Computing the shortest path between a pair of nodes is a fundamental graph primitive, which has critical applications in vehicle routing, finding functional pathways in biological networks, survivable network design, among many others. In this work, we study shortest-path queries over uncertain networks, i.e., graphs where every edge is associated with a probability of existence. We show that, for a given path, it is # P -hard to compute the probability of it being the shortest path, and we also derive other interesting properties highlighting the complexity of computing the Most Probable Shortest Paths (MPSPs). We thus devise sampling-based efficient algorithms, with end-to-end accuracy guarantees, to compute the MPSP. As a concrete application, we show how to compute a novel concept of betweenness centrality in an uncertain graph using MPSPs. Our thorough experimental results and rich real-world case studies on sensor networks and brain networks validate the effectiveness, efficiency, scalability, and usefulness of our solution.

Appointment scheduling is generally applied in outpatient clinics and other healthcare services. The challenge in scheduling is to find a strategy for dealing with variability and unpredictability in service duration and patient arrivals. The consequences of an ineffective strategy include long waiting times for patients and idle time for the healthcare provider. In turn, these have implications for the perceived quality, cost-efficiency, and capacity of healthcare services. The generation of optimal schedules is a notoriously intractable problem, and earlier attempts at designing effective strategies for appointment scheduling were based on approximation, simulation, or simplification. We propose a novel strategy for scheduling that exploits three tactical ideas to make the problem manageable. We compare the proposed strategy to other approaches, and show that it matches or outperforms competing methods in terms of flexibility, ease of use, and speed. More importantly, it outperforms competing approaches nearly uniformly in approaching the desired balance between waiting and idle times as specified in a chosen objective function. Therefore, the strategy is a good basis for further enrichments.

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