Weconsider the largest number of minimal separators a graph on n vertices can have. - We give a new proof that this number is in O((1+root 5/2)(n).n). We prove that this number is in omega(1.4457(n)), improving on the...
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Weconsider the largest number of minimal separators a graph on n vertices can have. - We give a new proof that this number is in O((1+root 5/2)(n).n). We prove that this number is in omega(1.4457(n)), improving on the previous best lower bound of Omega(3(n/3)) subset of omega(1.4422(n)). This gives also an improved lower bound on the number of potential maximal cliques in a graph. We would like to emphasize that our proofs are short, simple, and elementary.
A class of counting problems asks for the number of regions of a central hyperplane arrangement. By duality, this is the same as counting the vertices of a zonotope. Efficient algorithms are known that solve this prob...
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A class of counting problems asks for the number of regions of a central hyperplane arrangement. By duality, this is the same as counting the vertices of a zonotope. Efficient algorithms are known that solve this problem by computing the vertices of a zonotope from its set of generators. Here, we give an efficient algorithm, based on a linear optimization oracle, that performs the inverse task and recovers the generators of a zonotope from its set of vertices. We also provide a variation of that algorithm that allows to decide whether a polytope, given as its vertex set, is a zonotope and when it is not a zonotope, to compute its greatest zonotopal summand. (C) 2021 Elsevier B.V. All rights reserved.
Herein, we discuss the existence of overlapping edge unfoldings for convex regular-faced polyhedra. Horiyama and Shoji showed that there are no overlapping edge unfoldings for all platonic solids and five of the Archi...
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Herein, we discuss the existence of overlapping edge unfoldings for convex regular-faced polyhedra. Horiyama and Shoji showed that there are no overlapping edge unfoldings for all platonic solids and five of the Archimedean solids. The remaining five Archimedean solids were found to have edge unfoldings that overlap. In this study, we propose a method called rotational unfolding to find an overlapping edge unfolding of a polyhedron. We show that all the edge unfoldings of an icosidodecahedron, a rhombitruncated cuboctahedron, an n-gonal Archimedean prism (3 <= n <= 23), an m-gonal Archimedean antiprism (3 <= m <= 11), and 48 types of Johnson solids do not overlap. Our algorithm finds overlapping edge unfoldings for the snub cube, and 44 types of Johnson solids. We present analytic proof that an overlapping edge unfolding exists in an n-gonal Archimedean prism (n >= 24), and an m-gonal Archimedean antiprism (m >= 12). Our results prove the existence of overlapping edge unfoldings for convex regular-faced polyhedra.
Consider a set P of n points in the plane, where each point is associated with one of three colours. We give an output-sensitive algorithm that enumerates a set of triangles T, where each triangle in T contains the or...
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Consider a set P of n points in the plane, where each point is associated with one of three colours. We give an output-sensitive algorithm that enumerates a set of triangles T, where each triangle in T contains the origin and its three vertices are points in P with distinct colours. Our algorithm requires O( n + vertical bar T vertical bar) time, and hence it is asymptotically optimal in terms of n and vertical bar T vertical bar. (C) 2012 Elsevier B.V. All rights reserved.
Cytoplasmic incompatibility (CI) relates to the manipulation by the parasiteWolbachiaof its host reproduction. Despite its widespread occurrence, the molecular basis of CI remains unclear and theoretical models have b...
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Cytoplasmic incompatibility (CI) relates to the manipulation by the parasiteWolbachiaof its host reproduction. Despite its widespread occurrence, the molecular basis of CI remains unclear and theoretical models have been proposed to understand the phenomenon. We consider in this paper the quantitative Lock-Key model which currently represents a good hypothesis that is consistent with the data available. CI is in this case modelled as the problem of covering the edges of a bipartite graph with the minimum number of chain subgraphs. This problem is already known to be NP-hard, and we provide an exponential algorithm with a non trivial complexity. It is frequent that depending on the dataset, there may be many optimal solutions which can be biologically quite different among them. To rely on a single optimal solution may therefore be problematic. To this purpose, we address the problem of enumerating (listing) all minimal chain subgraph covers of a bipartite graph and show that it can be solved in quasi-polynomial time. Interestingly, in order to solve the above problems, we considered also the problem of enumerating all the maximal chain subgraphs of a bipartite graph and improved on the current results in the literature for the latter. Finally, to demonstrate the usefulness of our methods we show an application on a real dataset.
RFD (Reverse flow divert) set is a kind of maintenance-free delivery system driving by compress-air. It intermittently discharges through its delivery pipe. Without moving part, the optimized design of RFD set is a cr...
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ISBN:
(纸本)9781510804159
RFD (Reverse flow divert) set is a kind of maintenance-free delivery system driving by compress-air. It intermittently discharges through its delivery pipe. Without moving part, the optimized design of RFD set is a critical technical for efficient and stable operation. The deficiencies of traditional enumeration algorithms and marginal utility method have been indicated. Then, as the main point of the paper, Genetic Algorithm is discussed to solve the multi-objective and multidimensional optimization problem. By comparing the results of the three optimization methods, we can have the superiority of GA. Based on the needs of flow and head in industry, serial design of RFD has been made by using GA, thus the relationships of the structural parameters and operational parameters have been analyzed. The conversion relationship between different density and viscosity in average flow has been provided, which will be beneficial for the RFD set design in industry.
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