RELIABLE INTERNET-BASED MASTER-WORKER COMPUTING IN THE PRESENCE OF MALICIOUS WORKERS

2012 ◽  
Vol 22 (01) ◽  
pp. 1250002 ◽  
Author(s):  
ANTONIO FERNÁNDEZ ANTA ◽  
CHRYSSIS GEORGIOU ◽  
LUIS LÓPEZ ◽  
AGUSTÍN SANTOS
Keyword(s):  
Lower Bounds ◽  
Distributed System ◽  
High Probability ◽  
Upper Bounds ◽  
The Internet ◽  
Decision Strategy ◽  
Single Task ◽  
Asymptotically Optimal ◽  
A Value ◽  
Probability Of Success

We consider a Master-Worker distributed system where a master processor assigns, over the Internet, tasks to a collection of n workers, which are untrusted and might act maliciously. In addition, a worker may not reply to the master, or its reply may not reach the master, due to unavailabilities or failures of the worker or the network. Each task returns a value, and the goal is for the master to accept only correct values with high probability. Furthermore, we assume that the service provided by the workers is not free; for each task that a worker is assigned, the master is charged with a work-unit. Therefore, considering a single task assigned to several workers, our objective is to have the master processor to accept the correct value of the task with high probability, with the smallest possible amount of work (number of workers the master assigns the task). We probabilistically bound the number of faulty processors by assuming a known probability p < 1/2 of any processor to be faulty. Our work demonstrates that it is possible to obtain, with provable analytical guarantees, high probability of correct acceptance with low work. In particular, we first show lower bounds on the minimum amount of (expected) work required, so that any algorithm accepts the correct value with probability of success 1 - ε, where ε ≪ 1 (e.g., 1/n). Then we develop and analyze two algorithms, each using a different decision strategy, and show that both algorithms obtain the same probability of success 1 - ε, and in doing so, they require similar upper bounds on the (expected) work. Furthermore, under certain conditions, these upper bounds are asymptotically optimal with respect to our lower bounds.

TIGHT QUANTUM BOUNDS FOR COMPUTATIONAL GEOMETRY PROBLEMS

2009 ◽  
Vol 07 (05) ◽  
pp. 935-947
Author(s):  
NILTON VOLPATO ◽  
ARNALDO MOURA
Keyword(s):  
Computational Geometry ◽  
Lower Bounds ◽  
Open Problem ◽  
Arbitrary Order ◽  
Order Relation ◽  
Upper Bounds ◽  
General Algorithm ◽  
Asymptotically Optimal ◽  
Optimal Bounds

We present new quantum lower bounds and upper bounds for several computational geometry problems. The bounds presented here improve on currently known results in a number of ways. We give asymptotically optimal bounds for one of the problems considered, and we provide, up to logarithmic factors, optimal bounds for a number of other problems and, in particular, we settle an open problem of Bahadur et al. Some of these new bounds are obtained using a general algorithm for finding a minimum pair over a given arbitrary order relation.

MINIMIZING CONGESTION OF LAYOUTS FOR ATM NETWORKS WITH FAULTY LINKS

1999 ◽  
Vol 10 (04) ◽  
pp. 503-512 ◽  
Author(s):  
LESZEK GASIENIEC ◽  
EVANGELOS KRANAKIS ◽  
DANNY KRIZANC ◽  
ANDREZEJ PELC
Keyword(s):  
Lower Bounds ◽  
High Probability ◽  
Upper Bounds ◽  
Upper And Lower Bounds ◽  
Atm Networks ◽  
Worst Case ◽  
Precise Analysis ◽  
Order Of Magnitude ◽  
Bounded Size ◽  
Fault Distribution

We consider the problem of constructing virtual path layouts for an ATM network consisting of a complete network Kn of n processors in which a certain number of links may fail. Our main goal is to construct layouts which tolerate any configuration of up to f faults and have the least possible congestion. First, we study the minimal congestion of 1-hop f-tolerant layouts in Kn. For any positive integer f we give upper and lower bounds on this minimal congestion and construct f-tolerant layouts with congestion corresponding to the upper bounds. Our results are based on a precise analysis of the diameter of the network Kn[ℱ] which results from Kn by deleting links from a set ℱ of bounded size. Next we study the minimal congestion of h-hop f-tolerant layouts in Kn, for larger values of the number h of hops. We give upper and lower bounds on the order of magnitude of this congestion, based on results for 1-hop layouts. Finally, we consider a random, rather than worst case, fault distribution where links fail independently with constant probability p<1. Our goal now is to construct layouts with low congestion that tolerate the existing faults with high probability. For any p<1, we show the existence of 1-hop layouts in Kn, with congestion O( log n).

scholarly journals Stochastic Online Learning with Probabilistic Graph Feedback

2020 ◽  
Vol 34 (04) ◽  
pp. 4675-4682
Author(s):  
Shuai Li ◽  
Wei Chen ◽  
Zheng Wen ◽  
Kwong-Sak Leung
Keyword(s):  
Online Learning ◽  
Lower Bounds ◽  
Random Graphs ◽  
High Probability ◽  
Upper Bounds ◽  
Directed Edge ◽  
Probabilistic Graph ◽  
One Step ◽  
The One ◽  
Independent Probability

We consider a problem of stochastic online learning with general probabilistic graph feedback, where each directed edge in the feedback graph has probability pij. Two cases are covered. (a) The one-step case, where after playing arm i the learner observes a sample reward feedback of arm j with independent probability pij. (b) The cascade case where after playing arm i the learner observes feedback of all arms j in a probabilistic cascade starting from i – for each (i,j) with probability pij, if arm i is played or observed, then a reward sample of arm j would be observed with independent probability pij. Previous works mainly focus on deterministic graphs which corresponds to one-step case with pij ∈ {0,1}, an adversarial sequence of graphs with certain topology guarantees, or a specific type of random graphs. We analyze the asymptotic lower bounds and design algorithms in both cases. The regret upper bounds of the algorithms match the lower bounds with high probability.

The Ethics of Unwinnable War

2017 ◽  
Author(s):  
Dominic Tierney
Keyword(s):  
High Probability ◽  
Just War ◽  
Just War Theory ◽  
Moral Dilemmas ◽  
Probability Of Success ◽  
Military Campaigns ◽  
Military Campaign

According to just war theory, military campaigns should only be fought as a last resort, with the goal of correcting a grave evil, and where there is a high probability of success. But what happens when a military campaign unravels and becomes unwinnable? How can a leader reconcile just war theory with the need to extricate the country from a quagmire? In recent decades, US presidents have repeatedly faced such moral dilemmas, as campaigns in Korea, Vietnam, Afghanistan, and Iraq all became unwinnable. When victory is no longer achievable, leaders should dial down the goals of the war, resist the pressure to embrace barbarism, negotiate with the adversary, and seek the best possible peace from the range of plausible alternatives.

scholarly journals Multilevel Monte Carlo methods and lower–upper bounds in initial margin computations

2020 ◽  
Vol 26 (2) ◽  
pp. 131-161
Author(s):  
Florian Bourgey ◽  
Stefano De Marco ◽  
Emmanuel Gobet ◽  
Alexandre Zhou
Keyword(s):  
Monte Carlo ◽  
Lower Bounds ◽  
Asymptotic Optimality ◽  
Upper Bounds ◽  
Upper And Lower Bounds ◽  
Independent Random Variables ◽  
Outer Function ◽  
Control Problems ◽  
Multilevel Monte Carlo ◽  
Primal Dual

AbstractThe multilevel Monte Carlo (MLMC) method developed by M. B. Giles [Multilevel Monte Carlo path simulation, Oper. Res. 56 2008, 3, 607–617] has a natural application to the evaluation of nested expectations {\mathbb{E}[g(\mathbb{E}[f(X,Y)|X])]}, where {f,g} are functions and {(X,Y)} a couple of independent random variables. Apart from the pricing of American-type derivatives, such computations arise in a large variety of risk valuations (VaR or CVaR of a portfolio, CVA), and in the assessment of margin costs for centrally cleared portfolios. In this work, we focus on the computation of initial margin. We analyze the properties of corresponding MLMC estimators, for which we provide results of asymptotic optimality; at the technical level, we have to deal with limited regularity of the outer function g (which might fail to be everywhere differentiable). Parallel to this, we investigate upper and lower bounds for nested expectations as above, in the spirit of primal-dual algorithms for stochastic control problems.

scholarly journals IoT Resource Allocation and Optimization Based on Heuristic Algorithm

Sensors ◽  
2020 ◽  
Vol 20 (2) ◽  
pp. 539 ◽  
Author(s):  
Arun Kumar Sangaiah ◽  
Ali Asghar Rahmani Hosseinabadi ◽  
Morteza Babazadeh Shareh ◽  
Seyed Yaser Bozorgi Rad ◽  
Atekeh Zolfagharian ◽  
...  
Keyword(s):  
Resource Allocation ◽  
Distributed System ◽  
Communication Cost ◽  
The Internet ◽  
Multiple Resources ◽  
Whale Optimization ◽  
Total Communication ◽  
The Internet Of Things ◽  
Proper Performance ◽  
Better Than

The Internet of Things (IoT) is a distributed system that connects everything via internet. IoT infrastructure contains multiple resources and gateways. In such a system, the problem of optimizing IoT resource allocation and scheduling (IRAS) is vital, because resource allocation (RA) and scheduling deals with the mapping between recourses and gateways and is also responsible for optimally allocating resources to available gateways. In the IoT environment, a gateway may face hundreds of resources to connect. Therefore, manual resource allocation and scheduling is not possible. In this paper, the whale optimization algorithm (WOA) is used to solve the RA problem in IoT with the aim of optimal RA and reducing the total communication cost between resources and gateways. The proposed algorithm has been compared to the other existing algorithms. Results indicate the proper performance of the proposed algorithm. Based on various benchmarks, the proposed method, in terms of “total communication cost”, is better than other ones.

ON THE AVERAGE CASE CIRCUIT DELAY OF DISJUNCTION

1995 ◽  
Vol 05 (02) ◽  
pp. 275-280 ◽  
Author(s):  
BEATE BOLLIG ◽  
MARTIN HÜHNE ◽  
STEFAN PÖLT ◽  
PETR SAVICKÝ
Keyword(s):  
Lower Bounds ◽  
Wide Class ◽  
Time Complexity ◽  
Upper And Lower Bounds ◽  
Average Case ◽  
Asymptotically Optimal ◽  
Circuit Delay ◽  
Suitable Measure

For circuits the expected delay is a suitable measure for the average case time complexity. In this paper, new upper and lower bounds on the expected delay of circuits for disjunction and conjunction are derived. The circuits presented yield asymptotically optimal expected delay for a wide class of distributions on the inputs even when the parameters of the distribution are not known in advance.

scholarly journals Bounding the Size and Probability of Epidemics on Networks

2008 ◽  
Vol 45 (2) ◽  
pp. 498-512 ◽  
Author(s):  
Joel C. Miller
Keyword(s):  
Infectious Disease ◽  
Lower Bounds ◽  
Upper Bounds ◽  
Marginal Probability ◽  
Transmission Properties ◽  
Disease Spreading ◽  
Special Case

We consider an infectious disease spreading along the edges of a network which may have significant clustering. The individuals in the population have heterogeneous infectiousness and/or susceptibility. We define the out-transmissibility of a node to be the marginal probability that it would infect a randomly chosen neighbor given its infectiousness and the distribution of susceptibility. For a given distribution of out-transmissibility, we find the conditions which give the upper (or lower) bounds on the size and probability of an epidemic, under weak assumptions on the transmission properties, but very general assumptions on the network. We find similar bounds for a given distribution of in-transmissibility (the marginal probability of being infected by a neighbor). We also find conditions giving global upper bounds on the size and probability. The distributions leading to these bounds are network independent. In the special case of networks with high girth (locally tree-like), we are able to prove stronger results. In general, the probability and size of epidemics are maximal when the population is homogeneous and minimal when the variance of in- or out-transmissibility is maximal.

Alphabetic points in compositions and words

2021 ◽  
Vol 31 (4) ◽  
pp. 241-250
Author(s):  
Margaret Archibald ◽  
Aubrey Blecher ◽  
Arnold Knopfmacher
Keyword(s):  
Lower Bounds ◽  
Generating Functions ◽  
Upper And Lower Bounds ◽  
A Value

Abstract We use generating functions to account for alphabetic points (or the lack thereof) in compositions and words. An alphabetic point is a value j such that all the values to its left are not larger than j and all the values to its right are not smaller than j. We also provide the asymptotics for compositions and words which have no alphabetic points, as the size tends to infinity. This is achieved by the construction of upper and lower bounds which converge to each other, and in the latter case by probabilistic arguments.

scholarly journals The Essential Dimension of Stacks of Parabolic Vector Bundles over Curves

2012 ◽  
Vol 10 (3) ◽  
pp. 455-488 ◽  
Author(s):  
Indranil Biswas ◽  
Ajneet Dhillon ◽  
Nicole Lemire
Keyword(s):  
Lower Bounds ◽  
Upper Bound ◽  
Vector Bundles ◽  
Upper Bounds ◽  
Essential Dimension ◽  
Parabolic Structure ◽  
Moduli Stack

AbstractWe find upper bounds on the essential dimension of the moduli stack of parabolic vector bundles over a curve. When there is no parabolic structure, we improve the known upper bound on the essential dimension of the usual moduli stack. Our calculations also give lower bounds on the essential dimension of the semistable locus inside the moduli stack of vector bundles of rank r and degree d without parabolic structure.

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