1,721,032 research outputs found
Cubicity, Degeneracy, and Crossing Number
Get PDFA k-box B=(R_1,R_2,...,R_k), where each R_i is a closed interval on the real line, is defined to be the Cartesian product R_1 X R_2 X ... X R_k. If each R_i is a unit length interval, we call B a k-cube. Boxicity of a graph G, denoted as box(G), is the minimum integer k such that G is an intersection graph of k-boxes. Similarly, the cubicity of G, denoted as cub(G), is the minimum integer k such that G is an intersection graph of k-cubes.
It was shown in [L. Sunil Chandran, Mathew C. Francis, and Naveen Sivadasan. Representing graphs as the intersection of axis-parallel cubes. MCDES-2008, IISc Centenary Conference, available at CoRR, abs/cs/0607092, 2006.] that, for a graph G with maximum degree \Delta, cub(G) <= \lceil 4(\Delta +1) ln n\rceil. In this paper we show that, for a k-degenerate graph G, cub(G) <= (k+2) \lceil 2e log n \rceil. Since k is at most \Delta and can be much lower, this clearly is a stronger result. We also give an efficient deterministic algorithm that runs in O(n^2k) time to output a 8k(\lceil 2.42 log n\rceil + 1) dimensional cube representation for G.
The crossing number of a graph G, denoted as CR(G), is the minimum number of crossing pairs of edges, over all drawings of G in the plane. An important consequence of the above result is that if the crossing number of a graph G is t, then box(G) is O(t^{1/4}{\lceil log t\rceil}^{3/4}) . This bound is tight upto a factor of O((log t)^{3/4}).
Let (P,\leq) be a partially ordered set and let G_{P} denote its underlying comparability graph. Let dim(P) denote the poset dimension of P. Another interesting consequence of our result is to show that dim(P) \leq 2(k+2) \lceil 2e \log n \rceil, where k denotes the degeneracy of G_{P}. Also, we get a deterministic algorithm that runs in O(n^2k) time to construct a 16k(\lceil 2.42 log n\rceil + 1) sized realizer for P. As far as we know, though very good upper bounds exist for poset dimension in terms of maximum degree of its underlying comparability graph, no upper bounds in terms of the degeneracy of the underlying comparability graph is seen in the literature
Algorithmic and Combinatorial Questions on Some Geometric Problems on Graphs
Get PDFThis thesis mainly focuses on algorithmic and combinatorial questions related to some geometric problems on graphs. In the last part of this thesis, a graph coloring problem is also discussed.
Boxicity and Cubicity: These are graph parameters dealing with geomet-ric representations of graphs in higher dimensions. Both these parameters are known to be NP-Hard to compute in general and are even hard to approximate within an O(n1− ) factor for any > 0, under standard complexity theoretic assumptions.
We studied algorithmic questions for these problems, for certain graph classes, to yield efficient algorithms or approximations. Our results include a polynomial time constant factor approximation algorithm for computing the cubicity of trees and a polynomial time constant (≤ 2.5) factor approximation algorithm for computing the boxicity of circular arc graphs. As far as we know, there were no constant factor approximation algorithms known previously, for computing boxicity or cubicity of any well known graph class for which the respective parameter value is unbounded.
We also obtained parameterized approximation algorithms for boxicity with various edit distance parameters. An o(n) factor approximation algorithm for computing the boxicity and cubicity of general graphs also evolved as an interesting corollary of one of these parameterized algorithms. This seems to be the first sub-linear factor approximation algorithm known for computing the boxicity and cubicity of general graphs.
Planar grid-drawings of outerplanar graphs: A graph is outerplanar, if it has a planar embedding with all its vertices lying on the outer face. We give an efficient algorithm to 2-vertex-connect any connected outerplanar graph G by adding more edges to it, in order to obtain a supergraph of G such that the resultant graph is still outerplanar and its pathwidth is within a constant times the pathwidth of G. This algorithm leads to a constant factor approximation algorithm for computing minimum height planar straight line grid-drawings of outerplanar graphs, extending the existing algorithm known for 2-vertex connected outerplanar graphs.
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Maximum matchings in triangle distance Delaunay graphs: Delau-nay graphs of point sets are well studied in Computational Geometry. Instead of the Euclidean metric, if the Delaunay graph is defined with respect to the convex distance function defined by an equilateral triangle, it is called a Trian-gle Distance Delaunay graph. TD-Delaunay graphs are known to be equivalent to geometric spanners called half-Θ6 graphs.
It is known that classical Delaunay graphs of point sets always contain a near perfect matching, for non-degenerate point sets. We show that Triangle Distance Delaunay graphs of a set of n points in general position will always l m contain a matching of size and this bound is tight. We also show that Θ6 graphs, a class of supergraphs of half-Θ6 graphs, can have at most 5n − 11 edges, for point sets in general position.
Heterochromatic Paths in Edge Colored Graphs: Conditions on the coloring to guarantee the existence of long heterochromatic paths in edge col-ored graphs is a well explored problem in literature. The objective here is to obtain a good lower bound for λ(G) - the length of a maximum heterochro-matic path in an edge-colored graph G, in terms of ϑ(G) - the minimum color degree of G under the given coloring. There are graph families for which λ(G) = ϑ(G) − 1 under certain colorings, and it is conjectured that ϑ(G) − 1 is a tight lower bound for λ(G).
We show that if G has girth is at least 4 log2(ϑ(G))+2, then λ(G) ≥ ϑ(G)− 2. It is also proved that a weaker requirement that G just does not contain four-cycles is enough to guarantee that λ(G) is at least ϑ(G) −o(ϑ(G)). Other special cases considered include lower bounds for λ(G) in edge colored bipartite graphs, triangle-free graphs and graphs without heterochromatic triangles
Going Beyond Counting First Authors in Author Co-citation Analysis
Get PDFThe present study examines one of the fundamental aspects of author co-citation analysis (ACA) - the way co-citation
counts are defined. Co-citation counting provides the data on which all subsequent statistical analyses and mappings
are based, and we compare ACA results based on two different types of co-citation counting - the traditional type that
only counts the first one among a cited work's authors on the one hand and a non-traditional type that takes into
account the first 5 authors of a cited work on the other hand. Results indicate that the picture produced through this non-traditional author co-citation counting contains more coherent author groups and is therefore considerably clearer. However, this picture represents fewer specialties in the research field being studied than that produced through the traditional first-author co-citation counting when the same number of top-ranked authors is selected and analyzed. Reasons for these effects are discussed
Variations on the Author
Get PDF“Variations on the Author” discusses two of Eduardo Coutinho’s recent films (Um Dia na Vida, from 2010, and Últimas Conversas, posthumously released in 2015) and their contribution to the general question of documentary authorship. The director’s filmography is characterized by a consistent yet self-effacing form of authorial self-inscription: Coutinho often features as an interviewer that rather than express opinions propels discourses; an interviewer that is good at listening. This mode of self-inscription characterizes him as an author who is not expressive but who is nonetheless markedly present on the screen. In Um Dia na Vida, however, Coutinho is completely absent form the image, while Últimas Conversas, on the contrary, includes a confessional prologue that moves the director from the margins to the center of his films. This article examines the ways in which these works stand out in the filmography of a director who offers new insights into the notion of cinematic authorship
Appropriate Similarity Measures for Author Cocitation Analysis
Get PDFWe provide a number of new insights into the methodological discussion about author cocitation analysis. We first argue that the use of the Pearson correlation for measuring the similarity between authors’ cocitation profiles is not very satisfactory. We then discuss what kind of similarity measures may be used as an alternative to the Pearson correlation. We consider three similarity measures in particular. One is the well-known cosine. The other two similarity measures have not been used before in the bibliometric literature. Finally, we show by means of an example that our findings have a high practical relevance.information science;Pearson correlation;cosine;similarity measure;author cocitation analysis
The stable set problem and the thinness of a graph
No full textWe introduce a poly-time algorithm for the maximum weighted stable set problem, when a certain representation is given for a graph. The algorithm generalizes the algorithm for interval graphs and that for graphs with bounded pathwidth. By a suitable application to the frequency assignment problem, we improved several solutions to relevant benchmark instances. (c) 2006 Elsevier B.V. All rights reserved
Dispelling the Myths Behind First-author Citation Counts
Get PDFWe conducted a full-scale evaluative citation analysis study of scholars in the XML research field to explore just how different from each other author rankings resulting from different citation counting methods actually are, and to demonstrate the capability of emerging data and tools on the Web in supporting more realistic citation counting methods. Our results contest some common arguments for the continued
use of first-author citation counts in the evaluation of scholars, such as high correlations between author rankings by first-author citation counts and other citation
counting methods, and high costs of using more realistic citation counting methods that are not well-supported by the ISI databases. It is argued that increasingly available digital full text research papers make it possible for citation analysis studies to go beyond what the ISI databases have directly supported and to employ more
sophisticated methods
koamabayili/VECTRON-author-checklist: VECTRON author checklist
No full textWe have done our best to complete the author checklist relating to the use of animals in the hut study. Note that the objective for the hut study was to evaluate the IRS treatment applications for residual efficacy against Anopheles mosquitoes, including the local An. coluzzii mosquito population. Cows were only used to attract mosquitoes into the huts and no tests were carried out directly on the cows. The author checklist is intended for use with studies where experiments are carried out on animals, which is why we have had such difficulty in completing this for the hut study, as many of the questions do not relate to how the cows were used
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