scholarly journals On the Parameterized Complexity of Maximum Degree Contraction Problem

Algorithmica ◽  
2022 ◽  
Author(s):  
Saket Saurabh ◽  
Prafullkumar Tale
Keyword(s):  
Parameterized Complexity ◽  
Maximum Degree

scholarly journals Learning Bayesian Networks Under Sparsity Constraints: A Parameterized Complexity Analysis

2020 ◽  
Author(s):  
Niels Grüttemeier ◽  
Christian Komusiewicz
Keyword(s):  
Parameterized Complexity ◽  
Maximum Degree ◽  
Complexity Analysis ◽  
Structural Constraints ◽  
Sparse Graph ◽  
Fixed Parameter Tractable ◽  
Optimal Network ◽  
Fixed Parameter ◽  
Graph Class ◽  
Sparsity Constraints

We study the problem of learning the structure of an optimal Bayesian network when additional structural constraints are posed on the network or on its moralized graph. More precisely, we consider the constraint that the moralized graph can be transformed to a graph from a sparse graph class Π by at most k vertex deletions. We show that for Π being the graphs with maximum degree 1, an optimal network can be computed in polynomial time when k is constant, extending previous work that gave an algorithm with such a running time for Π being the class of edgeless graphs [Korhonen & Parviainen, NIPS 2015]. We then show that further extensions or improvements are presumably impossible. For example, we show that when Π is the set of graphs in which each component has size at most three, then learning an optimal network is NP-hard even if k=0. Finally, we show that learning an optimal network with at most k edges in the moralized graph presumably is not fixed-parameter tractable with respect to k and that, in contrast, computing an optimal network with at most k arcs can be computed is fixed-parameter tractable in k.

Non-standard methods for converting numbers from one number system to another

2020 ◽  
Vol 1 (9) ◽  
pp. 28-30
Author(s):  
D. M. Zlatopolski
Keyword(s):  
Binary System ◽  
Maximum Degree ◽  
Number System ◽  
Binary Form ◽  
Binary Number ◽  
Standard Methods ◽  
Optimal Variant ◽  
Decimal System ◽  
Large Numbers ◽  
Independent Work

The article describes a number of little-known methods for translating natural numbers from one number system to another. The first is a method for converting large numbers from the decimal system to the binary system, based on multiple divisions of a given number and all intermediate quotients by 64 (or another number equal to 2n ), followed by writing the last quotient and the resulting remainders in binary form. Then two methods of mutual translation of decimal and binary numbers are described, based on the so-called «Horner scheme». An optimal variant of converting numbers into the binary number system by the method of division by 2 is also given. In conclusion, a fragment of a manuscript from the beginning of the late 16th — early 17th centuries is published with translation into the binary system by the method of highlighting the maximum degree of number 2. Assignments for independent work of students are offered.

The Image of the Accountant in a German Context

2004 ◽  
Vol 4 (1) ◽  
pp. 62-89 ◽  
Author(s):  
Andreas Hoffjan
Keyword(s):  
Content Analysis ◽  
Empirical Study ◽  
Cost Reduction ◽  
Maximum Degree ◽  
Work Ethic ◽  
Personal Characteristics ◽  
Management Accountant ◽  
The Subject ◽  
Professional Context

This study introduces content analysis as a method of examining the accountant's role. The empirical study is based on 73 advertisements, which are directed primarily at employees who are affected by the management accountant's work. The findings of the study indicate that the subject of accountancy is used particularly in connection with promises of “cost reduction.” Consequently, the majority of advertisements use the accountant stereotype of “savings personified.” In a professional context, the work ethic of the management accountant is given particular emphasis in the advertisements. He/she identifies him/herself with his/her task to the maximum degree, is regarded as loyal to his/her company and, for the most part, is well organized in his/her work. However, the characterization of the management accountant as a well disciplined company-person conflicts with the negative portrayal of his/her professional qualities. In advertisements, the management accountant is portrayed as a rather inflexible, passive, and uncreative specialist who, as a result of these qualities, often demotivates others. The personal characteristics of the management accountant are shown in a negative light. This gives him/her the unappealing image of a humorless, envious, dissociated, and ascetic corporate-person.

scholarly journals Clustered 3-colouring graphs of bounded degree

2021 ◽  
pp. 1-13
Author(s):  
Vida Dujmović ◽  
Louis Esperet ◽  
Pat Morin ◽  
Bartosz Walczak ◽  
David R. Wood
Keyword(s):  
Planar Graphs ◽  
Maximum Degree ◽  
Bounded Degree ◽  
Bounded Number ◽  
Proper Vertex ◽  
Vertex Colouring

Abstract A (not necessarily proper) vertex colouring of a graph has clustering c if every monochromatic component has at most c vertices. We prove that planar graphs with maximum degree $\Delta$ are 3-colourable with clustering $O(\Delta^2)$ . The previous best bound was $O(\Delta^{37})$ . This result for planar graphs generalises to graphs that can be drawn on a surface of bounded Euler genus with a bounded number of crossings per edge. We then prove that graphs with maximum degree $\Delta$ that exclude a fixed minor are 3-colourable with clustering $O(\Delta^5)$ . The best previous bound for this result was exponential in $\Delta$ .

On the Parameterized Complexity of Finding Small Unsatisfiable Subsets of CNF Formulas and CSP Instances

2017 ◽  
Vol 18 (3) ◽  
pp. 1-46
Author(s):  
Ronald De Haan ◽  
Iyad Kanj ◽  
Stefan Szeider
Keyword(s):  
Parameterized Complexity ◽  
Cnf Formulas

Parameterized complexity of fair feedback vertex set problem

2021 ◽  
Vol 867 ◽  
pp. 1-12
Author(s):  
Lawqueen Kanesh ◽  
Soumen Maity ◽  
Komal Muluk ◽  
Saket Saurabh
Keyword(s):  
Parameterized Complexity ◽  
Feedback Vertex Set ◽  
Vertex Set ◽  
Feedback Vertex Set Problem

A compendium of parameterized complexity results

1994 ◽  
Vol 25 (3) ◽  
pp. 122-123 ◽  
Author(s):  
Michael T. Hallett ◽  
H. Todd Wareham
Keyword(s):  
Parameterized Complexity ◽  
Complexity Results

scholarly journals Revisiting the parameterized complexity of Maximum-Duo Preservation String Mapping

2020 ◽  
Vol 847 ◽  
pp. 27-38
Author(s):  
Christian Komusiewicz ◽  
Mateus de Oliveira Oliveira ◽  
Meirav Zehavi
Keyword(s):  
Parameterized Complexity

The Book Review Column1

2021 ◽  
Vol 51 (4) ◽  
pp. 4-5
Author(s):  
Frederic Green
Keyword(s):  
Parameterized Complexity ◽  
Property Testing ◽  
The Third ◽  
Geometric Problems ◽  
The Subject

The three books reviewed in this column are about central ideas in algorithms, complexity, and geometry. The third one brings together topics from the first two by applying techniques of both property testing (the subject of the first book) and parameterized complexity (including its more focused incarnation studied in the second book, kernelization) to geometric problems.

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