A New Characterization of Tree Medians with Applications to Distributed Algorithms

A new characterization of tree medians is presented: we show that a vertex m is a median of a tree T with n vertices iff there exists a partition of the vertex set into [n/2] disjoint pairs (excluding m when n is odd), such that all the paths connecting the two vertices in any of the pairs pass through m. We show that in this case this sum is the largest possible among all such partitions, and we use this fact to discuss lower bounds on the message complexity of the distributed sorting problem. This lower bound implies that, given a network of a tree topology, choosing a median and then route all the information through it is the best possible strategy, in terms of worst-case number of messages sent during any execution of any distributed sorting algorithm. We also discuss the implications for networks of a general topology and for the distributed ranking problem

Placing regenerators in optical networks to satisfy multiple sets of requests.

The placement of regenerators in optical networks has become an active area of research during the last years. Given a set of lightpaths in a network G and a positive integer d, regenerators must be placed in such a way that in any lightpath there are no more than d hops without meeting a regenerator. While most of the research has focused on heuristics and simulations, the first theoretical study of the problem has been recently provided in [10], where the considered cost function is the number of locations in the network hosting regenerators. Nevertheless, in many situations a more accurate estimation of the real cost of the network is given by the total number of regenerators placed at the nodes, and this is the cost function we consider. Furthermore, in our model we assume that we are given a finite set of p possible traffic patterns (each given by a set of lightpaths), and our objective is to place the minimum number of regenerators at the nodes so that each of the traffic patterns is satisfied. While this problem can be easily solved when d = 1 or p = 1, we prove that for any fixed d,p ≥ 2 it does not admit a PTASUnknown control sequence '\textsc', even if G has maximum degree at most 3 and the lightpaths have length O(d)(d). We complement this hardness result with a constant-factor approximation algorithm with ratio ln (d ·p). We then study the case where G is a path, proving that the problem is NP-hard for any d,p ≥ 2, even if there are two edges of the path such that any lightpath uses at least one of them. Interestingly, we show that the problem is polynomial-time solvable in paths when all the lightpaths share the first edge of the path, as well as when the number of lightpaths sharing an edge is bounded. Finally, we generalize our model in two natural directions, which allows us to capture the model of [10] as a particular case, and we settle some questions that were left open in [10]

Experimental demonstration of flexible bandwidth networking with real-time impairment awareness

We demonstrate a flexible-bandwidth network testbed with a real-time, adaptive control plane that adjusts modulation format and spectrum-positioning to maintain quality of service (QoS) and high spectral efficiency. Here, low-speed supervisory channels and field-programmable gate arrays (FPGAs) enabled real-time impairment detection of high-speed flexible bandwidth channels (flexpaths). Using premeasured correlation data between the supervisory channel quality of transmission (QoT) and flexpath QoT, the control plane adapted flexpath spectral efficiency and spectral location based on link quality. Experimental demonstrations show a back-to-back link with a 360-Gb/s flexpath in which the control plane adapts to varying link optical signal to noise ratio (OSNR) by adjusting the flexpath's spectral efficiency (i.e., changing the flexpath modulation format) between binary phase-shift keying (BPSK), quaternary phase-shift keying (QPSK), and eight phase-shift keying (8PSK). This enables maintaining the data rate while using only the minimum necessary bandwidth and extending the OSNR range over which the bit error rate in the flexpath meets the quality of service (QoS) requirement (e. g. the forward error correction (FEC) limit). Further experimental demonstrations with two flexpaths show a control plane adapting to changes in OSNR on one link by changing the modulation format of the affected flexpath (220 Gb/s), and adjusting the spectral location of the other flexpath (120 Gb/s) to maintain a defragmented spectrum. (C) 2011 Optical Society of Americ

Traffic Grooming in Unidirectional WDM Rings with Bounded Degree Request Graph

Traffic grooming is a major issue in optical networks. It refers to grouping low rate signals into higher speed streams, in order to reduce the equipment cost. In SONET WDM networks, this cost is mostly given by the number of electronic terminations, namely ADMs. We consider the case when the topology is a unidirectional ring. In graph-theoretical terms, the traffic grooming problem in this case consists in partitioning the edges of a request graph into subgraphs with a maximum number of edges, while minimizing the total number of vertices of the decomposition. We consider the case when the request graph has bounded maximum degree $\Delta$, and our aim is to design a network being able to support any request graph satisfying the degree constraints. The existing theoretical models in the literature are much more rigid, and do not allow such adaptability. We formalize the problem, and solve the cases $\Delta=2$ (for all values of $C$) and $\Delta = 3$ (except the case C=4). We also provide lower and upper bounds for the general case

Ultra-high bandwidth quantum secured data transmission

Quantum key distribution (QKD) provides an attractive means for securing communications in optical fibre networks. However, deployment of the technology has been hampered by the frequent need for dedicated dark fibres to segregate the very weak quantum signals from conventional traffic. Up until now the coexistence of QKD with data has been limited to bandwidths that are orders of magnitude below those commonly employed in fibre optic communication networks. Using an optimised wavelength divisional multiplexing scheme, we transport QKD and the prevalent 100 Gb/s data format in the forward direction over the same fibre for the first time. We show a full quantum encryption system operating with a bandwidth of 200 Gb/s over a 100 km fibre. Exploring the ultimate limits of the technology by experimental measurements of the Raman noise, we demonstrate it is feasible to combine QKD with 10 Tb/s of data over a 50 km link. These results suggest it will be possible to integrate QKD and other quantum photonic technologies into high bandwidth data communication infrastructures, thereby allowing their widespread deployment

Hardness and approximation for the geodetic set problem in some graph classes

In this paper, we study the computational complexity of finding the \emph{geodetic number} of graphs. A set of vertices $S$ of a graph $G$ is a \emph{geodetic set} if any vertex of $G$ lies in some shortest path between some pair of vertices from $S$. The \textsc{Minimum Geodetic Set (MGS)} problem is to find a geodetic set with minimum cardinality. In this paper, we prove that solving the \textsc{MGS} problem is NP-hard on planar graphs with a maximum degree six and line graphs. We also show that unless $P=NP$, there is no polynomial time algorithm to solve the \textsc{MGS} problem with sublogarithmic approximation factor (in terms of the number of vertices) even on graphs with diameter $2$. On the positive side, we give an $O\left(\sqrt[3]{n}\log n\right)$-approximation algorithm for the \textsc{MGS} problem on general graphs of order $n$. We also give a $3$-approximation algorithm for the \textsc{MGS} problem on the family of solid grid graphs which is a subclass of planar graphs

Observation of an Excited Bc+ State

Using pp collision data corresponding to an integrated luminosity of 8.5 fb-1 recorded by the LHCb experiment at center-of-mass energies of s=7, 8, and 13 TeV, the observation of an excited Bc+ state in the Bc+π+π- invariant-mass spectrum is reported. The observed peak has a mass of 6841.2±0.6(stat)±0.1(syst)±0.8(Bc+) MeV/c2, where the last uncertainty is due to the limited knowledge of the Bc+ mass. It is consistent with expectations of the Bc∗(2S31)+ state reconstructed without the low-energy photon from the Bc∗(1S31)+→Bc+γ decay following Bc∗(2S31)+→Bc∗(1S31)+π+π-. A second state is seen with a global (local) statistical significance of 2.2σ (3.2σ) and a mass of 6872.1±1.3(stat)±0.1(syst)±0.8(Bc+) MeV/c2, and is consistent with the Bc(2S10)+ state. These mass measurements are the most precise to date

Pneumococcal polysaccharide vaccination in adults undergoing immunosuppressive treatment for inflammatory diseases - a longitudinal study.

INTRODUCTION: Patients undergoing immunosuppressive therapy are at increased risk of infection. Community-acquired pneumonia and invasive pneumococcal disease account for substantial morbidity and mortality in this population and may be prevented by vaccination. Ideally, immunization to pneumococcal antigens should take place before the start of immunosuppressive treatment. Often, however, the treatment cannot be delayed. Little is known about the efficacy of pneumococcal vaccines during immunosuppressive treatment. The objectives of this study were to determine the percentage of vaccine-naïve, immunosuppressed adults with inflammatory diseases seroprotected against Streptococcus pneumoniae and to assess factors associated with the immunogenicity, clinical impact and safety of 23-valent pneumococcal polysaccharide vaccine (PPV) in seronegative subjects. METHODS: This observational study included patients 18 years of age and older who were receiving prednisone ≥20 mg/day or other immunosuppressive drugs. Exclusion criteria were PPV administration in the previous 5 years, intravenous immunoglobulins and pregnancy. Serum immunoglobulin G (IgG) antibody levels against six pneumococcal serotypes were measured. Seropositivity was defined as IgG of 0.5 μg/ml or greater for at least four of six serotypes. Seronegative patients received PPV, and seropositive patients were included as a comparison group. Vaccine response and tolerance were assessed after 4-8 weeks. Disease activity was evaluated on the basis of the Physician Global Assessment scores. Serology was repeated after 1 year, and information on any kind of infection needing medical attention was collected. Outcomes were the proportion of seropositivity and infections between vaccinated and unvaccinated patients. RESULTS: Of 201 included patients, 35 received high-dose corticosteroids and 181 were given immunosuppressive drugs. Baseline seronegativity in 60 (30 %) patients was associated with corticotherapy and lower total IgG. After PPV, disease activity remained unchanged or decreased in 81 % of patients, and 87 % became seropositive. After 1 year, 67 % of vaccinated compared with 90 % of observed patients were seropositive (p < 0.001), whereas the rate of infections did not differ between groups. Those still taking prednisone ≥10 mg/day tended to have poorer serological responses and had significantly more infections. CONCLUSIONS: PPV was safe and moderately effective based on serological response. Seropositivity to pneumococcal antigens significantly reduced the risk of infections. Sustained high-dose corticosteroids were associated with poor vaccine response and more infections