scholarly journals An Improved Approximation Bound for Spanning Star Forest and Color Saving

2009 ◽  
pp. 90-101 ◽  
Author(s):  
Stavros Athanassopoulos ◽  
Ioannis Caragiannis ◽  
Christos Kaklamanis ◽  
Maria Kyropoulou
Keyword(s):  
Approximation Bound

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.

A Family of Scheduling Algorithms for Hybrid Parallel Platforms

2018 ◽  
Vol 29 (01) ◽  
pp. 63-90 ◽  
Author(s):  
Safia Kedad-Sidhoum ◽  
Florence Monna ◽  
Grégory Mounié ◽  
Denis Trystram
Keyword(s):  
Graphics Processing Units ◽  
Dynamic Programming Algorithm ◽  
Computational Cost ◽  
General Purpose ◽  
Parallel Applications ◽  
Programming Algorithm ◽  
Approximation Bound ◽  
Computing Platforms ◽  
Graphics Processing ◽  
Independent Tasks

More and more parallel computing platforms are built upon hybrid architectures combining multi-core processors (CPUs) and hardware accelerators like General Purpose Graphics Processing Units (GPGPUs). We present in this paper a new method for scheduling efficiently parallel applications with [Formula: see text] CPUs and [Formula: see text] GPGPUs, where each task of the application can be processed either on an usual core (CPU) or on a GPGPU. We consider the problem of scheduling [Formula: see text] independent tasks with the objective to minimize the time for completing the whole application (makespan). This problem is NP-hard, thus, we present two families of approximation algorithms that can achieve approximation ratios of [Formula: see text] or [Formula: see text] for any integer [Formula: see text] when only one GPGPU is considered, and [Formula: see text] or [Formula: see text] for [Formula: see text] GPGPUs, where [Formula: see text] is an arbitrary small value which corresponds to the target accuracy of a binary search. The proposed method is based on a dual approximation scheme that uses a dynamic programming algorithm. The associated computational costs are for the first (resp. second) family in [Formula: see text] (resp. [Formula: see text]) per step of dual approximation. The greater the value of parameter [Formula: see text], the better the approximation, but the more expensive the computational cost. Finally, we propose a relaxed version of the algorithm which achieves a running time in [Formula: see text] with a constant approximation bound of [Formula: see text]. This last result is compared to the state-of-the-art algorithm HEFT. The proposed solving method is the first general purpose algorithm for scheduling on hybrid machines with a theoretical performance guarantee that can be used for practical purposes.

scholarly journals Revisiting the Approximation Bound for Stochastic Submodular Cover

2018 ◽  
Vol 63 ◽  
pp. 265-279
Author(s):  
Lisa Hellerstein ◽  
Devorah Kletenik
Keyword(s):  
Utility Function ◽  
Utility Functions ◽  
The State ◽  
Single Item ◽  
Set Size ◽  
Approximation Bound ◽  
Maximum Utility ◽  
Independent States ◽  
Stochastic Setting ◽  
Expected Increase

Deshpande et al. presented a k(ln R + 1) approximation bound for Stochastic Submodular Cover, where k is the state set size, R is the maximum utility of a single item, and the utility function is integer-valued. This bound is similar to the ln Q/(eta+1) bound given by Golovin and Krause, whose analysis was recently found to have an error. Here Q >= R is the goal utility and eta is the minimum gap between Q and any attainable utility Q' < Q. We revisit the proof of the k(ln R + 1) bound of Deshpande et al., fill in the details of the proof of a key lemma, and prove two bounds for real-valued utility functions: k(ln R_1 + 1) and (ln R_E + 1). Here R_1 equals the maximum ratio between the largest increase in utility attainable from a single item, and the smallest non-zero increase attainable from that same item (in the same state). The quantity R_E equals the maximum ratio between the largest expected increase in utility from a single item, and the smallest non-zero expected increase in utility from that same item. Our bounds apply only to the stochastic setting with independent states.

scholarly journals Near-Optimal Graph Signal Sampling by Pareto Optimization

Sensors ◽  
2021 ◽  
Vol 21 (4) ◽  
pp. 1415
Author(s):  
Dongqi Luo ◽  
Binqiang Si ◽  
Saite Zhang ◽  
Fan Yu ◽  
Jihong Zhu
Keyword(s):  
State Of The Art ◽  
Greedy Algorithms ◽  
Empirical Studies ◽  
Subset Selection ◽  
Reconstruction Error ◽  
Pareto Optimization ◽  
Signal Sampling ◽  
Approximation Bound ◽  
Sampling Problem ◽  
Optimal Graph

In this paper, we focus on the bandlimited graph signal sampling problem. To sample graph signals, we need to find small-sized subset of nodes with the minimal optimal reconstruction error. We formulate this problem as a subset selection problem, and propose an efficient Pareto Optimization for Graph Signal Sampling (POGSS) algorithm. Since the evaluation of the objective function is very time-consuming, a novel acceleration algorithm is proposed in this paper as well, which accelerates the evaluation of any solution. Theoretical analysis shows that POGSS finds the desired solution in quadratic time while guaranteeing nearly the best known approximation bound. Empirical studies on both Erdos-Renyi graphs and Gaussian graphs demonstrate that our method outperforms the state-of-the-art greedy algorithms.

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