Algorithm efficiency

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  • Introduction to java programming: Chapter 23 - Algorithm Efficiency and Sorting's Objectives is to estimate algorithm efficiency using the Big O notation; understand growth rates and why constants and smaller terms can be ignored in the estimation.

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  • Algorithms play the central role both in the science and practice of computing. Recognition of this fact has led to the appearance of a considerable number of textbooks on the subject. By and large, they follow one of two alternatives in presenting algorithms. One classifies algorithms according to a problem type. Such a book would have separate chapters on algorithms for sorting, searching, graphs, and so on. The advantage of this approach is that it allows an immediate comparison of, say, the efficiency of different algorithms for the same problem.

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  • • Algorithm efficiency is considered with only big problem sizes. • We are not concerned with an exact measurement of an algorithm's efficiency. • Terms that do not substantially change the function’s magnitude are eliminated.

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  • A comprehensive treatment focusing on the creation of efficient data structures and algorithms, this text explains how to select or design the data structure best suited to specific problems. It uses C++ as the programming language and is suitable for second-year data structure courses and computer science courses in algorithmic analysis.

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  • The best selling 'Algorithmics' presents the most important, concepts, methods and results that are fundamental to the science of computing. It starts by introducing the basic ideas of algorithms, including their structures and methods of data manipulation. It then goes on to demonstrate how to design accurate and efficient algorithms, and discusses their inherent limitations.

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  • Data Structures and Algorithm Analysis Edition 3.2 (Java Version) a comprehensive treatment focusing on the creation of efficient data structures and algorithms, this text explains how to select or design the data structure best suited to specific problems. It uses Java as the programming language and is suitable for second-year data structure courses and computer science courses in algorithmic analysis.

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  • The field of information and communication technologies continues to evolve and grow in both the research and the practical domains. However, energy efficiency is an aspect in communication technologies that until recently was only considered for embedded, mobile or handheld battery constraint devices.

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  • In recent years, the credit derivatives market has become extremely active. Especially credit default swaps (CDSs) and collateralized debt obligations (CDOs) have contributed to what has been an amazing development. The most important benefit of credit derivatives is their ability to transfer the credit risk of an arbitrary number of obligors in a simple, efficient, and standardized way, giving rise to a liquid market for credit risk that can be easily accessed by many market participants.

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  • Question 1. Reorder the following efficiencies from the smallest to the largest: a. 2n3 + n5 b. 2000 c. 4n+1 d. n4 e. (n-1)! f. nlog2(n) g. 2klogk(n) (k is a predefined constant) Solution: Efficiency: a measure of amount of time for an algorithm to execute (Time Efficiency) or a measure of amount of memory needed for an algorithm to execute (Space Efficiency).

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  • Several recent stochastic parsers use bilexical grammars, where each word type idiosyncratically prefers particular complements with particular head words. We present O(n 4) parsing algorithms for two bilexical formalisms, improving the prior upper bounds of O(n5). For a common special case that was known to allow O(n 3) parsing (Eisner, 1997), we present an O(n 3) algorithm with an improved grammar constant.

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  • We investigate the problem of determining a compact underspecified semantical representation for sentences that may be highly ambiguous. Due to combinatorial explosion, the naive method of building semantics for the different syntactic readings independently is prohibitive. We present a method that takes as input a syntactic parse forest with associated constraintbased semantic construction rules and directly builds a packed semantic structure. The algorithm is fully implemented and runs in O(n4log(n)) in sentence length, if the grammar meets some reasonable 'normality' restrictions. ...

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  • The purpose of this paper is to examine the oft-repeated assertion regarding the efficiency of a "simple parsing algorithm" combinable with a variety of different grammars written in the form of appropriate tables of rules.

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  • In this paper we compare two grammar-based generation algorithms: the Semantic-Head-Driven Generation Algorithm (SHDGA), and the Essential Arguments Algorithm (EAA). Both algorithms have successfully addressed several outstanding problems in grammarbased generation, including dealing with non-monotonic compositionality of representation, left-recursion, deadlock-prone rules, and nondeterminism. We concentrate here on the comparison of selected properties: generality, efficiency, and determinism.

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  • We present an efficient procedure for cost-based abduction, which is based on the idea of using chart parsers as proof procedures. We discuss in detail three features of our algorithm - - goal-driven bottom-up derivation, tabulation of the partial results, and agenda control mechanism - - and report the results of the preliminary experiments, which show how these features improve the computational efficiency of cost-based abduction.

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  • In statistical natural language processing we always face the problem of sparse data. One way to reduce this problem is to group words into equivalence classes which is a standard method in statistical language modeling. In this paper we describe a method to determine bilingual word classes suitable for statistical machine translation. We develop an optimization criterion based on a maximumlikelihood approach and describe a clustering algorithm. We will show that the usage of the bilingual word classes we get can improve statistical machine translation. ...

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  • What is an algorithm? The logical steps to solve a problem. What is a program? Program = Data structures + Algorithms (Niklaus Wirth) The most common tool to define algorithms. • English-like representation of the code required for an algorithm. Pseudocode = English + Code relaxed syntax being instructions using easy to read basic control structures (sequential, conditional, iterative)

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  • be used for efficiency by providing a best-first search heuristic to order the parsing agenda. This paper proposes an agenda-based probabilistic chart parsing algorithm which is both robust and efficient. The algorithm, 7)icky 1, is considered robust because it will potentially generate all constituents produced by a pure bottom-up parser and rank these constituents by likelihood. The efficiency of the algorithm is achieved through a technique called probabilistic prediction, which helps the algorithm avoid worst-case behavior. ...

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  • The lexicalist approach to Machine Translation offers significant advantages in the development of linguistic descriptions. However, the Shake-and-Bake generation algorithm of (Whitelock, 1992) is NPcomplete. We present a polynomial time algorithm for lexicalist MT generation provided that sufficient information can be transferred to ensure more determinism.

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  • We discuss algorithms for generation within the Lambek Theorem Proving Framework. Efficient algorithms for generation in this framework take a semantics-driven strategy. This strategy can be modeled by means of rules in the calculus that are geared to generation, or by means of an algorithm for the Theorem Prover. The latter possibility enables processing of a bidirectional calculus. Therefore Lambek Theorem Proving is a natural candidate for a 'uniform' architecture for natural language parsing and generation.

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  • In the literature, Tree Adjoining Grammars (TAGs) are propagated to be adequate for natural language description - - analysis as well as generation. In this paper we concentrate on the direction of analysis. Especially important for an implementation of that task is how efficiently this can be done, i.e., how readily the word problem can be solved for TAGs. Up to now, a parser with O(n 6) steps in the worst case was known where n is the length of the input string. In this paper, the result is improved to O(n 4 log n) as a new lowest...

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