Recent developments in the use of greedy algorithms in linear programming are reviewed and extended. We find a common generalization of some theorems of Queyranne–Spieksma– Tardella, Faigle–Kern, and Fujishige about greedy algorithms for linear programs in diverse contexts. Additionally, we extend a well-known theorem of Topkis about submodular functions on the product of chains to submodular f...

Deep belief networks (DBN) are generative neural network models with many layers of hidden explanatory factors, recently introduced by Hinton, Osindero, and Teh (2006) along with a greedy layer-wise unsupervised learning algorithm. The building block of a DBN is a probabilistic model called a restricted Boltzmann machine (RBM), used to represent one layer of the model. Restricted Boltzmann mach...

Updating probabilities by conditioning can lead to bad predictions, unless one explicitly takes into account the mechanisms that determine (1) what is observed and (2) what has to be predicted. Analogous to the observation-CAR (coarsening at random) condition, used in existing analyses of (1), we propose a new prediction task-CAR condition to analyze (2). We redefine conditioning so that it rem...

Minimizing total energy to keep an ad hoc wireless network symmetrically connected is an NP-hard problem. Recently, several greedy approximations have been proposed, based on k-restricted decompositions of the network. Their performance ratios are established through estimations of the least upper bound ρk for the ratio between total powers of best possible k-restricted decomposition and the op...

One of the major problems in Data Envelopment Analysis (DEA) is to determine the projection of inefficient Decision Making Units (DMUs) into the efficient frontier. In conventional DEA models, inputs and outputs of inefficient DMUs alter arbitrarily for reaching to the efficient frontier. Nevertheless, sometimes the ability of DMUs is defined and restricted. Moreover, there are situations in th...

Krause et al. [2008] has an indirect proof that F ′ is not submodular. They give an example that shows the greedy algorithm can do arbitrarily bad when maximizing F ′ under a cardinality constraint. If F ′ were submodular the greedy algorithm would give a (1 − 1/e) approximation for maximizing under a cardinality constraint. We give a direct proof that F ′ is not submodular for completeness. In...

one of the major problems in data envelopment analysis (dea) is to determine the projection of inefficient decision making units (dmus) into the efficient frontier. in conventional dea models, inputs and outputs of inefficient dmus alter arbitrarily for reaching to the efficient frontier. nevertheless, sometimes the ability of dmus is defined and restricted. moreover, there are situations in th...

A/B checking is a regular measure in many marketing procedures for e-Commerce companies. Through well-designed research, advertisers can gain insight about when and how efforts be maximized active promotions driven. Whilst algorithms the problem are theoretically well developed, empirical confirmation typically restricted. In practical terms, standard experimentation makes less money relative t...

We investigate the shortest common superstring problem (SCSSP). As SCSSP is APX-complete it cannot be approximated within an arbitrarily small performance ratio. One heuristic that is widely used is the notorious greedy heuristic. It is known, that the performance ratio of this heuristic is at least 2 and not worse than 4. It is conjectured that the greedy heuristic’s performance ratio is in fa...