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A Practical Shortest Path Algorithm with Linear Expected Time
 SUBMITTED TO SIAM J. ON COMPUTING
, 2001
"... We present an improvement of the multilevel bucket shortest path algorithm of Denardo and Fox [9] and justify this improvement, both theoretically and experimentally. We prove that if the input arc lengths come from a natural probability distribution, the new algorithm runs in linear average time ..."
Abstract

Cited by 16 (8 self)
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We present an improvement of the multilevel bucket shortest path algorithm of Denardo and Fox [9] and justify this improvement, both theoretically and experimentally. We prove that if the input arc lengths come from a natural probability distribution, the new algorithm runs in linear average time while the original algorithm does not. We also describe an implementation of the new algorithm. Our experimental data suggests that the new algorithm is preferable to the original one in practice. Furthermore, for integral arc lengths that fit into a word of today's computers, the performance is close to that of breadthfirst search, suggesting limitations on further practical improvements.
EIKONAL EQUATIONS: NEW TWOSCALE ALGORITHMS AND ERROR ANALYSIS
, 2014
"... HamiltonJacobi equations arise in a number of seemingly disparate applications, from front propagation to photolithography to robotic navigation. Eikonal equations fall into an important subset representing isotropic optimal control and often are used as a first benchmark for numerical methods. Man ..."
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HamiltonJacobi equations arise in a number of seemingly disparate applications, from front propagation to photolithography to robotic navigation. Eikonal equations fall into an important subset representing isotropic optimal control and often are used as a first benchmark for numerical methods. Many of the interesting geometrical properties of Eikonal and related equations are exploited in two families of popular algorithms: the singlepass Fast Marching Methods and the iterative Fast Sweeping Methods. We start by developing a class of twoscale hybrid algorithms that combine the ideas of these prior methods on different scales. These hybrid methods are shown to have a clear advantage compared to other serial algorithms, but more importantly, one of them (“HCM”) is very suitable for parallelization on a shared memory architecture. Our extensive numerical experiments benchmark this parallel HCM against current serial methods and another parallel stateoftheart solver for the same computer architecture. We demonstrate the robustness of the parallel HCM on a wide range of problems, its good scaling in the number of processors, and its efficiency in solving a problem from exploratory geophysics. In the last part, we focus on estimat