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Algorithms
Special Issues
Selected Algorithmic Papers From CSR 2020
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Selected Algorithmic Papers From CSR 2020

A special issue of Algorithms (ISSN 1999-4893).

Deadline for manuscript submissions: closed (30 November 2020) | Viewed by 17100

Special Issue Editor

Prof. Dr. Henning Fernau

E-Mail Website
Guest Editor
Informatikwissenschaften, Fachbereich 4, Universität Trier, Universitätsring 15, 54296 Trier, Germany
Interests: complexity theory; fixed parameter algorithms; formal languages; fractal geometry; learning algorithms (machine learning) and pattern recognition
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

The 15th International Computer Science Symposium in Russia (CSR) is an annual international conference held in Russia that is designed to cover a broad range of topics in Theoretical Computer Science. Further details can be found here: https://csr2020.sciencesconf.org/

A number of extended conference papers regarding algorithms will be invited to this special issue of Algorithms journal to be published in Open Access form.

Prof. Dr. Henning Fernau
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All papers will be peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 100 words) can be sent to the Editorial Office for announcement on this website.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Algorithms is an international peer-reviewed open access monthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • algorithms and data structures
  • computational complexity, including hardness of approximation and parameterized complexity
  • randomness in computing, approximation algorithms, fixed-parameter algorithms
  • combinatorial optimization, constraint satisfaction, operations research
  • computational geometry
  • string algorithms
  • computational biology
  • distributed computing
  • fundamentals of machine learning, including learning theory, grammatical inference and neural computing
  • quantum computing and quantum cryptography
  • algorithmic aspects of big data

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Published Papers (6 papers)

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Editorial

Jump to: Research

2 pages, 163 KiB  
Editorial
Special Issue “Selected Algorithmic Papers From CSR 2020”
by Henning Fernau
Algorithms 2022, 15(11), 426; https://doi.org/10.3390/a15110426 - 14 Nov 2022
Cited by 1 | Viewed by 1334
Abstract
The 15th International Computer Science Symposium in Russia (CSR 2020) was organized by the Ural Federal University located in Ekaterinburg, Russian Federation [...] Full article
(This article belongs to the Special Issue Selected Algorithmic Papers From CSR 2020)

Research

Jump to: Editorial

19 pages, 3269 KiB  
Article
A Lower Bound for the Query Phase of Contraction Hierarchies and Hub Labels and a Provably Optimal Instance-Based Schema
by Tobias Rupp and Stefan Funke
Algorithms 2021, 14(6), 164; https://doi.org/10.3390/a14060164 - 25 May 2021
Cited by 5 | Viewed by 2647
Abstract
We prove a Ω(n) lower bound on the query time for contraction hierarchies (CH) as well as hub labels, two popular speed-up techniques for shortest path routing. Our construction is based on a graph family not too far from subgraphs [...] Read more.
We prove a Ω(n) lower bound on the query time for contraction hierarchies (CH) as well as hub labels, two popular speed-up techniques for shortest path routing. Our construction is based on a graph family not too far from subgraphs that occur in real-world road networks, in particular, it is planar and has a bounded degree. Additionally, we borrow ideas from our lower bound proof to come up with instance-based lower bounds for concrete road network instances of moderate size, reaching up to 96% of an upper bound given by a constructed CH. For a variant of our instance-based schema applied to some special graph classes, we can even show matching upper and lower bounds. Full article
(This article belongs to the Special Issue Selected Algorithmic Papers From CSR 2020)
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25 pages, 573 KiB  
Article
Lexicographic Unranking of Combinations Revisited
by Antoine Genitrini and Martin Pépin
Algorithms 2021, 14(3), 97; https://doi.org/10.3390/a14030097 - 19 Mar 2021
Cited by 11 | Viewed by 3313
Abstract
In the context of combinatorial sampling, the so-called “unranking method” can be seen as a link between a total order over the objects and an effective way to construct an object of given rank. The most classical order used in this context is [...] Read more.
In the context of combinatorial sampling, the so-called “unranking method” can be seen as a link between a total order over the objects and an effective way to construct an object of given rank. The most classical order used in this context is the lexicographic order, which corresponds to the familiar word ordering in the dictionary. In this article, we propose a comparative study of four algorithms dedicated to the lexicographic unranking of combinations, including three algorithms that were introduced decades ago. We start the paper with the introduction of our new algorithm using a new strategy of computations based on the classical factorial numeral system (or factoradics). Then, we present, in a high level, the three other algorithms. For each case, we analyze its time complexity on average, within a uniform framework, and describe its strengths and weaknesses. For about 20 years, such algorithms have been implemented using big integer arithmetic rather than bounded integer arithmetic which makes the cost of computing some coefficients higher than previously stated. We propose improvements for all implementations, which take this fact into account, and we give a detailed complexity analysis, which is validated by an experimental analysis. Finally, we show that, even if the algorithms are based on different strategies, all are doing very similar computations. Lastly, we extend our approach to the unranking of other classical combinatorial objects such as families counted by multinomial coefficients and k-permutations. Full article
(This article belongs to the Special Issue Selected Algorithmic Papers From CSR 2020)
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17 pages, 361 KiB  
Article
On Computational Hardness of Multidimensional Subtraction Games
by Vladimir Gurvich and Mikhail Vyalyi
Algorithms 2021, 14(3), 71; https://doi.org/10.3390/a14030071 - 25 Feb 2021
Cited by 2 | Viewed by 2207
Abstract
We study the algorithmic complexity of solving subtraction games in a fixed dimension with a finite difference set. We prove that there exists a game in this class such that solving the game is EXP-complete and requires time [...] Read more.
We study the algorithmic complexity of solving subtraction games in a fixed dimension with a finite difference set. We prove that there exists a game in this class such that solving the game is EXP-complete and requires time 2Ω(n), where n is the input size. This bound is optimal up to a polynomial speed-up. The results are based on a construction introduced by Larsson and Wästlund. It relates subtraction games and cellular automata. Full article
(This article belongs to the Special Issue Selected Algorithmic Papers From CSR 2020)
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33 pages, 3538 KiB  
Article
Determinization and Minimization of Automata for Nested Words Revisited
by Joachim Niehren and Momar Sakho
Algorithms 2021, 14(3), 68; https://doi.org/10.3390/a14030068 - 24 Feb 2021
Cited by 5 | Viewed by 2634
Abstract
We consider the problem of determinizing and minimizing automata for nested words in practice. For this we compile the nested regular expressions (NREs) from the usual XPath benchmark to nested word automata (NWAs). The determinization of these NWAs, [...] Read more.
We consider the problem of determinizing and minimizing automata for nested words in practice. For this we compile the nested regular expressions (NREs) from the usual XPath benchmark to nested word automata (NWAs). The determinization of these NWAs, however, fails to produce reasonably small automata. In the best case, huge deterministic NWAs are produced after few hours, even for relatively small NREs of the benchmark. We propose a different approach to the determinization of automata for nested words. For this, we introduce stepwise hedge automata (SHAs) that generalize naturally on both (stepwise) tree automata and on finite word automata. We then show how to determinize SHAs, yielding reasonably small deterministic automata for the NREs from the XPath benchmark. The size of deterministic SHAs automata can be reduced further by a novel minimization algorithm for a subclass of SHAs. In order to understand why the new approach to determinization and minimization works so nicely, we investigate the relationship between NWAs and SHAs further. Clearly, deterministic SHAs can be compiled to deterministic NWAs in linear time, and conversely NWAs can be compiled to nondeterministic SHAs in polynomial time. Therefore, we can use SHAs as intermediates for determinizing NWAs, while avoiding the huge size increase with the usual determinization algorithm for NWAs. Notably, the NWAs obtained from the SHAs perform bottom-up and left-to-right computations only, but no top-down computations. This NWA behavior can be distinguished syntactically by the (weak) single-entry property, suggesting a close relationship between SHAs and single-entry NWAs. In particular, it turns out that the usual determinization algorithm for NWAs behaves well for single-entry NWAs, while it quickly explodes without the single-entry property. Furthermore, it is known that the class of deterministic multi-module single-entry NWAs enjoys unique minimization. The subclass of deterministic SHAs to which our novel minimization algorithm applies is different though, in that we do not impose multiple modules. As further optimizations for reducing the sizes of the constructed SHAs, we propose schema-based cleaning and symbolic representations based on apply-else rules that can be maintained by determinization. We implemented the optimizations and report the experimental results for the automata constructed for the XPathMark benchmark. Full article
(This article belongs to the Special Issue Selected Algorithmic Papers From CSR 2020)
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25 pages, 2485 KiB  
Article
Constructing Minimally 3-Connected Graphs
by João Paulo Costalonga, Robert J. Kingan and Sandra R. Kingan
Algorithms 2021, 14(1), 9; https://doi.org/10.3390/a14010009 - 1 Jan 2021
Cited by 1 | Viewed by 3581
Abstract
A 3-connected graph is minimally 3-connected if removal of any edge destroys 3-connectivity. We present an algorithm for constructing minimally 3-connected graphs based on the results in (Dawes, JCTB 40, 159-168, 1986) using two operations: adding an edge between non-adjacent vertices and splitting [...] Read more.
A 3-connected graph is minimally 3-connected if removal of any edge destroys 3-connectivity. We present an algorithm for constructing minimally 3-connected graphs based on the results in (Dawes, JCTB 40, 159-168, 1986) using two operations: adding an edge between non-adjacent vertices and splitting a vertex. To test sets of vertices and edges for 3-compatibility, which depends on the cycles of the graph, we develop a method for obtaining the cycles of G′ from the cycles of G, where G′ is obtained from G by one of the two operations above. We eliminate isomorphic duplicates using certificates generated by McKay’s isomorphism checker nauty. The algorithm consecutively constructs the non-isomorphic minimally 3-connected graphs with n vertices and m edges from the non-isomorphic minimally 3-connected graphs with n−1 vertices and m−2 edges, n−1 vertices and m−3 edges, and n−2 vertices and m−3 edges. Full article
(This article belongs to the Special Issue Selected Algorithmic Papers From CSR 2020)
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