Tight bounds for online TSP on the line

We consider the online traveling salesperson problem (TSP), where requests appear online over time on the real line and need to be visited by a server initially located at the origin. We distinguish between closed and open online TSP, depending on whether the server eventually needs to return to the origin or not. While online TSP on the line is a very natural online problem that was introduced more than two decades ago, no tight competitive analysis was known to date. We settle this problem by providing tight bounds on the competitive ratios for both the closed and the open variant of the problem. In particular, for closed online TSP, we provide a 1.64-competitive algorithm,thus matching a known lower bound. For open online TSP, we give a new upper bound as well as a matching lower bound that establish the remarkable competitive ratio of 2.04. Additionally, we consider the online Dial-A-Ride problem on the line, where each request needs to be transported to a specified destination. We provide an improved non-preemptive lower bound of 1.75 for this setting, as well as an improved preemptive algorithm with competitive ratio 2.41.Finally, we generalize known and give new complexity results for the underlying offline problems. In particular, we give an algorithm with running time O(n2) for closed offline TSP on the line with release dates and show that both variants of offline Dial-A-Ride on the line are NP-hard for any capacity c≥2 of the server

Prognostic factors in 264 adults with invasive Scedosporium spp. and Lomentospora prolificans infection reported in the literature and FungiScope

Invasive Scedosporium spp. and Lomentospora prolificans infections are an emerging threat in immunocompromised and occasionally in healthy hosts. Scedosporium spp. is intrinsically resistant to most, L. prolificans to all the antifungal drugs currently approved, raising concerns about appropriate treatment decisions. High mortality rates of up to 90% underline the need for comprehensive diagnostic workup and even more for new, effective antifungal drugs to improve patient outcome. For a comprehensive analysis, we identified cases of severe Scedosporium spp. and L. prolificans infections from the literature diagnosed in 2000 or later and the FungiScopeVR registry. For 208 Scedosporium spp. infections solid organ transplantation (n¼58, 27.9%) and for 56 L. prolificans infection underlying malignancy (n¼28, 50.0%) were the most prevalent risk factors. L. prolificans infections frequently presented as fungemia (n¼26, 46.4% versus n¼12, 5.8% for Scedosporium spp.). Malignancy, fungemia, CNS and lung involvement predicted worse outcome for scedosporiosis and lomentosporiosis. Patients treated with voriconazole had a better overall outcome in both groups compared to treatment with amphotericin B formulations. This review discusses the epidemiology, prognostic factors, pathogen susceptibility to approved and investigational antifungals, and treatment strategies of severe infections caused by Scedosporium spp. and L. prolificansWe thank Sabine Wrackmeyer for her private donation to support the projec