scholarly journals Tight Bounds on Subexponential Time Approximation of Set Cover and Related Problems

2021 ◽  
pp. 159-173
Author(s):  
Magnús M. Halldórsson ◽  
Guy Kortsarz ◽  
Marek Cygan
Keyword(s):  
Set Cover ◽  
Time Approximation ◽  
Subexponential Time

scholarly journals Exponential-time approximation of weighted set cover

2009 ◽  
Vol 109 (16) ◽  
pp. 957-961 ◽  
Author(s):  
Marek Cygan ◽  
Łukasz Kowalik ◽  
Mateusz Wykurz
Keyword(s):  
Set Cover ◽  
Exponential Time ◽  
Time Approximation

scholarly journals Combinatorial Dominance Guarantees for Heuristic Algorithms

2007 ◽  
Vol DMTCS Proceedings vol. AH,... (Proceedings) ◽  
Author(s):  
Daniel Berend ◽  
Steven S. Skiena ◽  
Yochai Twitto
Keyword(s):  
Polynomial Time ◽  
Heuristic Algorithms ◽  
Optimization Problems ◽  
Vertex Cover ◽  
Approximation Schemes ◽  
Set Cover ◽  
Time Approximation ◽  
Analysis Techniques ◽  
Wide Range ◽  
International Audience

International audience An $f(n)$ $\textit{dominance bound}$ on a heuristic for some problem is a guarantee that the heuristic always returns a solution not worse than at least $f(n)$ solutions. In this paper, we analyze several heuristics for $\textit{Vertex Cover}$, $\textit{Set Cover}$, and $\textit{Knapsack}$ for dominance bounds. In particular, we show that the well-known $\textit{maximal matching}$ heuristic of $\textit{Vertex Cover}$ provides an excellent dominance bound. We introduce new general analysis techniques which apply to a wide range of problems and heuristics for this measure. Certain general results relating approximation ratio and combinatorial dominance guarantees for optimization problems over subsets are established. We prove certain limitations on the combinatorial dominance guarantees of polynomial-time approximation schemes (PTAS), and give inapproximability results for the problems above.

Real-time Approximation of Photometric Polygonal Lights

2020 ◽  
Vol 3 (1) ◽  
pp. 1-18
Author(s):  
Christian Luksch ◽  
Lukas Prost ◽  
Michael Wimmer
Keyword(s):  
Real Time ◽  
Specular Reflection ◽  
Near Field ◽  
Measurement Data ◽  
Data Sets ◽  
Photometric Measurement ◽  
Integration Technique ◽  
Time Approximation ◽  
Light Emitter ◽  
Selection Of

We present a real-time rendering technique for photometric polygonal lights. Our method uses a numerical integration technique based on a triangulation to calculate noise-free diffuse shading. We include a dynamic point in the triangulation that provides a continuous near-field illumination resembling the shape of the light emitter and its characteristics. We evaluate the accuracy of our approach with a diverse selection of photometric measurement data sets in a comprehensive benchmark framework. Furthermore, we provide an extension for specular reflection on surfaces with arbitrary roughness that facilitates the use of existing real-time shading techniques. Our technique is easy to integrate into real-time rendering systems and extends the range of possible applications with photometric area lights.

scholarly journals Quit When You Can: Efficient Evaluation of Ensembles by Optimized Ordering

2021 ◽  
Vol 17 (4) ◽  
pp. 1-20
Author(s):  
Serena Wang ◽  
Maya Gupta ◽  
Seungil You
Keyword(s):  
Optimization Problem ◽  
Optimal Solution ◽  
Combinatorial Optimization Problem ◽  
Joint Optimization ◽  
Early Stopping ◽  
Time Approximation ◽  
Approximation Bound ◽  
Evaluation Time ◽  
Speed Up ◽  
Real World Problems

Given a classifier ensemble and a dataset, many examples may be confidently and accurately classified after only a subset of the base models in the ensemble is evaluated. Dynamically deciding to classify early can reduce both mean latency and CPU without harming the accuracy of the original ensemble. To achieve such gains, we propose jointly optimizing the evaluation order of the base models and early-stopping thresholds. Our proposed objective is a combinatorial optimization problem, but we provide a greedy algorithm that achieves a 4-approximation of the optimal solution under certain assumptions, which is also the best achievable polynomial-time approximation bound. Experiments on benchmark and real-world problems show that the proposed Quit When You Can (QWYC) algorithm can speed up average evaluation time by 1.8–2.7 times on even jointly trained ensembles, which are more difficult to speed up than independently or sequentially trained ensembles. QWYC’s joint optimization of ordering and thresholds also performed better in experiments than previous fixed orderings, including gradient boosted trees’ ordering.

PE-MSC: partial entailment-based minimum set cover for text summarization

2021 ◽  
Author(s):  
Anand Gupta ◽  
Manpreet Kaur ◽  
Sonaali Mittal ◽  
Swati Garg
Keyword(s):  
Text Summarization ◽  
Set Cover
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