pure neutron star to 1 for a pure quark star, depending on the equation of state of matter at high density. From an astrophysical viewpoint, these two extreme cases are generally expected to manifest different observational signatures. An intermediate fraction implies a hybrid star, where the interior consists of mixed or homogeneous phases of quark and nuclear matter, depending on surface and Coulomb energy costs, as well as other finite size and screening effects. In this brief review article, we discuss what we can deduce about quark matter in neutron stars in light of recent exciting developments in neutron star observations. We state the theoretical ideas underlying the equation of state of dense quark matter, including color superconducting quark matter. We also highlight recent advances stemming from re-examination of an old paradigm for the surface structure of quark stars and discuss possible evolutionary scenarios from neutron stars to quark stars, with emphasis on astrophysical observations.Comment: 15 pages, 1 figure. Invited review for Modern Physics Letters