scholarly journals Average-Case Approximation Ratio of Scheduling without Payments

Algorithmica ◽  
2021 ◽  
Author(s):  
Jie Zhang
Keyword(s):  
Mechanism Design ◽  
Case Analysis ◽  
Theoretical Computer Science ◽  
Approximation Ratio ◽  
Approximation Schemes ◽  
Worst Case Analysis ◽  
Algorithmic Mechanism Design ◽  
Worst Case ◽  
Average Case ◽  
Optimal Mechanism

AbstractApart from the principles and methodologies inherited from Economics and Game Theory, the studies in Algorithmic Mechanism Design typically employ the worst-case analysis and design of approximation schemes of Theoretical Computer Science. For instance, the approximation ratio, which is the canonical measure of evaluating how well an incentive-compatible mechanism approximately optimizes the objective, is defined in the worst-case sense. It compares the performance of the optimal mechanism against the performance of a truthful mechanism, for all possible inputs. In this paper, we take the average-case analysis approach, and tackle one of the primary motivating problems in Algorithmic Mechanism Design—the scheduling problem (Nisan and Ronen, in: Proceedings of the 31st annual ACM symposium on theory of computing (STOC), 1999). One version of this problem, which includes a verification component, is studied by Koutsoupias (Theory Comput Syst 54(3):375–387, 2014). It was shown that the problem has a tight approximation ratio bound of $$(n+1)/2$$ ( n + 1 ) / 2 for the single-task setting, where n is the number of machines. We show, however, when the costs of the machines to executing the task follow any independent and identical distribution, the average-case approximation ratio of the mechanism given by Koutsoupias (Theory Comput Syst 54(3):375–387, 2014) is upper bounded by a constant. This positive result asymptotically separates the average-case ratio from the worst-case ratio. It indicates that the optimal mechanism devised for a worst-case guarantee works well on average.

scholarly journals A Multi-Objective Optimization Problem on Evacuating 2 Robots from the Disk in the Face-to-Face Model; Trade-Offs between Worst-Case and Average-Case Analysis

Information ◽  
2020 ◽  
Vol 11 (11) ◽  
pp. 506
Author(s):  
Huda Chuangpishit ◽  
Konstantinos Georgiou ◽  
Preeti Sharma
Keyword(s):  
Optimization Problem ◽  
Case Analysis ◽  
Worst Case Analysis ◽  
Computer Assisted ◽  
Average Case Analysis ◽  
Worst Case ◽  
Average Case ◽  
Face Model ◽  
Face To Face ◽  
The Face

The problem of evacuating two robots from the disk in the face-to-face model was first introduced by Czyzowicz et al. [DISC’2014], and has been extensively studied (along with many variations) ever since with respect to worst-case analysis. We initiate the study of the same problem with respect to average-case analysis, which is also equivalent to designing randomized algorithms for the problem. In particular, we introduce constrained optimization problem 2EvacF2F, in which one is trying to minimize the average-case cost of the evacuation algorithm given that the worst-case cost does not exceed w. The problem is of special interest with respect to practical applications, since a common objective in search-and-rescue operations is to minimize the average completion time, given that a certain worst-case threshold is not exceeded, e.g., for safety or limited energy reasons. Our main contribution is the design and analysis of families of new evacuation parameterized algorithms which can solve 2EvacF2F, for every w for which the problem is feasible. Notably, the worst-case analysis of the problem, since its introduction, has been relying on technical numerical, computer-assisted calculations, following tedious robot trajectory analysis. Part of our contribution is a novel systematic procedure, which given any evacuation algorithm, can derive its worst- and average-case performance in a clean and unified way.

Optimizing Complex Service-Based Workflows for Stochastic QoS Parameters

2013 ◽  
Vol 10 (4) ◽  
pp. 1-38
Author(s):  
Dieter Schuller ◽  
Ulrich Lampe ◽  
Julian Eckert ◽  
Ralf Steinmetz ◽  
Stefan Schulte
Keyword(s):  
Quality Of Service ◽  
Service Selection ◽  
Case Analysis ◽  
Selection Problem ◽  
Worst Case Analysis ◽  
Average Case Analysis ◽  
Worst Case ◽  
Average Case ◽  
Qos Parameters

The challenge of optimally selecting services from a set of functionally appropriate ones under Quality of Service (QoS) constraints – the Service Selection Problem – has been extensively addressed in the literature based on deterministic parameters. In practice, however, Quality of Service QoS parameters rather follow a stochastic distribution. In the work at hand, we present an integrated approach which addresses the Service Selection Problem for complex structured as well as unstructured workflows in conjunction with stochastic Quality of Service parameters. Accounting for penalty cost which accrue due to Quality of Service violations, we perform a worst-case analysis as opposed to an average-case analysis aiming at avoiding additional penalties. Although considering conservative computations, QoS violations due to stochastic QoS behavior still may occur resulting in potentially severe penalties. Our proposed approach reduces this impact of stochastic QoS behavior on total cost significantly.

scholarly journals A Combined Average-Case and Worst-Case Analysis for an Integrated Hub Location and Revenue Management Problem

2019 ◽  
Vol 2019 ◽  
pp. 1-13 ◽  
Author(s):  
Jia-Zhen Huo ◽  
Yan-Ting Hou ◽  
Feng Chu ◽  
Jun-Kai He
Keyword(s):  
Revenue Management ◽  
Profit Maximization ◽  
Transportation Cost ◽  
Case Analysis ◽  
Capacity Allocation ◽  
Worst Case Analysis ◽  
Management Problem ◽  
Hub Location ◽  
Worst Case ◽  
Average Case

This paper investigates joint decisions on airline network design and capacity allocation by integrating an uncapacitated single allocation p-hub median location problem into a revenue management problem. For the situation in which uncertain demand can be captured by a finite set of scenarios, we extend this integrated problem with average profit maximization to a combined average-case and worst-case analysis of this integration. We formulate this problem as a two-stage stochastic programming framework to maximize the profit, including the cost of installing the hubs and a weighted sum of average and worst case transportation cost and the revenue from tickets over all scenarios. This model can give flexible decisions by putting the emphasis on the importance of average and worst case profits. To solve this problem, a genetic algorithm is applied. Computational results demonstrate the outperformance of the proposed formulation.

A Genetic Model: Analysis and Application to MAXSAT

2000 ◽  
Vol 8 (3) ◽  
pp. 291-309 ◽  
Author(s):  
Alberto Bertoni ◽  
Marco Carpentieri ◽  
Paola Campadelli ◽  
Giuliano Grossi
Keyword(s):  
Combinatorial Optimization ◽  
Genetic Model ◽  
Optimization Problems ◽  
Case Analysis ◽  
Optimization Techniques ◽  
Worst Case Analysis ◽  
Worst Case ◽  
Average Case ◽  
Combinatorial Optimization Problems

In this paper, a genetic model based on the operations of recombination and mutation is studied and applied to combinatorial optimization problems. Results are: The equations of the deterministic dynamics in the thermodynamic limit (infinite populations) are derived and, for a sufficiently small mutation rate, the attractors are characterized; A general approximation algorithm for combinatorial optimization problems is designed. The algorithm is applied to the Max Ek-Sat problem, and the quality of the solution is analyzed. It is proved to be optimal for k≥3 with respect to the worst case analysis; for Max E3-Sat the average case performances are experimentally compared with other optimization techniques.

scholarly journals Junta Distributions and the Average-Case Complexity of Manipulating Elections

2007 ◽  
Vol 28 ◽  
pp. 157-181 ◽  
Author(s):  
A. D. Procaccia ◽  
J. S. Rosenschein
Keyword(s):  
Computational Complexity ◽  
Strategic Behavior ◽  
Case Analysis ◽  
Worst Case Analysis ◽  
Worst Case ◽  
Average Case ◽  
Case Complexity ◽  
Average Case Complexity ◽  
New Concepts ◽  
Np Hardness

Encouraging voters to truthfully reveal their preferences in an election has long been an important issue. Recently, computational complexity has been suggested as a means of precluding strategic behavior. Previous studies have shown that some voting protocols are hard to manipulate, but used NP-hardness as the complexity measure. Such a worst-case analysis may be an insufficient guarantee of resistance to manipulation. Indeed, we demonstrate that NP-hard manipulations may be tractable in the average case. For this purpose, we augment the existing theory of average-case complexity with some new concepts. In particular, we consider elections distributed with respect to junta distributions, which concentrate on hard instances. We use our techniques to prove that scoring protocols are susceptible to manipulation by coalitions, when the number of candidates is constant.

scholarly journals On U-Statistics and Compressed Sensing II: Non-Asymptotic Worst-Case Analysis

2013 ◽  
Vol 61 (10) ◽  
pp. 2486-2497 ◽  
Author(s):  
Fabian Lim ◽  
Vladimir Stojanovic
Keyword(s):  
Compressed Sensing ◽  
Case Analysis ◽  
Poisson Approximation ◽  
Companion Paper ◽  
Worst Case Analysis ◽  
Average Case Analysis ◽  
Mutual Coherence ◽  
Worst Case ◽  
Average Case ◽  
U Statistics

In another related work, U-statistics were used for non-asymptotic average-case analysis of random compressed sensing matrices. In this companion paper the same analytical tool is adopted differently-here we perform non-asymptotic worst-case analysis. Simple union bounds are a natural choice for worst-case analyses, however their tightness is an issue (and questioned in previous works). Here we focus on a theoretical U-statistical result, which potentially allows us to prove that these union bounds are tight. To our knowledge, this kind of (powerful) result is completely new in the context of CS. This general result applies to a wide variety of parameters, and is related to (Stein-Chen) Poisson approximation. In this paper, we consider i) restricted isometries, and ii) mutual coherence. For the bounded case, we show that -th order restricted isometry constants have tight union bounds, when the measurements m = O (k(1.5(+ log(n/k))). Here, we require the restricted isometries to grow linearly in , however we conjecture that this result can be improved to allow them to be fixed. Also, we show that mutual coherence (with the standard estimate √(4 log n)/m) have very tight union bounds. For coherence, the normalization complicates general discussion, and we consider only Gaussian and Bernoulli cases here.

Hierarchical Programming for Worst-Case Analysis of Power Grids

2018 ◽  
Author(s):  
Hatim Djelassi ◽  
Stephane Fliscounakis ◽  
Alexander Mitsos ◽  
Patrick Panciatici
Keyword(s):  
Case Analysis ◽  
Power Grids ◽  
Worst Case Analysis ◽  
Worst Case

Formal Worst-Case Analysis of Crosstalk Noise in Mesh-Based Optical Networks-on-Chip

2013 ◽  
Vol 21 (10) ◽  
pp. 1823-1836 ◽  
Author(s):  
Yiyuan Xie ◽  
Mahdi Nikdast ◽  
Jiang Xu ◽  
Xiaowen Wu ◽  
Wei Zhang ◽  
...  
Keyword(s):  
Optical Networks ◽  
Case Analysis ◽  
Worst Case Analysis ◽  
Crosstalk Noise ◽  
Worst Case ◽  
Networks On Chip ◽  
On Chip
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