FORMALIZATION OF THE PROBLEM OF THE SDN NETWORK PARTITIONING INTO ROUTING ZONES

On of the key goals that should be solved to efficiently organize network routing is splitting the network to, in some sense, optimal set of routing zones. The work considers generalized mathematical formalization of the graph partition problem. Graph defines SDN network topology. According to this topology possible objective functions and constraints were formulated. Objective functions take into account cut parameters, subgraphs and\or cuts boundary vertices characteristics. Constraints take into account weights and probabilities .Key words: software-defined networking, routing zones, graph partition, graph cut, total cut weightкандидат технічних наук, Коган А. В., доктор технічних наук, професор, Кулаков Ю. О., кандидат технічних наук, Сперкач М. О., кандидат технічних наук, доцент, Жданова О. Г. Формалізація задачі розбиття мережі SDN на зони маршрутизації / Національний технічний університет України “Київський політехнічний інститут імені Ігоря Сікорського”, Україна, Київ Однією з ключових задач, що повинні бути розв’язані для організації ефективної маршрутизації в мережах, є розбиття всієї мережі на оптимальну в деякому сенсі кількість зон маршрутизації. В роботі розглядається узагальнена математична формалізація задачі розбиття графу, який описує фізичну топологію мережі SDN. Відповідно цієї топології були сформульовані можливі цільові функції та визначені обмеження задач розбиття графу. Цільові функції враховують параметри розрізів, підграфів та/або характеристики граничних вершин розбиття. Обмеження враховують ваги та ймовірності виключення/виходу з ладу вершин і ребер.Ключові слова: програмно-конфігурована мережа, зони маршрутизації, граф, розбиття графу, розріз графу, гранична вершина, сумарна вага розрізу

Метод оптимизации ярусно-параллельной формы представления задачи для реконфигурируемых вычислительных систем

В роботі запропонований метод оптимізації структури графа задачі, поданого в ярусно-паралельній формі, що враховує вимоги мінімізації часу виконання задачі та обмеження апаратних ресурсів, та дозволяє підвищити продуктивність реконфігурованих обчислювальних систем.The method of optimizing the structure of the task graph represented by a macro dataflow graph, is proposed. The method takes into account the requirement to minimize execution time and the limitations of hardware resources. The method improves the performance of reconfigurable computing systems.В статье предложен метод оптимизации структуры графа задачи, представленного в ярусно-параллельной форме, который учитывает требования минимизации времени выполнения задачи, ограничения аппаратных ресурсов и позволяет повысить производительность реконфигурируемых вычислительных систем

Centrality dependence of identified particle elliptic flow in relativistic heavy ion collisions at sqrt(s)= 7.7--62.4 GeV

Elliptic flow (v_2) values for identified particles at midrapidity in Au + Au collisions measured by the STAR experiment in the Beam Energy Scan at the Relativistic Heavy Ion Collider at sqrt{s_{NN}}= 7.7--62.4 GeV are presented for three centrality classes. The centrality dependence and the data at sqrt{s_{NN}}= 14.5 GeV are new. Except at the lowest beam energies we observe a similar relative v_2 baryon-meson splitting for all centrality classes which is in agreement within 15% with the number-of-constituent quark scaling. The larger v_2 for most particles relative to antiparticles, already observed for minimum bias collisions, shows a clear centrality dependence, with the largest difference for the most central collisions. Also, the results are compared with A Multiphase Transport Model and fit with a Blast Wave model.Comment: 14 pages, 12 figures, Phys. Rev. C, to be published. Data tables available at https://drupal.star.bnl.gov/STAR/publications/centrality-dependence-identified-particle-elliptic-flow-relativistic-heavy-ion-collisi

Observation of charge asymmetry dependence of pion elliptic flow and the possible chiral magnetic wave in heavy-ion collisions

We present measurements of $\pi^-$ and $\pi^+$ elliptic flow, $v_2$, at midrapidity in Au+Au collisions at $\sqrt{s_{_{\rm NN}}} =$ 200, 62.4, 39, 27, 19.6, 11.5 and 7.7 GeV, as a function of event-by-event charge asymmetry, $A_{ch}$, based on data from the STAR experiment at RHIC. We find that $\pi^-$ ($\pi^+$) elliptic flow linearly increases (decreases) with charge asymmetry for most centrality bins at $\sqrt{s_{_{\rm NN}}} = \text{27 GeV}$ and higher. At $\sqrt{s_{_{\rm NN}}} = \text{200 GeV}$, the slope of the difference of $v_2$ between $\pi^-$ and $\pi^+$ as a function of $A_{ch}$ exhibits a centrality dependence, which is qualitatively similar to calculations that incorporate a chiral magnetic wave effect. Similar centrality dependence is also observed at lower energies.Comment: 6 pages, 4 figure

Azimuthal anisotropy in U+U and Au+Au collisions at RHIC

Collisions between prolate uranium nuclei are used to study how particle production and azimuthal anisotropies depend on initial geometry in heavy-ion collisions. We report the two- and four-particle cumulants, $v_2\{2\}$ and $v_2\{4\}$, for charged hadrons from U+U collisions at $\sqrt{s_{\rm NN}}$ = 193 GeV and Au+Au collisions at $\sqrt{s_{\rm NN}}$ = 200 GeV. Nearly fully overlapping collisions are selected based on the amount of energy deposited by spectators in the STAR Zero Degree Calorimeters (ZDCs). Within this sample, the observed dependence of $v_2\{2\}$ on multiplicity demonstrates that ZDC information combined with multiplicity can preferentially select different overlap configurations in U+U collisions. An initial-state model with gluon saturation describes the slope of $v_2\{2\}$ as a function of multiplicity in central collisions better than one based on Glauber with a two-component multiplicity model.Comment: Final paper version accepted for publication in Phys. Rev. Lett. New version includes comparisons to a constituent quark glauber mode

Centrality and transverse momentum dependence of elliptic flow of multi-strange hadrons and ϕ\phi meson in Au+Au collisions at sNN\sqrt{s_{NN}} = 200 GeV

We present high precision measurements of elliptic flow near midrapidity ($|y|<1.0$) for multi-strange hadrons and $\phi$ meson as a function of centrality and transverse momentum in Au+Au collisions at center of mass energy $\sqrt{s_{NN}}=$ 200 GeV. We observe that the transverse momentum dependence of $\phi$ and $\Omega$ $v_{2}$ is similar to that of $\pi$ and $p$, respectively, which may indicate that the heavier strange quark flows as strongly as the lighter up and down quarks. This observation constitutes a clear piece of evidence for the development of partonic collectivity in heavy-ion collisions at the top RHIC energy. Number of constituent quark scaling is found to hold within statistical uncertainty for both 0-30$\%$ and 30-80$\%$ collision centrality. There is an indication of the breakdown of previously observed mass ordering between $\phi$ and proton $v_{2}$ at low transverse momentum in the 0-30$\%$ centrality range, possibly indicating late hadronic interactions affecting the proton $v_{2}$.Comment: 7 pages and 4 figures, Accepted for publication in Physical Review Letter

Isolation of Flow and Nonflow Correlations by Two- and Four-Particle Cumulant Measurements of Azimuthal Harmonics in sNN=\sqrt{s_{_{\rm NN}}} = 200 GeV Au+Au Collisions

A data-driven method was applied to measurements of Au+Au collisions at $\sqrt{s_{_{\rm NN}}} =$ 200 GeV made with the STAR detector at RHIC to isolate pseudorapidity distance $\Delta\eta$-dependent and $\Delta\eta$-independent correlations by using two- and four-particle azimuthal cumulant measurements. We identified a component of the correlation that is $\Delta\eta$-independent, which is likely dominated by anisotropic flow and flow fluctuations. It was also found to be independent of $\eta$ within the measured range of pseudorapidity $|\eta|<1$. The relative flow fluctuation was found to be $34\% \pm 2\% (stat.) \pm 3\% (sys.)$ for particles of transverse momentum $p_{T}$ less than $2$ GeV/$c$. The $\Delta\eta$-dependent part may be attributed to nonflow correlations, and is found to be $5\% \pm 2\% (sys.)$ relative to the flow of the measured second harmonic cumulant at $|\Delta\eta| > 0.7$

Inclusive charged hadron elliptic flow in Au + Au collisions at sNN\sqrt{s_{NN}} = 7.7 - 39 GeV

A systematic study is presented for centrality, transverse momentum ($p_T$) and pseudorapidity ($\eta$) dependence of the inclusive charged hadron elliptic flow ($v_2$) at midrapidity($|\eta| < 1.0$) in Au+Au collisions at $\sqrt{s_{NN}}$ = 7.7, 11.5, 19.6, 27 and 39 GeV. The results obtained with different methods, including correlations with the event plane reconstructed in a region separated by a large pseudorapidity gap and 4-particle cumulants ($v_2{4}$), are presented in order to investigate non-flow correlations and $v_2$ fluctuations. We observe that the difference between $v_2{2}$ and $v_2{4}$ is smaller at the lower collision energies. Values of $v_2$, scaled by the initial coordinate space eccentricity, $v_{2}/\varepsilon$, as a function of $p_T$ are larger in more central collisions, suggesting stronger collective flow develops in more central collisions, similar to the results at higher collision energies. These results are compared to measurements at higher energies at the Relativistic Heavy Ion Collider ($\sqrt{s_{NN}}$ = 62.4 and 200 GeV) and at the Large Hadron Collider (Pb + Pb collisions at $\sqrt{s_{NN}}$ = 2.76 TeV). The $v_2(p_T)$ values for fixed $p_T$ rise with increasing collision energy within the $p_T$ range studied ($< 2 {\rm GeV}/c$). A comparison to viscous hydrodynamic simulations is made to potentially help understand the energy dependence of $v_{2}(p_{T})$. We also compare the $v_2$ results to UrQMD and AMPT transport model calculations, and physics implications on the dominance of partonic versus hadronic phases in the system created at Beam Energy Scan (BES) energies are discussed.Comment: 20 pages, 12 figures. Version accepted by PR

Energy dependence of acceptance-corrected dielectron excess mass spectrum at mid-rapidity in Au+Au collisions at sNN=19.6\sqrt{s_{NN}} = 19.6 and 200 GeV

The acceptance-corrected dielectron excess mass spectra, where the known hadronic sources have been subtracted from the inclusive dielectron mass spectra, are reported for the first time at mid-rapidity $|y_{ee}|<1$ in minimum-bias Au+Au collisions at $\sqrt{s_{NN}}$ = 19.6 and 200 GeV. The excess mass spectra are consistently described by a model calculation with a broadened $\rho$ spectral function for $M_{ee}<1.1$ GeV/$c^{2}$. The integrated dielectron excess yield at $\sqrt{s_{NN}}$ = 19.6 GeV for $0.4<M_{ee}<0.75$ GeV/$c^2$, normalized to the charged particle multiplicity at mid-rapidity, has a value similar to that in In+In collisions at $\sqrt{s_{NN}}$ = 17.3 GeV. For $\sqrt{s_{NN}}$ = 200 GeV, the normalized excess yield in central collisions is higher than that at $\sqrt{s_{NN}}$ = 17.3 GeV and increases from peripheral to central collisions. These measurements indicate that the lifetime of the hot, dense medium created in central Au+Au collisions at $\sqrt{s_{NN}}$ = 200 GeV is longer than those in peripheral collisions and at lower energies.Comment: 9 pages, 6 figure

Charged-to-neutral correlation at forward rapidity in Au+Au collisions at sNN\sqrt{s_{NN}}=200 GeV

Event-by-event fluctuations of the ratio of inclusive charged to photon multiplicities at forward rapidity in Au+Au collision at $\sqrt{s_{NN}}$=200 GeV have been studied. Dominant contribution to such fluctuations is expected to come from correlated production of charged and neutral pions. We search for evidences of dynamical fluctuations of different physical origins. Observables constructed out of moments of multiplicities are used as measures of fluctuations. Mixed events and model calculations are used as baselines. Results are compared to the dynamical net-charge fluctuations measured in the same acceptance. A non-zero statistically significant signal of dynamical fluctuations is observed in excess to the model prediction when charged particles and photons are measured in the same acceptance. We find that, unlike dynamical net-charge fluctuation, charge-neutral fluctuation is not dominated by correlation due to particle decay. Results are compared to the expectations based on the generic production mechanism of pions due to isospin symmetry, for which no significant (<1%) deviation is observed.Comment: 14 pages, 6 figure