DAGmaps and ε-Visibility Representations of DAGs
نویسندگان
چکیده
DAGmaps are space filling visualizations of DAGs that generalize treemaps. Deciding whether or not a DAG admits a DAGmap is NP-complete. Recently we defined a special case called one-dimensional DAGmap where the admissibility is decided in linear time. However there is no complete characterization of the class of DAGs that admit a onedimensional DAGmap. In this paper we prove that a DAG admits a one-dimensional DAGmap if and only if it admits a directed ε-visibility representation. Then we give a characterization of the DAGs that admit directed ε-visibility representations. Finally we show that a DAGmap defines a directed three-dimensional ε-visibility representation of a DAG.
منابع مشابه
DAGmaps and ε-Visibility Representations for DAGs: Algorithms and Characterizations
DAGmaps are space filling visualizations of DAGs that generalize treemaps. Deciding whether or not a DAG admits a DAGmap is NPcomplete. Although any layered planar DAG admits a one-dimensional DAGmap there was no complete characterization of the class of DAGs that admit a one-dimensional DAGmap. In this paper we prove that a DAG admits a one-dimensional DAGmap if and only if it admits a directe...
متن کاملCombinatorial decomposition approaches for efficient counting and random generation FPTASes
Given a combinatorial decomposition for a counting problem, we resort to the simplescheme of approximating large numbers by floating-point representations in order to obtainefficient Fully Polynomial Time Approximation Schemes (FPTASes) for it. The numberof bits employed for the exponent and the mantissa will depend on the error parameter0 < ε ≤ 1 and on the characteristics ...
متن کاملItalian Political Communication and Gender Bias: Press Representations of Men/Women Presidents of the Houses of Parliament (1979, 1994, and 2013)
The study considers mass media communication as intertwined with social norms, as assumed by the perspective of social representations. It explores the Italian press communication by focusing on three pairs of men and women politicians with different political orientations and all serving as presidents of the Houses of Parliament in three legislatures. The article concentrates on five newspaper...
متن کاملOn a Regularized Scheme for Approximate Acoustic Cloaking Using Transformation Optics
In this paper, we study approximate cloaking for the Helmholtz equation in three dimensions where the cloaking device is based on transformations which blow up a cylinder of fixed height and small cross section of radius ε into the cloaked region. Assuming the zero Dirichlet boundary condition is imposed on the boundary of the cloaked region, we show that the degree of visibility is of order ε ...
متن کاملAlgorithms for Visualizing Phylogenetic Networks
We study the problem of visualizing phylogenetic networks, which are extensions of the Tree of Life in biology. We use a space filling visualization method, called DAGmaps, in order to obtain clear visualizations using limited space. In this paper, we restrict our attention to galled trees and galled networks and present linear time algorithms for visualizing them as DAGmaps.
متن کامل