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» A bound on the number of points of a plane curve
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JOC
2011
81views more  JOC 2011»
13 years 2 months ago
An L(1/3) Discrete Logarithm Algorithm for Low Degree Curves
We present an algorithm for solving the discrete logarithm problem in Jacobians of families of plane curves whose degrees in X and Y are low with respect to their genera. The fin...
Andreas Enge, Pierrick Gaudry, Emmanuel Thom&eacut...
COMPGEOM
2010
ACM
14 years 14 days ago
Better bounds on the union complexity of locally fat objects
We prove that the union complexity of a set of n constantcomplexity locally fat objects (which can be curved and/or non-convex) in the plane is O(λt+2(n) log n), where t is the m...
Mark de Berg
IPCO
2007
114views Optimization» more  IPCO 2007»
13 years 8 months ago
Distinct Triangle Areas in a Planar Point Set
Erd˝os, Purdy, and Straus conjectured that the number of distinct (nonzero) areas of the triangles determined by n noncollinear points in the plane is at least n−1 2 , which is...
Adrian Dumitrescu, Csaba D. Tóth
WALCOM
2010
IEEE
206views Algorithms» more  WALCOM 2010»
14 years 2 months ago
Crossings between Curves with Many Tangencies
Let A and B be two families of two-way infinite x-monotone curves, no three of which pass through the same point. Assume that every curve in A lies above every curve in B and that...
Jacob Fox, Fabrizio Frati, János Pach, Rom ...
COMPGEOM
1996
ACM
13 years 11 months ago
On the Number of Arrangements of Pseudolines
Given a simple arrangementof n pseudolines in the Euclidean plane, associate with line i the list i of the lines crossing i in the order of the crossings on line i. i = ( i 1; i 2;...
Stefan Felsner