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Logarithmic inapproximability results for the minimum shortest path routing conflict problem

Nowadays most data networks use shortest path protocols such as OSPF or IS-IS to route traffic. Given administrative routing lengths for the links of a network, all data packets are sent along shortest paths with respect to these lengths from their source to their destination. One of the most fundamental problems in planning shortest path networks is to decide whether a given set S of routing paths forms a valid routing and, if this is not the case, to find a small subset R of paths that cannot occur together in any valid routing. In this paper we show that it is NP-hard to approximate the minimal size or the minimal weight of a shortest path conflict $R\subseteq S$ by a factor less than $c\log |S|$ for some $c>0$

Approximation algorithms for connected facility location with buy-at-bulk edge costs

We consider a generalization of the Connected Facility Location problem where clients may connect to open facilities via access trees shared by multiple clients. The task is to choose facilities to open, to connect these facilities by a core Steiner tree (of infinite capacity), and to design and dimension the access trees, such that the capacities installed on the edges of these trees suffice to simultaneously route all clients' demands to the open facilities. We assume that the available edge capacities are given by a set of different cable types whose costs obey economies of scale. The objective is to minimize the total cost of opening facilities, building the core Steiner tree among them, and installing capacities on the access tree edges. In this paper, we devise the first constant-factor approximation algorithm for this problem. We also present a factor 6.72 approximation algorithm for a simplified version of the problem where multiples of only one single cable type can be installed on the access edges

Lagrangian Decompositions for the Two-Level FTTx Network Design Problem

We consider the design of a passive optical telecommunication access network, where clients have to be connected to an intermediate level of distribution points (DPs) and further on to some central offices (COs) in a tree-like fashion. Each client demands a given number of fiber connections to its CO. Passive optical splitters installed at the DPs allow k connections to share a single common fiber between the DP and the CO. We consider fixed charge costs for the use of an edge of the underlying street network, of a DP, and of a CO and variable costs for installing fibers along the street edges and for installing splitters at the DPs. We present two Lagrangian decomposition approaches that decompose the problem based on the network structure and on the cost structure, respectively. The subproblems are solved using MIP techniques. We report computational results for realistic instances and compare the efficiency of the Lagrangian approaches to the solutions of an integrated MIP model

The incremental connected facility location problem

We consider the incremental connected facility location problem (incremental ConFL), in which we are given a set of potential facilities, a set of interconnection nodes, a set of customers with demands, and a planning horizon. For each time period, we have to select a set of facilities to open, a set of customers to be served, the assignment of these customers to the open facilities, and a network that connects the open facilities. Once a customer is served, it must remain served in subsequent periods. Furthermore, in each time period the total demand of all customers served must be at least equal to a given minimum coverage requirement for that period. The objective is to minimize the total cost for building the network given by the investment and maintenance costs for the facilities and the network summed up over all time periods. We propose a mixed integer programming approach in which, in each time period, a single period ConFL with coverage restrictions has to be solved. For this latter problem, which is of particular interest in itself, new families of valid inequalities are proposed: these are set union knapsack cover (SUKC) inequalities, which are further enhanced by lifting and/or combined with cut-set inequalities, which are primarily used to ensure connectivity requirements. Details of an efficient branch-and-cut implementation are presented and computational results on a benchmark set of large instances are given, including examples of telecommunication networks in German

State-of-the-Art and Requirements for Collecting and Managing Sustainability Data Along Today's Supply Chains

Today, companies of all sizes need to gather, manage and deliver a wide range of sustainability information due to public demand, regulations and laws. However, in order to calculate reliable measurements, they face the tremendous challenge to gather heterogeneous sustainability information along their dynamic and complex supply chains. As there is no systematic support yet, the EU project SustainHub aims to develop an information system supporting complex sustainability data collection processes along supply chains. Therefore, the project’s consortium has established a solid base of requirements and state of the art which are presented in this paper in a consolidated way to enrich the discussion about life cycle management

Early biochemical and radiographic response after one cycle of [177Lu]Lu-PSMA I&T radioligand therapy in metastatic castration-resistant prostate cancer patients

Purpose The aim of this study was to investigate very early radiographic PSMA PET response after one cycle of [177Lu]Lu-PSMA I&T radioligand therapy (RLT) of metastatic castration-resistant prostate cancer (mCRPC) and to assess its role in predicting overall response and survival. Methods This retrospective study enrolled 40 mCRPC patients who were treated with a median of 3 (2–9) [177Lu]Lu-PSMA I&TRLT cycles. Biochemical response was based on the relative change of serum PSA according to PCWG3 criteria, while radiographic response referred to the relative change of PSMA-derived total viable tumor volumes expressed as total lesion PSMA (TLP). Results After one cycle of RLT, biochemical partial response (PR) was seen in 8/40 (20.0%), stable disease (SD) in 22/40 (55.0%), and progressive disease (PD) in 10/40 (25%) patients. In PSMA PET, very early molecular PR was observed in 12 (30.0%), SD in 19 (47.5%), and PD in 9 (22.5%) subjects. The PSA and TLP nadir were achieved after a median of 1 (1–5) and 2 (1–6) cycles, respectively. Nineteen (47.5%) patients showed overall biochemical PR, 11 (27.5%) had SD, and 10 (25%) experienced PD. In PSMA-directed PET, 4 patients experienced molecular complete response (CR), 24 (60.0%) had PR, 4 (10.0%) SD, and 8 (20.0%) PD. Early biochemical or radiographic response was not associated with longer overall survival (OS). Overall biochemical responders had a nearly signifcantly longer median OS (22.7 months) than non-responders (14.4 months, p=0.08). Early PSA progression was associated with shorter OS (12.2 months), compared to biochemical SD/PR (18.7 months, p=0.09). Conclusion In this retrospective cohort, there was no association between early PSMA PET radiographic response and overall survival; hence, treatment should not be prematurely discontinued. In contrast, early PSA progression after onecycle of [177Lu]Lu-PSMA I&T RLT was an indicator of overall progression and poor clinical outcome

Pulmonary vasculitis due to infection with Mycobacterium goodii : A case report

A 57-year-old Caucasian woman suffered from dyspnea on exertion. One year following a supposed pulmonary embolism event, a chronic thromboembolic vasculopathy was diagnosed and a pulmonary thromboendarterectomy was performed. However, a granulomatous pulmonary arterial vasculitis was identified upon examination. DNA of Mycobacterium goodii was detected as the most likely causative agent. Anti-inflammatory and anti-mycobacterial therapy was initiated for more than 12 months. Regular PET-CT scans revealed improvement under therapy. The last PET-CT did not show any tracer uptake following 10 months of therapy