Maximizing Revenues for Online-Dial-a-Ride

In the classic Dial-a-Ride Problem, a server travels in some metric space to serve requests for rides. Each request has a source, destination, and release time. We study a variation of this problem where each request also has a revenue that is earned if the request is satisfied. The goal is to serve requests within a time limit such that the total revenue is maximized. We first prove that the version of this problem where edges in the input graph have varying weights is NP-complete. We also prove that no algorithm can be competitive for this problem. We therefore consider the version where edges in the graph have unit weight and develop a 2-competitive algorithm for this problem

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

Persistence of Livestock Associated MRSA CC398 in Humans Is Dependent on Intensity of Animal Contact

INTRODUCTION: The presence of Livestock Associated MRSA (LA-MRSA) in humans is associated with intensity of animal contact. It is unknown whether the presence of LA-MRSA is a result of carriage or retention of MRSA-contaminated dust. We conducted a longitudinal study among 155 veal farmers in which repeated nasal and throat swabs were taken for MRSA detection. Periods with and without animal exposure were covered. METHODS: Randomly, 51 veal calf farms were visited from June-December 2008. Participants were asked to fill in questionnaires (n = 155) to identify potential risk factors for MRSA colonisation. Nasal and throat swabs were repeatedly taken from each participant for approximately 2 months. Swabs were analysed for MRSA and MSSA by selective bacteriological culturing. Spa-types of the isolates were identified and a ST398 specific PCR was performed. Data were analyzed using generalized estimation equations (GEE) to allow for correlated observations within individuals. RESULTS: Mean MRSA prevalence was 38% in farmers and 16% in family members. Presence of MRSA in farmers was strongly related to duration of animal contact and was strongly reduced in periods with absence of animal contact (-58%). Family members, especially children, were more often carriers when the farmer was a carrier (OR = 2,

Online k-server routing problems

In an online k-server routing problem, a crew of k servers has to visit points in a metric space as they arrive in real time. Possible objective functions include minimizing the makespan (k-Traveling Salesman Problem) and minimizing the sum of completion times (k-Traveling Repairman Problem). We give competitive algorithms, resource augmentation results and lower bounds for k-server routing problems in a wide class of metric spaces. In some cases the competitive ratio is dramatically better than that of the corresponding single server problem. Namely, we give a 1+O((log¿k)/k)-competitive algorithm for the k-Traveling Salesman Problem and the k-Traveling Repairman Problem when the underlying metric space is the real line. We also prove that a similar result cannot hold for the Euclidean plane