14,908 research outputs found
Tractable Pathfinding for the Stochastic On-Time Arrival Problem
We present a new and more efficient technique for computing the route that
maximizes the probability of on-time arrival in stochastic networks, also known
as the path-based stochastic on-time arrival (SOTA) problem. Our primary
contribution is a pathfinding algorithm that uses the solution to the
policy-based SOTA problem---which is of pseudo-polynomial-time complexity in
the time budget of the journey---as a search heuristic for the optimal path. In
particular, we show that this heuristic can be exceptionally efficient in
practice, effectively making it possible to solve the path-based SOTA problem
as quickly as the policy-based SOTA problem. Our secondary contribution is the
extension of policy-based preprocessing to path-based preprocessing for the
SOTA problem. In the process, we also introduce Arc-Potentials, a more
efficient generalization of Stochastic Arc-Flags that can be used for both
policy- and path-based SOTA. After developing the pathfinding and preprocessing
algorithms, we evaluate their performance on two different real-world networks.
To the best of our knowledge, these techniques provide the most efficient
computation strategy for the path-based SOTA problem for general probability
distributions, both with and without preprocessing.Comment: Submission accepted by the International Symposium on Experimental
Algorithms 2016 and published by Springer in the Lecture Notes in Computer
Science series on June 1, 2016. Includes typographical corrections and
modifications to pre-processing made after the initial submission to SODA'15
(July 7, 2014
A Method for Reducing the Severity of Epidemics by Allocating Vaccines According to Centrality
One long-standing question in epidemiological research is how best to
allocate limited amounts of vaccine or similar preventative measures in order
to minimize the severity of an epidemic. Much of the literature on the problem
of vaccine allocation has focused on influenza epidemics and used mathematical
models of epidemic spread to determine the effectiveness of proposed methods.
Our work applies computational models of epidemics to the problem of
geographically allocating a limited number of vaccines within several Texas
counties. We developed a graph-based, stochastic model for epidemics that is
based on the SEIR model, and tested vaccine allocation methods based on
multiple centrality measures. This approach provides an alternative method for
addressing the vaccine allocation problem, which can be combined with more
conventional approaches to yield more effective epidemic suppression
strategies. We found that allocation methods based on in-degree and inverse
betweenness centralities tended to be the most effective at containing
epidemics.Comment: 10 pages, accepted to ACM BCB 201
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