scholarly journals How to Approximate Ontology-Mediated Queries

2021 ◽  
Author(s):  
Anneke Haga ◽  
Carsten Lutz ◽  
Leif Sabellek ◽  
Frank Wolter
Keyword(s):  
Computational Complexity ◽  
Linear Time ◽  
Description Logics ◽  
Data Complexity ◽  
Fixed Parameter Tractable ◽  
Ontology Language ◽  
Fixed Parameter ◽  
Almost All

We introduce and study several notions of approximation for ontology-mediated queries based on the description logics ALC and ALCI. Our approximations are of two kinds: we may (1) replace the ontology with one formulated in a tractable ontology language such as ELI or certain TGDs and (2) replace the database with one from a tractable class such as the class of databases whose treewidth is bounded by a constant. We determine the computational complexity and the relative completeness of the resulting approximations. (Almost) all of them reduce the data complexity from coNP-complete to PTime, in some cases even to fixed-parameter tractable and to linear time. While approximations of kind (1) also reduce the combined complexity, this tends to not be the case for approximations of kind (2). In some cases, the combined complexity even increases.

scholarly journals Low complexity algorithms in knot theory

2019 ◽  
Vol 29 (02) ◽  
pp. 245-262
Author(s):  
Olga Kharlampovich ◽  
Alina Vdovina
Keyword(s):  
Computational Complexity ◽  
Time Complexity ◽  
Linear Time ◽  
Circuit Complexity ◽  
Equivalence Problem ◽  
Low Complexity ◽  
Combinatorial Structure ◽  
Complexity Classes ◽  
Np Complete ◽  
Almost All

Agol, Haas and Thurston showed that the problem of determining a bound on the genus of a knot in a 3-manifold, is NP-complete. This shows that (unless P[Formula: see text]NP) the genus problem has high computational complexity even for knots in a 3-manifold. We initiate the study of classes of knots where the genus problem and even the equivalence problem have very low computational complexity. We show that the genus problem for alternating knots with n crossings has linear time complexity and is in Logspace[Formula: see text]. Alternating knots with some additional combinatorial structure will be referred to as standard. As expected, almost all alternating knots of a given genus are standard. We show that the genus problem for these knots belongs to [Formula: see text] circuit complexity class. We also show, that the equivalence problem for such knots with [Formula: see text] crossings has time complexity [Formula: see text] and is in Logspace[Formula: see text] and [Formula: see text] complexity classes.

scholarly journals Ontology-Mediated Querying with Horn Description Logics

2020 ◽  
Vol 34 (4) ◽  
pp. 533-537 ◽  
Author(s):  
Leif Sabellek
Keyword(s):  
Computational Complexity ◽  
Description Logics ◽  
Data Access ◽  
Logical Reasoning ◽  
Data Complexity ◽  
Conjunctive Query ◽  
Database Query ◽  
Query By Example ◽  
Open Questions ◽  
Verification Problem

AbstractAn ontology-mediated query (OMQ) consists of a database query paired with an ontology. When evaluated on a database, an OMQ returns not only the answers that are already in the database, but also those answers that can be obtained via logical reasoning using rules from ontology. There are many open questions regarding the complexities of problems related to OMQs. Motivated by the use of ontologies in practice, new reasoning problems which have never been considered in the context of ontologies become relevant, since they can improve the usability of ontology enriched systems. This thesis deals with various reasoning problems that emerge from ontology-mediated querying and it investigates the computational complexity of these problems. We focus on ontologies formulated in Horn description logics, which are a popular choice for ontologies in practice. In particular, the thesis gives results regarding the data complexity of OMQ evaluation by completely classifying complexity and rewritability questions for OMQs based on an EL ontology and a conjunctive query. Furthermore, the query-by-example problem, and the expressibility and verification problem in ontology-based data access are introduced and investigated.

scholarly journals A Multivariate Complexity Analysis of Lobbying in Multiple Referenda

2014 ◽  
Vol 50 ◽  
pp. 409-446 ◽  
Author(s):  
R. Bredereck ◽  
J. Chen ◽  
S. Hartung ◽  
S. Kratsch ◽  
R. Niedermeier ◽  
...  
Keyword(s):  
Computational Complexity ◽  
Complexity Analysis ◽  
Central Question ◽  
Logarithmic Factor ◽  
Fixed Parameter Tractable ◽  
Complete Problem ◽  
Fixed Parameter ◽  
Matrix Modification ◽  
Simple Matrix ◽  
Limited Nondeterminism

Assume that each of n voters may or may not approve each of m issues. If an agent (the lobby) may influence up to k voters, then the central question of the NP-hard Lobbying problem is whether the lobby can choose the voters to be influenced so that as a result each issue gets a majority of approvals. This problem can be modeled as a simple matrix modification problem: Can one replace k rows of a binary n x m-matrix by k all-1 rows such that each column in the resulting matrix has a majority of 1s? Significantly extending on previous work that showed parameterized intractability (W[2]-completeness) with respect to the number k of modified rows, we study how natural parameters such as n, m, k, or the "maximum number of 1s missing for any column to have a majority of 1s" (referred to as "gap value g") govern the computational complexity of Lobbying. Among other results, we prove that Lobbying is fixed-parameter tractable for parameter m and provide a greedy logarithmic-factor approximation algorithm which solves Lobbying even optimally if m < 5. We also show empirically that this greedy algorithm performs well on general instances. As a further key result, we prove that Lobbying is LOGSNP-complete for constant values g>0, thus providing a first natural complete problem from voting for this complexity class of limited nondeterminism.

scholarly journals Dividing Splittable Goods Evenly and With Limited Fragmentation

Algorithmica ◽  
2019 ◽  
Vol 82 (5) ◽  
pp. 1298-1328
Author(s):  
Peter Damaschke
Keyword(s):  
Related Problem ◽  
Linear Time ◽  
Np Hard ◽  
Weighted Graphs ◽  
Fixed Parameter Tractable ◽  
Averaging Problem ◽  
Fixed Parameter ◽  
Splitting Problem ◽  
Structural Characterizations ◽  
Balanced Solutions

Abstract A splittable good provided in n pieces shall be divided as evenly as possible among m agents, where every agent can take shares from at most F pieces. We call F the fragmentation and mainly restrict attention to the cases $$F=1$$F=1 and $$F=2$$F=2. For $$F=1$$F=1, the max–min and min–max problems are solvable in linear time. The case $$F=2$$F=2 has neat formulations and structural characterizations in terms of weighted graphs. First we focus on perfectly balanced solutions. While the problem is strongly NP-hard in general, it can be solved in linear time if $$m\ge n-1$$m≥n-1, and a solution always exists in this case, in contrast to $$F=1$$F=1. Moreover, the problem is fixed-parameter tractable in the parameter $$2m-n$$2m-n. (Note that this parameter measures the number of agents above the trivial threshold $$m=n/2$$m=n/2.) The structural results suggest another related problem where unsplittable items shall be assigned to subsets so as to balance the average sizes (rather than the total sizes) in these subsets. We give an approximation-preserving reduction from our original splitting problem with fragmentation $$F=2$$F=2 to this averaging problem, and some approximation results in cases when m is close to either n or n / 2.

scholarly journals Soft Constraints of Difference and Equality

2011 ◽  
Vol 41 ◽  
pp. 97-130 ◽  
Author(s):  
E. Hebrard ◽  
D. Marx ◽  
B. O'Sullivan ◽  
I. Razgon
Keyword(s):  
Linear Time ◽  
Combinatorial Problems ◽  
Global Constraints ◽  
Fixed Parameter Tractable ◽  
Common Value ◽  
Arc Consistency ◽  
Standard Cost ◽  
Fixed Parameter ◽  
Difference And Equality ◽  
Np Hardness

In many combinatorial problems one may need to model the diversity or similarity of assignments in a solution. For example, one may wish to maximise or minimise the number of distinct values in a solution. To formulate problems of this type, we can use soft variants of the well known AllDifferent and AllEqual constraints. We present a taxonomy of six soft global constraints, generated by combining the two latter ones and the two standard cost functions, which are either maximised or minimised. We characterise the complexity of achieving arc and bounds consistency on these constraints, resolving those cases for which NP-hardness was neither proven nor disproven. In particular, we explore in depth the constraint ensuring that at least k pairs of variables have a common value. We show that achieving arc consistency is NP-hard, however achieving bounds consistency can be done in polynomial time through dynamic programming. Moreover, we show that the maximum number of pairs of equal variables can be approximated by a factor 1/2 with a linear time greedy algorithm. Finally, we provide a fixed parameter tractable algorithm with respect to the number of values appearing in more than two distinct domains. Interestingly, this taxonomy shows that enforcing equality is harder than enforcing difference.

scholarly journals Towards fixed-parameter tractable algorithms for abstract argumentation

2012 ◽  
Vol 186 ◽  
pp. 1-37 ◽  
Author(s):  
Wolfgang Dvořák ◽  
Reinhard Pichler ◽  
Stefan Woltran
Keyword(s):  
Fixed Parameter Tractable ◽  
Abstract Argumentation ◽  
Fixed Parameter

scholarly journals Interval Completion Is Fixed Parameter Tractable

2009 ◽  
Vol 38 (5) ◽  
pp. 2007-2020 ◽  
Author(s):  
Yngve Villanger ◽  
Pinar Heggernes ◽  
Christophe Paul ◽  
Jan Arne Telle
Keyword(s):  
Fixed Parameter Tractable ◽  
Fixed Parameter
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