Graphs That Admit Polyline Drawings with Few Crossing Angles
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A graph drawn in the plane is called k-quasi-planar if it does not contain k pair-wise crossing edges. It has been conjectured for a long time that for every fixed k, the maximum number of edges of a k-quasi-planar graph with n vertices is O(n). The best k ...
Modern data processing tasks frequently involve structured data, for example signals defined on the vertex set of a weighted graph. In this paper, we address the problem of inference of mobility patterns from data defined on geographical graphs based on sp ...
We study some variants of Conway’s thrackle conjecture. A tangle is a graph drawn in the plane such that its edges are represented by continuous arcs, and any two edges share precisely one point, which is either a common endpoint or an interior point at wh ...
We propose a method for learning dictionaries towards sparse approximation of signals defined on vertices of arbitrary graphs. Dictionaries are expected to describe effectively the main spatial and spectral components of the signals of interest, so that th ...
We consider straight-line outerplanar drawings of outerplanar graphs in which a small number of distinct edge slopes are used, that is, the segments representing edges are parallel to a small number of directions. We prove that Delta - 1 edge slopes suffic ...
Many problems in combinatorial geometry can be formulated in terms of curves or surfaces containing many points of a cartesian product. In 2000, Elekes and Rónyai proved that if the graph of a polynomial f(x, y) contains cn2 points of an n × n × n cartesia ...
We introduce a precise interprocedural effect analysis for programs with mutable state, dynamic object allocation, and dynamic dispatch. Our analysis is precise even in the presence of dynamic dispatch where the context-insensitive estimate on the number o ...
We analyze the relations between several graph transformations that were introduced to be used in procedures determining the stability number of a graph. We show that all these transformations can be decomposed into a sequence of edge deletions and twin de ...
Shortest paths are not always simple. In planar networks, they can be very different from those with the smallest number of turns - the simplest paths. The statistical comparison of the lengths of the shortest and simplest paths provides a non trivial and ...
Given a graph G, an obstacle representation of G is a set of points in the plane representing the vertices of G, together with a set of connected obstacles such that two vertices of G are joined by an edge if and only if the corresponding points can be con ...
