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Algorithms, Volume 4, Issue 2 (June 2011), Pages 75-154

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Research

Open AccessArticle Approximating the Minimum Tour Cover of a Digraph
Algorithms 2011, 4(2), 75-86; doi:10.3390/a4020075
Received: 2 March 2011 / Revised: 24 March 2011 / Accepted: 2 April 2011 / Published: 20 April 2011
Cited by 1 | PDF Full-text (179 KB) | HTML Full-text | XML Full-text
Abstract
Given a directed graph G with non-negative cost on the arcs, a directed tour cover T of G is a cycle (not necessarily simple) in G such that either head or tail (or both of them) of every arc in G is touched
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Given a directed graph G with non-negative cost on the arcs, a directed tour cover T of G is a cycle (not necessarily simple) in G such that either head or tail (or both of them) of every arc in G is touched by T. The minimum directed tour cover problem (DToCP), which is to find a directed tour cover of minimum cost, is NP-hard. It is thus interesting to design approximation algorithms with performance guarantee to solve this problem. Although its undirected counterpart (ToCP) has been studied in recent years, in our knowledge, the DToCP remains widely open. In this paper, we give a 2 log2(n)-approximation algorithm for the DToCP. Full article
Open AccessArticle Goodness-of-Fit Tests For Elliptical and Independent Copulas through Projection Pursuit
Algorithms 2011, 4(2), 87-114; doi:10.3390/a4020087
Received: 15 March 2011 / Revised: 5 April 2011 / Accepted: 8 April 2011 / Published: 26 April 2011
Cited by 1 | PDF Full-text (347 KB) | HTML Full-text | XML Full-text
Abstract
Two goodness-of-fit tests for copulas are being investigated. The first one deals with the case of elliptical copulas and the second one deals with independent copulas. These tests result from the expansion of the projection pursuit methodology that we will introduce in the
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Two goodness-of-fit tests for copulas are being investigated. The first one deals with the case of elliptical copulas and the second one deals with independent copulas. These tests result from the expansion of the projection pursuit methodology that we will introduce in the present article. This method enables us to determine on which axis system these copulas lie as well as the exact value of these very copulas in the basis formed by the axes previously determined irrespective of their value in their canonical basis. Simulations are also presented as well as an application to real datasets. Full article
Open AccessArticle Alternatives to the Least Squares Solution to Peelle’s Pertinent Puzzle
Algorithms 2011, 4(2), 115-130; doi:10.3390/a4020115
Received: 28 March 2011 / Revised: 1 June 2011 / Accepted: 8 June 2011 / Published: 23 June 2011
Cited by 4 | PDF Full-text (309 KB) | HTML Full-text | XML Full-text
Abstract
Peelle’s Pertinent Puzzle (PPP) was described in 1987 in the context of estimating fundamental parameters that arise in nuclear interaction experiments. In PPP, generalized least squares (GLS) parameter estimates fell outside the range of the data, which has raised concerns that GLS is
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Peelle’s Pertinent Puzzle (PPP) was described in 1987 in the context of estimating fundamental parameters that arise in nuclear interaction experiments. In PPP, generalized least squares (GLS) parameter estimates fell outside the range of the data, which has raised concerns that GLS is somehow flawed and has led to suggested alternatives to GLS estimators. However, there have been no corresponding performance comparisons among methods, and one suggested approach involving simulated data realizations is statistically incomplete. Here we provide performance comparisons among estimators, introduce approximate Bayesian computation (ABC) using density estimation applied to simulated data realizations to produce an alternative to the incomplete approach, complete the incompletely specified approach, and show that estimation error in the assumed covariance matrix cannot always be ignored. Full article
Open AccessArticle Requirements for Semantic Educational Recommender Systems in Formal E-Learning Scenarios
Algorithms 2011, 4(2), 131-154; doi:10.3390/a4030131
Received: 4 March 2011 / Revised: 23 May 2011 / Accepted: 1 July 2011 / Published: 20 July 2011
Cited by 23 | PDF Full-text (496 KB) | HTML Full-text | XML Full-text
Abstract
This paper analyzes how recommender systems can be applied to current e-learning systems to guide learners in personalized inclusive e-learning scenarios. Recommendations can be used to overcome current limitations of learning management systems in providing personalization and accessibility features. Recommenders can take advantage
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This paper analyzes how recommender systems can be applied to current e-learning systems to guide learners in personalized inclusive e-learning scenarios. Recommendations can be used to overcome current limitations of learning management systems in providing personalization and accessibility features. Recommenders can take advantage of standards-based solutions to provide inclusive support. To this end we have identified the need for developing semantic educational recommender systems, which are able to extend existing learning management systems with adaptive navigation support. In this paper we present three requirements to be considered in developing these semantic educational recommender systems, which are in line with the service-oriented approach of the third generation of learning management systems, namely: (i) a recommendation model; (ii) an open standards-based service-oriented architecture; and (iii) a usable and accessible graphical user interface to deliver the recommendations. Full article
(This article belongs to the Special Issue Recommender Systems in E-Learning Settings)
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