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Publications associées (15)

Space Efficient Approximation to Maximum Matching Size from Uniform Edge Samples

Mikhail Kapralov, Slobodan Mitrovic, Jakab Tardos, Ashkan Norouzi Fard

Given a source of iid samples of edges of an input graph G with n vertices and m edges, how many samples does one need to compute a constant factor approximation to the maximum matching size in G? Moreover, is it possible to obtain such an estimate in a sm ...

ASSOC COMPUTING MACHINERY2020

A finite element framework based on bivariate simplex splines on triangle configurations

Xiaodong Wei, Juan Cao

Recently, triangle configuration based bivariate simplex splines (referred to as TCB-spline) have been introduced to the geometric computing community. TCB-splines retain many attractive theoretic properties of classical B-splines, such as partition of uni ...

ELSEVIER SCIENCE SA2019

Thrackles: An improved upper bound

János Pach, Radoslav Fulek

A thrackle is a graph drawn in the plane so that every pair of its edges meet exactly once: either at a common end vertex or in a proper crossing. We prove that any thrackle of n vertices has at most 1.3984n edges. Quasi-thrackles are defined similarly, ex ...

ELSEVIER SCIENCE BV2019

Approximating the rectilinear crossing number

János Pach

A straight-line drawing of a graph G is a mapping which assigns to each vertex a point in the plane and to each edge a straight-line segment connecting the corresponding two points. The rectilinear crossing number of a graph G, (cr) over bar (G), is the mi ...

2019

On Simplices in Diameter Graphs in R-4

Andrei Kupavskii

A graph G is a diameter graph in R-d if its vertex set is a finite subset in R-d of diameter 1 and edges join pairs of vertices a unit distance apart. It is shown that if a diameter graph G in R-4 contains the complete subgraph K on five vertices, then any ...

Maik Nauka/Interperiodica/Springer2017

Remarks on Schur's conjecture

János Pach, Filip Moric

Let P be a set of n > d points in for d >= 2. It was conjectured by Zvi Schur that the maximum number of (d-1)-dimensional regular simplices of edge length diam(P), whose every vertex belongs to P, is n. We prove this statement under the condition that any ...

Elsevier Science Bv2015

Exponentiality of the exchange algorithm for finding another room-partitioning

Laura Sanità

Let T be a triangulated surface given by the list of vertex-triples of its triangles, called rooms. A room-partitioning for T is a subset R of the rooms such that each vertex of T is in exactly one room in R. Given a room-partitioning R for T, the exchange ...

Elsevier Science Bv2014

The number of distinct distances from a vertex of a convex polygon

János Pach, Gabriel Nivasch, Rom Pinchasi

Erd\H{o}s conjectured in 1946 that every n-point set P in convex position in the plane contains a point that determines at least floor(n/2) distinct distances to the other points of P. The best known lower bound due to Dumitrescu (2006) is 13n/36 - O(1). I ...

2013

Application of vertex and mass constraints in track-based alignment

Olivier Schneider, Christophe Salzmann, Vincent Fave, Matthew Needham, Maurizio Martinelli, Frédéric Guillaume Dupertuis, Géraldine Conti, Louis Nicolas, Gerhard Raven

The software alignment of planar tracking detectors using samples of charged particle trajectories may lead to global detector distortions that affect vertex and momentum resolution. We present an alignment procedure that constrains such distortions by mak ...

Elsevier Science Bv2013

k-Quasi-Planar Graphs

A topological graph is k-quasi-planar if it does not contain k pairwise crossing edges. A topological graph is simple if every pair of its edges intersect at most once (either at a vertex or at their intersection). In 1996, Pach, Shahrokhi. and Szegedy [16 ...

Springer-Verlag Berlin2012