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Algorithms
Special Issues
Parameterized Complexity and Algorithms for Nonclassical Logics
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Parameterized Complexity and Algorithms for Nonclassical Logics

A special issue of Algorithms (ISSN 1999-4893). This special issue belongs to the section "Analysis of Algorithms and Complexity Theory".

Deadline for manuscript submissions: closed (31 January 2021) | Viewed by 5877

Special Issue Editor

Dr. Arne Meier

E-Mail Website
Guest Editor
Institute of Theoretical Computer Science, Leibniz Universität Hannover
Interests: logic; complexity theory; algorithms; parameterized complexity; parameterized enumeration

Special Issue Information

Dear Colleagues,

Nonclassical logics occur in a wealth of areas of research and modern life. For instance, temporal logics play a prevalent role in program verification, nonmonotonic logics are omnipresent in artificial intelligence, hybrid, or modal logics, and description logics are central to ontology-based research. However, there are numerous other nonclassical logics that are also of interest.

For this Algorithms Special Issue on parameterized complexity and algorithms for nonclassical logics, we kindly invite you to submit your high-quality papers with subjects covering recent research on this (non-exhaustive) list of possible directions with an emphasis on nonclassical logics:

  • Parameterized complexity classifications
  • Parameterized proof-theoretic approaches
  • Parameterized counting complexity investigations
  • Parameterized enumeration complexity
  • Experimental studies
  • New results on lower bounds
  • Developments on fine-grained parameterized complexity

Dr. Arne Meier
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 submissions that pass pre-check are 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. The Article Processing Charge (APC) for publication in this open access journal is 1600 CHF (Swiss Francs). 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

  • nonclassical logics
  • parameterized complexity
  • parameterized enumeration complexity
  • parameterized counting complexity
  • FPT
  • lower bounds
  • ETH/SETH
  • parameterized counting complexity

Published Papers (2 papers)

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37 pages, 471 KiB  
Article
On the Descriptive Complexity of Color Coding
by Max Bannach and Till Tantau
Algorithms 2021, 14(3), 96; https://doi.org/10.3390/a14030096 - 19 Mar 2021
Viewed by 2600
Abstract
Color coding is an algorithmic technique used in parameterized complexity theory to detect “small” structures inside graphs. The idea is to derandomize algorithms that first randomly color a graph and then search for an easily-detectable, small color pattern. We transfer color coding to [...] Read more.
Color coding is an algorithmic technique used in parameterized complexity theory to detect “small” structures inside graphs. The idea is to derandomize algorithms that first randomly color a graph and then search for an easily-detectable, small color pattern. We transfer color coding to the world of descriptive complexity theory by characterizing—purely in terms of the syntactic structure of describing formulas—when the powerful second-order quantifiers representing a random coloring can be replaced by equivalent, simple first-order formulas. Building on this result, we identify syntactic properties of first-order quantifiers that can be eliminated from formulas describing parameterized problems. The result applies to many packing and embedding problems, but also to the long path problem. Together with a new result on the parameterized complexity of formula families involving only a fixed number of variables, we get that many problems lie in FPT just because of the way they are commonly described using logical formulas. Full article
(This article belongs to the Special Issue Parameterized Complexity and Algorithms for Nonclassical Logics)
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28 pages, 751 KiB  
Article
DynASP2.5: Dynamic Programming on Tree Decompositions in Action
by Johannes K. Fichte, Markus Hecher, Michael Morak and Stefan Woltran
Algorithms 2021, 14(3), 81; https://doi.org/10.3390/a14030081 - 2 Mar 2021
Viewed by 2619
Abstract
Efficient exact parameterized algorithms are an active research area. Such algorithms exhibit a broad interest in the theoretical community. In the last few years, implementations for computing various parameters (parameter detection) have been established in parameterized challenges, such as treewidth, treedepth, hypertree width, [...] Read more.
Efficient exact parameterized algorithms are an active research area. Such algorithms exhibit a broad interest in the theoretical community. In the last few years, implementations for computing various parameters (parameter detection) have been established in parameterized challenges, such as treewidth, treedepth, hypertree width, feedback vertex set, or vertex cover. In theory, instances, for which the considered parameter is small, can be solved fast (problem evaluation), i.e., the runtime is bounded exponential in the parameter. While such favorable theoretical guarantees exists, it is often unclear whether one can successfully implement these algorithms under practical considerations. In other words, can we design and construct implementations of parameterized algorithms such that they perform similar or even better than well-established problem solvers on instances where the parameter is small. Indeed, we can build an implementation that performs well under the theoretical assumptions. However, it could also well be that an existing solver implicitly takes advantage of a structure, which is often claimed for solvers that build on Sat-solving. In this paper, we consider finding one solution to instances of answer set programming (ASP), which is a logic-based declarative modeling and solving framework. Solutions for ASP instances are so-called answer sets. Interestingly, the problem of deciding whether an instance has an answer set is already located on the second level of the polynomial hierarchy. An ASP solver that employs treewidth as parameter and runs dynamic programming on tree decompositions is DynASP2. Empirical experiments show that this solver is fast on instances of small treewidth and can outperform modern ASP when one counts answer sets. It remains open, whether one can improve the solver such that it also finds one answer set fast and shows competitive behavior to modern ASP solvers on instances of low treewidth. Unfortunately, theoretical models of modern ASP solvers already indicate that these solvers can solve instances of low treewidth fast, since they are based on Sat-solving algorithms. In this paper, we improve DynASP2 and construct the solver DynASP2.5, which uses a different approach. The new solver shows competitive behavior to state-of-the-art ASP solvers even for finding just one solution. We present empirical experiments where one can see that our new implementation solves ASP instances, which encode the Steiner tree problem on graphs with low treewidth, fast. Our implementation is based on a novel approach that we call multi-pass dynamic programming (M-DPSINC). In the paper, we describe the underlying concepts of our implementation (DynASP2.5) and we argue why the techniques still yield correct algorithms. Full article
(This article belongs to the Special Issue Parameterized Complexity and Algorithms for Nonclassical Logics)
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