scholarly journals The Fibonacci Dimension of a Graph

10.37236/542 ◽  
2011 ◽  
Vol 18 (1) ◽  
Author(s):  
Sergio Cabello ◽  
David Eppstein ◽  
Sandi Klavžar
Keyword(s):  
Approximation Algorithm ◽  
Isometric Embedding ◽  
Point Of View ◽  
Approximation Ratio ◽  
Combinatorial Characterization ◽  
Fibonacci Cube ◽  
Np Complete ◽  
Lattice Dimension

The Fibonacci dimension ${\rm fdim}(G)$ of a graph $G$ is introduced as the smallest integer $f$ such that $G$ admits an isometric embedding into $\Gamma_f$, the $f$-dimensional Fibonacci cube. We give bounds on the Fibonacci dimension of a graph in terms of the isometric and lattice dimension, provide a combinatorial characterization of the Fibonacci dimension using properties of an associated graph, and establish the Fibonacci dimension for certain families of graphs. From the algorithmic point of view, we prove that it is NP-complete to decide whether ${\rm fdim}(G)$ equals the isometric dimension of $G$, and show that no algorithm to approximate ${\rm fdim}(G)$ has approximation ratio below $741/740$, unless P$=$NP. We also give a $(3/2)$-approximation algorithm for ${\rm fdim}(G)$ in the general case and a $(1+\varepsilon)$-approximation algorithm for simplex graphs.

HOLES AND DOMINOES IN MEYNIEL GRAPHS

1999 ◽  
Vol 10 (02) ◽  
pp. 127-146 ◽  
Author(s):  
FLORIAN ROUSSEL ◽  
IRENA RUSU
Keyword(s):  
General Structure ◽  
Practical Interest ◽  
Characterization Theorem ◽  
Recognition Algorithm ◽  
Point Of View ◽  
Vertex Coloring ◽  
Odd Cycle ◽  
Np Complete ◽  
As Graph

Many practical problems (frequency assignement, register allocation, timetables) may be formulated as graph (vertex-)coloring problems, but finding solutions for them is difficult as long as they are treated in the most general case (where the graph is arbitrary), since vertex coloring has been proved to be NP-complete. The problem becomes much easier to solve if the graph resulting from the modelisation of the practical application belongs to some particular class of graphs, for which solutions to the problem are known. Meyniel graphs form such a class (a fast coloring algorithm can be found in [9]), for which an efficient recognizing algorithm is therefore needed. A graph G=(V,E) is said to be a Meyniel graph if every odd cycle of G on at least five vertices contains at least two chords. Meyniel graphs generalize both i-triangulated and parity graphs, two well known classes of perfect graphs that will be present in our paper in Section 7. In [2], Burlet and Fonlupt propose a characterization of Meyniel graphs which relies on the following property: the class of Meyniel graphs may be obtained from some basic Meyniel graphs using a binary operation called amalgam. Besides the theoretical interest of this result, a practical interest arises because of the polynomial recognition algorithm which can be obtained. Unfortunately, it is quite expensive to verify if a given graph is the amalgam of two graphs (therefore the complexity of the whole algorithm is in O(n7)), and this supports the idea that a new point of view is needed to find a more efficient algorithm. Our approach of Meyniel graphs will be directed through the search of a general structure. Intuitively, a Meyniel graph either will be simple (i.e. with no hole or domino), or will have a skeleton around which the rest of the graph will be regularly organized. As suggested, the first type of Meyniel graphs is simple to identify. For the second type, a deeper analysis is necessary; it yields a characterization theorem, which is used to deduce the O(m2+mn) recognition algorithm.

scholarly journals Matchings under distance constraints I.

2021 ◽  
Author(s):  
Péter Madarasi
Keyword(s):  
Approximation Algorithm ◽  
Programming Model ◽  
Search Algorithm ◽  
Point Of View ◽  
Approximation Ratio ◽  
The Novel ◽  
Scheduling Problems ◽  
Matching Problem ◽  
Integrality Gap ◽  
Fpt Algorithm

AbstractThis paper introduces the d-distance matching problem, in which we are given a bipartite graph $$G=(S,T;E)$$ G = ( S , T ; E ) with $$S=\{s_1,\dots ,s_n\}$$ S = { s 1 , ⋯ , s n } , a weight function on the edges and an integer $$d\in \mathbb Z_+$$ d ∈ Z + . The goal is to find a maximum-weight subset $$M\subseteq E$$ M ⊆ E of the edges satisfying the following two conditions: (i) the degree of every node of S is at most one in M, (ii) if $$s_it,s_jt\in M$$ s i t , s j t ∈ M , then $$|j-i|\ge d$$ | j - i | ≥ d . This question arises naturally, for example, in various scheduling problems. We show that the problem is NP-complete in general and admits a simple 3-approximation. We give an FPT algorithm parameterized by d and also show that the case when the size of T is constant can be solved in polynomial time. From an approximability point of view, we show that the integrality gap of the natural integer programming model is at most $$2-\frac{1}{2d-1}$$ 2 - 1 2 d - 1 , and give an LP-based approximation algorithm for the weighted case with the same guarantee. A combinatorial $$(2-\frac{1}{d})$$ ( 2 - 1 d ) -approximation algorithm is also presented. Several greedy approaches are considered, and a local search algorithm is described that achieves an approximation ratio of $$3/2+\epsilon $$ 3 / 2 + ϵ for any constant $$\epsilon >0$$ ϵ > 0 in the unweighted case. The novel approaches used in the analysis of the integrality gap and the approximation ratio of locally optimal solutions might be of independent combinatorial interest.

The Analyses of Learning Strategies in English as a Second Language: Theoretical Classification and Measurement Test

2020 ◽  
Vol 4 (2) ◽  
pp. 118-129
Author(s):  
Asti Gumartifa ◽  
◽  
Indah Windra Dwie Agustiani
Keyword(s):  
Language Learning ◽  
Learning Outcomes ◽  
Learning Strategies ◽  
Learning Process ◽  
English Learners ◽  
English Language ◽  
Point Of View ◽  
Effective Learning ◽  
The Impact

Gaining English language learning effectively has been discussed all years long. Similarly, Learners have various troubles outcomes in the learning process. Creating a joyful and comfortable situation must be considered by learners. Thus, the implementation of effective learning strategies is certainly necessary for English learners. This descriptive study has two purposes: first, to introduce the classification and characterization of learning strategies such as; memory, cognitive, metacognitive, compensation, social, and affective strategies that are used by learners in the classroom and second, it provides some questionnaires item based on Strategy of Inventory for Language Learning (SILL) version 5.0 that can be used to examine the frequency of students’ learning strategies in the learning process. The summary of this study explains and discusses the researchers’ point of view on the impact of learning outcomes by learning strategies used. Finally, utilizing appropriate learning strategies are certainly beneficial for both teachers and learners to achieve the learning target effectively.

The Algorithm of Characterization of an Action as a Jointly Committed Crime

2018 ◽  
pp. 37-44
Keyword(s):  
Criminal Code ◽  
Point Of View

The article discusses a sequence of activities to identify a crime as jointly committed. The requirements to the algorithm of such activities are formulated. Programme-based and targeted methods applied by the authors allowed detecting a range of stages of the algorithm. The first four stages aim at defining mandatory elements of a crime allowing to characterize it as a jointly committed action. The rest of the stages focus on identifying a type of criminal complicity. In the article, each stage is described. It is emphasized that in each stage there is a special objective. At the same time, all these stages, taken together, constitute a separate module of the program of criminal characterization of an action. From the authors’ point of view, algorithms are necessary not only for detection of crimes and their criminal characterization, but also for answering the question on existence of criminal complicity in each case. Also the authors give their opinions on interpretation of criminal complicity as a legal category. In particular, it is emphasized that not all of crimes merely committed with participation of two or more persons should be understood as jointly committed. It is joint participation that makes a crime jointly committed. Various forms of criminal complicity and types of co-offenders are considered in the article as well. In various crimes, criminal complicity manifests itself differently. Therefore the proposed algorithm can be applied only after identification a specific article of the Russian Criminal Code stipulating the responsibility for the crime committed.

scholarly journals An Intrinsic Characterization of Five Points in a CAT(0) Space

2020 ◽  
Vol 8 (1) ◽  
pp. 114-165
Author(s):  
Tetsu Toyoda
Keyword(s):  
Metric Space ◽  
Isometric Embedding ◽  
Metric Spaces ◽  
Necessary Conditions ◽  
New Approach ◽  
Intrinsic Characterization ◽  
New Family

AbstractGromov (2001) and Sturm (2003) proved that any four points in a CAT(0) space satisfy a certain family of inequalities. We call those inequalities the ⊠-inequalities, following the notation used by Gromov. In this paper, we prove that a metric space X containing at most five points admits an isometric embedding into a CAT(0) space if and only if any four points in X satisfy the ⊠-inequalities. To prove this, we introduce a new family of necessary conditions for a metric space to admit an isometric embedding into a CAT(0) space by modifying and generalizing Gromov’s cycle conditions. Furthermore, we prove that if a metric space satisfies all those necessary conditions, then it admits an isometric embedding into a CAT(0) space. This work presents a new approach to characterizing those metric spaces that admit an isometric embedding into a CAT(0) space.

scholarly journals Processing Effect and Characterization of Olive Oils from Spanish Wild Olive Trees (Olea europaea var. sylvestris)

Molecules ◽  
2021 ◽  
Vol 26 (5) ◽  
pp. 1304
Author(s):  
Francisco Espínola ◽  
Alfonso M. Vidal ◽  
Juan M. Espínola ◽  
Manuel Moya
Keyword(s):  
Phenolic Compounds ◽  
Volatile Compounds ◽  
Olive Tree ◽  
Extraction Yield ◽  
Point Of View ◽  
Human Consumption ◽  
Analytical Point ◽  
Wild Olive ◽  
Olive Trees

Wild olive trees have important potential, but, to date, the oil from wild olives has not been studied significantly, especially from an analytical point of view. In Spain, the wild olive tree is called “Acebuche” and its fruit “Acebuchina”. The objective of this work is to optimize the olive oil production process from the Acebuchina cultivar and characterize the oil, which could be marketed as healthy and functional food. A Box–Behnken experimental design with five central points was used, along with the Response Surface Methodology to obtain a mathematical experimental model. The oils from the Acebuchina cultivar meet the requirements for human consumption and have a good balance of fatty acids. In addition, the oils are rich in antioxidants and volatile compounds. The highest extraction yield, 12.0 g oil/100 g paste, was obtained at 90.0 min and the highest yield of phenolic compounds, 870.0 mg/kg, was achieved at 40.0 °C, and 90.0 min; but the maximum content of volatile compounds, 26.9 mg/kg, was obtained at 20 °C and 30.0 min. The oil yield is lower than that of commercial cultivars, but the contents of volatile and phenolic compounds is higher.

scholarly journals Grounding semantic transparency in context

Morphology ◽  
2021 ◽  
Author(s):  
Rossella Varvara ◽  
Gabriella Lapesa ◽  
Sebastian Padó
Keyword(s):  
Large Scale ◽  
Point Of View ◽  
Distributional Semantics ◽  
Semantic Transparency ◽  
Inclusion Measure ◽  
The Difference ◽  
Semantic Point ◽  
The Many ◽  
The Relationship

AbstractWe present the results of a large-scale corpus-based comparison of two German event nominalization patterns: deverbal nouns in -ung (e.g., die Evaluierung, ‘the evaluation’) and nominal infinitives (e.g., das Evaluieren, ‘the evaluating’). Among the many available event nominalization patterns for German, we selected these two because they are both highly productive and challenging from the semantic point of view. Both patterns are known to keep a tight relation with the event denoted by the base verb, but with different nuances. Our study targets a better understanding of the differences in their semantic import.The key notion of our comparison is that of semantic transparency, and we propose a usage-based characterization of the relationship between derived nominals and their bases. Using methods from distributional semantics, we bring to bear two concrete measures of transparency which highlight different nuances: the first one, cosine, detects nominalizations which are semantically similar to their bases; the second one, distributional inclusion, detects nominalizations which are used in a subset of the contexts of the base verb. We find that only the inclusion measure helps in characterizing the difference between the two types of nominalizations, in relation with the traditionally considered variable of relative frequency (Hay, 2001). Finally, the distributional analysis allows us to frame our comparison in the broader coordinates of the inflection vs. derivation cline.

scholarly journals Encephalocele: know it to deal with it

2021 ◽  
Vol 52 (1) ◽  
Author(s):  
Nilkanth Laxman Pal ◽  
Ambika Sumeet Juwarkar ◽  
Sanjaya Viswamitra
Keyword(s):  
Prognostic Factors ◽  
Imaging Modality ◽  
Point Of View ◽  
Extensive Literature ◽  
Resonance Imaging ◽  
Imaging Protocol ◽  
Imaging Protocols ◽  
Associated Malformations ◽  
Associated Abnormalities

Abstract Background Encephaloceles refer to the herniation of intracranial contents through the defect in the dura and calvarium. This article aims to equip the radiologists with all the necessary information to approach a case of encephalocele in a systematic manner and report in an organized format. Thus reduce the reporting time without overlooking any detail. Main text An extensive literature review was performed searching through the standard textbooks and electronic databases to obtain thorough information on the various encephaloceles particularly from a radiological point of view. The author’s observations were also incorporated in the review. Among the available imaging modalities, magnetic resonance imaging is the most versatile and considered the imaging modality of choice because of superior anatomic resolution in the characterization of central nervous system malformation. This study provides the reporting radiologist with a methodical guide to approach a case of encephalocele discussing the imaging protocol, relevant anatomy, classification, associated abnormalities, and imaging prognostic factors. Conclusion Encephalocele has always been a subject of predicament for radiologists. Understanding the relevant terminologies, anatomy, imaging protocols, classification, associated malformations/anomalies, and imaging prognostic factors will help to methodically approach each case and provide a systematic and comprehensive report.

scholarly journals Crystallographic and structural characterization of heterometallic platinum compounds Part VII. Heterohepta- and heterooctanuclear clusters

2014 ◽  
Vol 13 (1) ◽  
Author(s):  
Milan Melnik ◽  
Peter Mikuš ◽  
Clive E. Holloway
Keyword(s):  
Structural Characterization ◽  
Structural Parameters ◽  
Bond Distance ◽  
Point Of View ◽  
Platinum Compounds ◽  
Metal Atoms ◽  
Platinum Clusters ◽  
Structural Point

AbstractThis review classifies and analyzes over fifty heterohepta- and heterooctanuclear platinum clusters. There are eight types of metal combinations in heteroheptanuclear: Pt6M, Pt5M2, Pt4M3, Pt3M4, Pt2M5, PtM6, Pt3Hg2Ru2 and Pt2Os3Fe2. The seven metal atoms are in a wide variety of arrangements, with the most common being one in which the central M atom (mostly M(I)) is sandwiched by two M3 triangles. Another arrangement often found is an octahedron of M6 atoms asymmetrically capped by an M atom. The shortest Pt-M bond distances (non-transition and transition) are 2.326(1) Å (M = Ga) and 2.537(6) Å (M = Fe). The shortest Pt-Pt bond distance is 2.576(2) Å.In heterooctanuclear platinum clusters there are eight types of metal combinations: Pt6M2, Pt4M4, Pt3Ru5, Pt2M6, PtM7, Pt2W4Ni2, PtAu6Hg and PtAu5Hg2. From a structural point of view, the clusters are complex with bicapped octahedrons of eight metal atoms prevailing. The shortest Pt-M bond distances (non-transition and transition) are 2.651(3) Å (M = Hg) and 2.624(1) Å (M = Os). The shortest Pt-Pt bond distance is 2.622(1) Å. These values are somewhat longer than those in the heteroheptanuclear clusters. Several relationships between the structural parameters were found, and are discussed and compared with the smaller heterometallic platinum clusters

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