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Full-Text Articles in Discrete Mathematics and Combinatorics
Approximation Algorithms For Problems In Makespan Minimization On Unrelated Parallel Machines, Daniel R. Page
Approximation Algorithms For Problems In Makespan Minimization On Unrelated Parallel Machines, Daniel R. Page
Electronic Thesis and Dissertation Repository
A fundamental problem in scheduling is makespan minimization on unrelated parallel machines (R||Cmax). Let there be a set J of jobs and a set M of parallel machines, where every job Jj ∈ J has processing time or length pi,j ∈ ℚ+ on machine Mi ∈ M. The goal in R||Cmax is to schedule the jobs non-preemptively on the machines so as to minimize the length of the schedule, the makespan. A ρ-approximation algorithm produces in polynomial time a feasible solution such that its objective value is within a multiplicative factor ρ of …
Advances In Graph-Cut Optimization: Multi-Surface Models, Label Costs, And Hierarchical Costs, Andrew T. Delong
Advances In Graph-Cut Optimization: Multi-Surface Models, Label Costs, And Hierarchical Costs, Andrew T. Delong
Electronic Thesis and Dissertation Repository
Computer vision is full of problems that are elegantly expressed in terms of mathematical optimization, or energy minimization. This is particularly true of "low-level" inference problems such as cleaning up noisy signals, clustering and classifying data, or estimating 3D points from images. Energies let us state each problem as a clear, precise objective function. Minimizing the correct energy would, hypothetically, yield a good solution to the corresponding problem. Unfortunately, even for low-level problems we are confronted by energies that are computationally hard—often NP-hard—to minimize. As a consequence, a rather large portion of computer vision research is dedicated to proposing …