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» Computing the betti numbers of arrangements
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FOCS
2003
IEEE
15 years 2 months ago
On Levels in Arrangements of Curves, II: A Simple Inequality and Its Consequences
We give a surprisingly short proof that in any planar arrangement of Ò curves where each pair intersects at most a fixed number (×) of times, the -level has subquadratic (Ç´...
Timothy M. Chan
IWPEC
2004
Springer
15 years 3 months ago
Computing Small Search Numbers in Linear Time
Let G = V; E be a graph. The linear-width of G is de ned as the smallest integer k such that E can be arranged in a linear ordering e1; : : : ; er such that for every i = 1; :...
Hans L. Bodlaender, Dimitrios M. Thilikos
WEA
2009
Springer
104views Algorithms» more  WEA 2009»
15 years 4 months ago
Univariate Algebraic Kernel and Application to Arrangements
We present a cgal-based univariate algebraic kernel, which provides certied real-root isolation of univariate polynomials with integer coecients and standard functionalities such...
Sylvain Lazard, Luis Mariano Peñaranda, Eli...
DGCI
2005
Springer
15 years 3 months ago
Computation of Homology Groups and Generators
Topological invariants are extremely useful in many applications related to digital imaging and geometric modeling, and homology is a classical one, which has not yet been fully e...
Samuel Peltier, Sylvie Alayrangues, Laurent Fuchs,...
COMPGEOM
2008
ACM
14 years 11 months ago
The complexity of the outer face in arrangements of random segments
We investigate the complexity of the outer face in arrangements of line segments of a fixed length in the plane, drawn uniformly at random within a square. We derive upper bounds ...
Noga Alon, Dan Halperin, Oren Nechushtan, Micha Sh...