Call Control in Rings

The call control problem is an important optimization problem encountered in the design and operation of communication networks. The goal of the call control problem in rings is to compute, for a given ring network with edge capacities and a set of paths in the ring, a maximum cardinality subset of the paths such that no edge capacity is violated. We give a polynomial-time algorithm to solve the problem optimally. The algorithm is based on a decision procedure that checks whether a solution with at least k paths exists, which is in turn implemented by an iterative greedy approach operating in rounds. We show that the algorithm can be implemented efficiently and, as a by-product, obtain a linear-time algorithm to solve the problem in chains optimally. For the weighted version of call control in rings, where each path is associated with a weight and the goal is to maximize the total weight of the paths in the solution, we present a simple 2-approximation algorithm and a polynomial-time approximation scheme. While the complexity of the weighted version remains open, we show that it is at least as hard as the bipartite exact matching problem, which has not been resolved to be in P or NP-hard. This latter result follows from recent work by Hochbaum and Levi

Renal replacement therapy in Europe: a summary of the 2013 ERA-EDTA Registry Annual Report with a focus on diabetes mellitus

Background: This article provides a summary of the 2013 European Renal Association-European Dialysis and Transplant Association (ERA-EDTA) Registry Annual Report (available at http://www.era-edta-reg.org), with a focus on patients with diabetes mellitus (DM) as the cause of end-stage renal disease (ESRD). Methods: In 2015, the ERA-EDTA Registry received data on renal replacement therapy (RRT) for ESRD from 49 national or regional renal registries in 34 countries in Europe and bordering the Mediterranean Sea. Individual patient data were provided by 31 registries, while 18 registries provided aggregated data. The total population covered by the participating registries comprised 650 million people. Results: In total, 72 933 patients started RRT for ESRD within the countries and regions reporting to the ERA-EDTA Registry, resulting in an overall incidence of 112 per million population (pmp). The overall prevalence on 31 December 2013 was 738 pmp (n = 478 990). Patients with DM as the cause of ESRD comprised 24% of the incident RRT patients (26 pmp) and 17% of the prevalent RRT patients (122 pmp). When compared with the USA, the incidence of patients starting RRT pmp secondary to DM in Europe was five times lower and the incidence of RRT due to other causes of ESRD was two times lower. Overall, 19 426 kidney transplants were performed (30 pmp). The 5-year adjusted survival for all RRT patients was 60.9% [95% confidence interval (CI) 60.5-61.3] and 50.6% (95% CI 49.9-51.2) for patients with DM as the cause of ESR