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Quantum algorithms know in advance 50% of the solution they will find in the future  [PDF]
Giuseppe Castagnoli
Physics , 2009, DOI: 10.1007/s10773-009-0143-6
Abstract: Quantum algorithms require less operations than classical algorithms. The exact reason of this has not been pinpointed until now. Our explanation is that quantum algorithms know in advance 50% of the solution of the problem they will find in the future. In fact they can be represented as the sum of all the possible histories of a respective "advanced information classical algorithm". This algorithm, given the advanced information (50% of the bits encoding the problem solution), performs the operations (oracle's queries) still required to identify the solution. Each history corresponds to a possible way of getting the advanced information and a possible result of computing the missing information. This explanation of the quantum speed up has an immediate practical consequence: the speed up comes from comparing two classical algorithms, with and without advanced information, with no physics involved. This simplification could open the way to a systematic exploration of the possibilities of speed up.
Discussing the explanation of the quantum speed up  [PDF]
Giuseppe Castagnoli
Physics , 2009,
Abstract: In former work, we showed that a quantum algorithm is the sum over the histories of a classical algorithm that knows in advance 50% of the information about the solution of the problem - each history is a possible way of getting the advanced information and a possible result of computing the missing information. We gave a theoretical justification of this 50% advanced information rule and checked that it holds for a large variety of quantum algorithms. Now we discuss the theoretical justification in further detail and counter a possible objection. We show that the rule is the generalization of a simple, well known, explanation of quantum nonlocality - where logical correlation between measurement outcomes is physically backed by a causal/deterministic/local process with causality allowed to go backward in time with backdated state vector reduction. The possible objection is that quantum algorithms often produce the solution of the problem in an apparently deterministic way (when their unitary part produces an eigenstate of the observable to be measured and measurement produces the corresponding eigenvalue - the solution - with probability 1), while the present explanation of the speed up relies on the nondeterministic character of quantum measurement. We show that this objection would mistake the nondeterministic production of a definite outcome for a deterministic production.
Advanced Approach in Sensitive Rule Hiding  [cached]
K. Duraiswamy,D. Manjula,N. Maheswari
Modern Applied Science , 2009, DOI: 10.5539/mas.v3n2p98
Abstract: Privacy preserving data mining is a novel research direction in data mining and statistical databases, which has recently been proposed in response to the concerns of preserving personal or sensible information derived from data mining algorithms. There have been two types of privacy proposed concerning data mining. The first type of privacy, called output privacy, is that the data is altered so that the mining result will preserve certain privacy. The second type of privacy, called input privacy, is that the data is manipulated so that the mining result is not affected or minimally affected. For output privacy in hiding association rules, current approaches require hidden rules or patterns to be given in advance. However, to specify hidden rules, entire data mining process needs to be executed. For some applications, only certain sensitive rules that contain sensitive items are required to hide. In this work, an algorithm ISSRH (Increase Support Sensitive Rule Hiding) is proposed, to hide the sensitive rules that contain sensitive items, so that sensitive rules containing specified sensitive items on the right hand side of the rule cannot be inferred through association rule mining. Example illustrating the proposed approach is given. The characteristics of the algorithm are discussed.
A REVIEW ON ASSOCIATION RULE MINING ALGORITHMS  [PDF]
JYOTI ARORA, NIDHI BHALLA, SANJEEV RAO
International Journal of Innovative Research in Computer and Communication Engineering , 2013,
Abstract: In this paper, a review of four different association rule mining algorithmsApriori, AprioriTid,Apriori hybrid and tertius algorithms and their drawbacks which would be helpful to find new solution for the Problems found in these algorithms and also presents a comparison between different association mining algorithms. Association rule mining is the one of the most important technique of the data mining. Its aim is to extract interesting correlations, frequent patterns and association among set of items in the transaction database.
Exploiting Parallelism in Association Rule Mining Algorithms
Rakhi Garg,Pramod Kumar Mishra
International Journal of Advancements in Technology , 2011,
Abstract: Association rule mining is one of the major technique of data mining, involves finding of frequent itemsets with minimum support and generating association rule among them with minimum confidence. The task of finding all frequent itemsets for a large datasets requires a lot of computation which can be minimized by exploiting parallelism to the sequential algorithms. In this paper, we provide the preliminaries of basic concepts about association rule mining, different sequential association rule mining algorithms on different hardware platforms and also focus on the challenges in exploiting parallelism to these algorithms. We also discusses up to what extent these challenges e.g. load balancing, efficient memory usage, minimization of communication cost among processors, efficient data and task decomposition etc. are congregate by a given parallel association rule mining algorithm and classifies them accordingly. Although, this survey cannot be complete review of all algorithms, but it provides information that will cover major theoretical issues and can be serve as a reference for both the researchers and the practitioners.
EVALUATING THE PERFORMANCE OF ASSOCIATION RULE MINING ALGORITHMS
K. Vanitha
Journal of Global Research in Computer Science , 2011,
Abstract: Association rule mining is one of the most popular data mining methods. However, mining association rules often results in a very large number of found rules, leaving the analyst with the task to go through all the rules and discover interesting ones. In this paper, we present the performance comparison of Apriori and FP-growth algorithms. The performance is analyzed based on the execution time for different number of instances and confidence in Super market data set. These algorithms are presented together with some experimental data. Our performance study shows that the FP-growth method is efficient and scalable and is about an order of magnitude faster than the Apriori algorithm.
EVALUATING THE PERFORMANCE OF ASSOCIATION RULE MINING ALGORITHMS  [cached]
K. Vanitha
Journal of Global Research in Computer Science , 2011,
Abstract: Association rule mining is one of the most popular data mining methods. However, mining association rules often results in a very large number of found rules, leaving the analyst with the task to go through all the rules and discover interesting ones. In this paper, we present the performance comparison of Apriori and FP-growth algorithms. The performance is analyzed based on the execution time for different number of instances and confidence in Super market data set. These algorithms are presented together with some experimental data. Our performance study shows that the FP-growth method is efficient and scalable and is about an order of magnitude faster than the Apriori algorithm.
Advanced Multilevel Node Separator Algorithms  [PDF]
Peter Sanders,Christian Schulz
Computer Science , 2015,
Abstract: A node separator of a graph is a subset S of the nodes such that removing S and its incident edges divides the graph into two disconnected components of about equal size. In this work, we introduce novel algorithms to find small node separators in large graphs. With focus on solution quality, we introduce novel flow-based local search algorithms which are integrated in a multilevel framework. In addition, we transfer techniques successfully used in the graph partitioning field. This includes the usage of edge ratings tailored to our problem to guide the graph coarsening algorithm as well as highly localized local search and iterated multilevel cycles to improve solution quality even further. Experiments indicate that flow-based local search algorithms on its own in a multilevel framework are already highly competitive in terms of separator quality. Adding additional local search algorithms further improves solution quality. Our strongest configuration almost always outperforms competing systems while on average computing 10% and 62% smaller separators than Metis and Scotch, respectively.
Relaxing the Geodesic Rule in Defect Formation Algorithms  [PDF]
Levon Pogosian,Tanmay Vachaspati
Physics , 1997, DOI: 10.1016/S0370-2693(98)00109-9
Abstract: In studying the formation of topological defects, it is conventional to assume the ``geodesic rule'' which is equivalent to minimizing gradients of the order parameter. This assumption has been called into question in field-theoretic studies of first order phase transitions and in the case of local defects. We present a scheme for numerically investigating the formation of strings without assuming the geodesic rule. Our results show that the fraction of string in infinite strings grows as we deviate from the geodesic rule.
Handling equality constraints by adaptive relaxing rule for swarm algorithms  [PDF]
Xiao-Feng Xie,Wen-Jun Zhang,De-Chun Bi
Computer Science , 2005,
Abstract: The adaptive constraints relaxing rule for swarm algorithms to handle with the problems with equality constraints is presented. The feasible space of such problems may be similiar to ridge function class, which is hard for applying swarm algorithms. To enter the solution space more easily, the relaxed quasi feasible space is introduced and shrinked adaptively. The experimental results on benchmark functions are compared with the performance of other algorithms, which show its efficiency.
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