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Algorithms, Volume 5, Issue 2 (June 2012), Pages 176-317

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Research

Open AccessArticle Finding All Solutions and Instances of Numberlink and Slitherlink by ZDDs
Algorithms 2012, 5(2), 176-213; doi:10.3390/a5020176
Received: 16 November 2011 / Revised: 29 February 2012 / Accepted: 19 March 2012 / Published: 5 April 2012
Cited by 4 | PDF Full-text (298 KB)
Abstract
Link puzzles involve finding paths or a cycle in a grid that satisfy given local and global properties. This paper proposes algorithms that enumerate solutions and instances of two link puzzles, Slitherlink and Numberlink, by zero-suppressed binary decision diagrams (ZDDs). A ZDD [...] Read more.
Link puzzles involve finding paths or a cycle in a grid that satisfy given local and global properties. This paper proposes algorithms that enumerate solutions and instances of two link puzzles, Slitherlink and Numberlink, by zero-suppressed binary decision diagrams (ZDDs). A ZDD is a compact data structure for a family of sets provided with a rich family of set operations, by which, for example, one can easily extract a subfamily satisfying a desired property. Thanks to the nature of ZDDs, our algorithms offer a tool to assist users to design instances of those link puzzles. Full article
(This article belongs to the Special Issue Puzzle/Game Algorithms)
Open AccessArticle An Online Algorithm for Lightweight Grammar-Based Compression
Algorithms 2012, 5(2), 214-235; doi:10.3390/a5020214
Received: 30 January 2012 / Revised: 26 March 2012 / Accepted: 28 March 2012 / Published: 10 April 2012
Cited by 11 | PDF Full-text (347 KB)
Abstract
Grammar-based compression is a well-studied technique to construct a context-free grammar (CFG) deriving a given text uniquely. In this work, we propose an online algorithm for grammar-based compression. Our algorithm guarantees O(log2 n)- approximation ratio for the minimum grammar size, [...] Read more.
Grammar-based compression is a well-studied technique to construct a context-free grammar (CFG) deriving a given text uniquely. In this work, we propose an online algorithm for grammar-based compression. Our algorithm guarantees O(log2 n)- approximation ratio for the minimum grammar size, where n is an input size, and it runs in input linear time and output linear space. In addition, we propose a practical encoding, which transforms a restricted CFG into a more compact representation. Experimental results by comparison with standard compressors demonstrate that our algorithm is especially effective for highly repetitive text. Full article
(This article belongs to the Special Issue Data Compression, Communication and Processing)
Open AccessArticle Content Sharing Graphs for Deduplication-Enabled Storage Systems
Algorithms 2012, 5(2), 236-260; doi:10.3390/a5020236
Received: 30 December 2011 / Revised: 28 March 2012 / Accepted: 29 March 2012 / Published: 10 April 2012
Cited by 2 | PDF Full-text (555 KB)
Abstract
Deduplication in storage systems has gained momentum recently for its capability in reducing data footprint. However, deduplication introduces challenges to storage management as storage objects (e.g., files) are no longer independent from each other due to content sharing between these storage objects. [...] Read more.
Deduplication in storage systems has gained momentum recently for its capability in reducing data footprint. However, deduplication introduces challenges to storage management as storage objects (e.g., files) are no longer independent from each other due to content sharing between these storage objects. In this paper, we present a graph-based framework to address the challenges of storage management due to deduplication. Specifically, we model content sharing among storage objects by content sharing graphs (CSG), and apply graph-based algorithms to two real-world storage management use cases for deduplication-enabled storage systems. First, a quasi-linear algorithm was developed to partition deduplication domains with a minimal amount of deduplication loss (i.e., data replicated across partitioned domains) in commercial deduplication-enabled storage systems, whereas in general the partitioning problem is NP-complete. For a real-world trace of 3 TB data with 978 GB of removable duplicates, the proposed algorithm can partition the data into 15 balanced partitions with only 54 GB of deduplication loss, that is, a 5% deduplication loss. Second, a quick and accurate method to query the deduplicated size for a subset of objects in deduplicated storage systems was developed. For the same trace of 3 TB data, the optimized graph-based algorithm can complete the query in 2.6 s, which is less than 1% of that of the traditional algorithm based on the deduplication metadata. Full article
(This article belongs to the Special Issue Data Compression, Communication and Processing)
Open AccessArticle A Polynomial-Time Reduction from the 3SAT Problem to the Generalized String Puzzle Problem
Algorithms 2012, 5(2), 261-272; doi:10.3390/a5020261
Received: 11 November 2011 / Revised: 27 February 2012 / Accepted: 7 April 2012 / Published: 13 April 2012
PDF Full-text (117 KB)
Abstract
A disentanglement puzzle consists of mechanically interlinked pieces, and the puzzle is solved by disentangling one piece from another set of pieces. A string puzzle consists of strings entangled with one or more wooden pieces. We consider the generalized string puzzle problem [...] Read more.
A disentanglement puzzle consists of mechanically interlinked pieces, and the puzzle is solved by disentangling one piece from another set of pieces. A string puzzle consists of strings entangled with one or more wooden pieces. We consider the generalized string puzzle problem whose input is the layout of strings and a wooden board with holes embedded in the 3-dimensional Euclidean space. We present a polynomial-time transformation from an arbitrary instance ƒ of the 3SAT problem to a string puzzle s such that ƒ is satisfiable if and only if s is solvable. Therefore, the generalized string puzzle problem is NP-hard. Full article
(This article belongs to the Special Issue Puzzle/Game Algorithms)
Open AccessArticle Imaginary Cubes and Their Puzzles
Algorithms 2012, 5(2), 273-288; doi:10.3390/a5020273
Received: 16 November 2011 / Revised: 15 April 2012 / Accepted: 8 May 2012 / Published: 9 May 2012
PDF Full-text (4034 KB)
Abstract
Imaginary cubes are three dimensional objects which have square silhouette projections in three orthogonal ways just as a cube has. In this paper, we study imaginary cubes and present assembly puzzles based on them. We show that there are 16 equivalence classes [...] Read more.
Imaginary cubes are three dimensional objects which have square silhouette projections in three orthogonal ways just as a cube has. In this paper, we study imaginary cubes and present assembly puzzles based on them. We show that there are 16 equivalence classes of minimal convex imaginary cubes, among whose representatives are a hexagonal bipyramid imaginary cube and a triangular antiprism imaginary cube. Our main puzzle is to put three of the former and six of the latter pieces into a cube-box with an edge length of twice the size of the original cube. Solutions of this puzzle are based on remarkable properties of these two imaginary cubes, in particular, the possibility of tiling 3D Euclidean space. Full article
(This article belongs to the Special Issue Puzzle/Game Algorithms)
Open AccessArticle Modeling and Performance Analysis to Predict the Behavior of a Divisible Load Application in a Cloud Computing Environment
Algorithms 2012, 5(2), 289-303; doi:10.3390/a5020289
Received: 10 April 2012 / Revised: 1 May 2012 / Accepted: 2 May 2012 / Published: 11 May 2012
Cited by 1 | PDF Full-text (324 KB)
Abstract
Cloud computing is an emerging technology where IT resources are virtualized to users as a set of a unified computing resources on a pay per use basis. The resources are dynamically chosen to satisfy a user Service Level Agreement and a required [...] Read more.
Cloud computing is an emerging technology where IT resources are virtualized to users as a set of a unified computing resources on a pay per use basis. The resources are dynamically chosen to satisfy a user Service Level Agreement and a required level of performance. Divisible load applications occur in many scientific and engineering applications and can easily be mapped to a Cloud using a master-worker pattern. However, those applications pose challenges to obtain the required performance. We model divisible load applications tasks processing on a set of cloud resources. We derive a novel model and formulas for computing the blocking probability in the system. The formulas are useful to analyze and predict the behavior of a divisible load application on a chosen set of resources to satisfy a Service Level Agreement before the implementation phase, thus saving time and platform energy. They are also useful as a dynamic feedback to a cloud scheduler for optimal scheduling. We evaluate the model in a set of illustrative scenarios. Full article
Open AccessArticle An Agent-Based Fuzzy Collaborative Intelligence Approach for Predicting the Price of a Dynamic Random Access Memory (DRAM) Product
Algorithms 2012, 5(2), 304-317; doi:10.3390/a5020304
Received: 9 April 2012 / Revised: 7 May 2012 / Accepted: 9 May 2012 / Published: 24 May 2012
PDF Full-text (291 KB) | HTML Full-text | XML Full-text
Abstract
Predicting the price of a dynamic random access memory (DRAM) product is a critical task to the manufacturer. However, it is not easy to contend with the uncertainty of the price. In order to effectively predict the price of a DRAM product, [...] Read more.
Predicting the price of a dynamic random access memory (DRAM) product is a critical task to the manufacturer. However, it is not easy to contend with the uncertainty of the price. In order to effectively predict the price of a DRAM product, an agent-based fuzzy collaborative intelligence approach is proposed in this study. In the agent-based fuzzy collaborative intelligence approach, each agent uses a fuzzy neural network to predict the DRAM price based on its view. The agent then communicates its view and forecasting results to other agents with the aid of an automatic collaboration mechanism. According to the experimental results, the overall performance was improved through the agents’ collaboration. Full article

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