11 research outputs found
Complexity of Discrete Energy Minimization Problems
Discrete energy minimization is widely-used in computer vision and machine
learning for problems such as MAP inference in graphical models. The problem,
in general, is notoriously intractable, and finding the global optimal solution
is known to be NP-hard. However, is it possible to approximate this problem
with a reasonable ratio bound on the solution quality in polynomial time? We
show in this paper that the answer is no. Specifically, we show that general
energy minimization, even in the 2-label pairwise case, and planar energy
minimization with three or more labels are exp-APX-complete. This finding rules
out the existence of any approximation algorithm with a sub-exponential
approximation ratio in the input size for these two problems, including
constant factor approximations. Moreover, we collect and review the
computational complexity of several subclass problems and arrange them on a
complexity scale consisting of three major complexity classes -- PO, APX, and
exp-APX, corresponding to problems that are solvable, approximable, and
inapproximable in polynomial time. Problems in the first two complexity classes
can serve as alternative tractable formulations to the inapproximable ones.
This paper can help vision researchers to select an appropriate model for an
application or guide them in designing new algorithms.Comment: ECCV'16 accepte
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Far-Field Modeling of a Deep-Sea Blowout: Sensitivity Studies of Initial Conditions, Biodegradation, Sedimentation, and Subsurface Dispersant Injection on Surface Slicks and Oil Plume Concentrations
Modeling of large-scale oil transport and fate resulting from deep-sea oil spills is highly complex due to a number of bio-chemo-geophysical interactions, which are often empirically based. Predicting mass-conserved total petroleum hydrocarbon concentrations is thus still a challenge for most oil spill models. In addition, dynamic quantification and visualization of spilled oil concentrations are necessary both for first response and basin-wide impact studies. This chapter presents a new implementation of the Connectivity Modeling System (CMS) oil application that tracks individual multi-fraction oil droplets and estimates oil concentrations and oil mass in a 3D space grid. We used the Deepwater Horizon (DWH) blowout as a case study and performed a sensitivity analysis of several modeling key factors, such as biodegradation, sedimentation, and alternative initial conditions, including droplet size distribution (DSD) corresponding to an untreated and treated live oil from subsurface dispersant injection (SSDI) predicted experimentally under high pressure and by the VDROP-J jet-droplet formation model. This quantitative analysis enabled the reconstruction of a time evolving three-dimensional (3D) oil plume in the ocean interior, the rising and spreading of oil on the ocean surface, and the effect of SSDI in shifting the oil to deeper waters while conserving the mass balance. Our modeling framework and analyses are thus important technical advances for understanding and mitigating deep-sea blowouts