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CORR
2011
Springer
174views Education» more  CORR 2011»
13 years 2 months ago
Lower bounds on the obstacle number of graphs
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 ...
Padmini Mukkamala, János Pach, Döm&oum...
JCT
2007
146views more  JCT 2007»
13 years 7 months ago
Laplacian spectral bounds for clique and independence numbers of graphs
Let G be a simple graph with n vertices and m edges. Let ω(G) and α(G) be the numbers of vertices of the largest clique and the largest independent set in G, respectively. In th...
Mei Lu, Huiqing Liu, Feng Tian
CIAC
2006
Springer
278views Algorithms» more  CIAC 2006»
13 years 11 months ago
Covering a Set of Points with a Minimum Number of Lines
We consider the minimum line covering problem: given a set S of n points in the plane, we want to find the smallest number l of straight lines needed to cover all n points in S. W...
Magdalene Grantson, Christos Levcopoulos
COMPGEOM
2004
ACM
14 years 28 days ago
Solution of Scott's problem on the number of directions determined by a point set in 3-space
Let P be a set of n points in Ê3 , not all in a common plane. We solve a problem of Scott (1970) by showing that the connecting lines of P assume at least 2n − 7 different dir...
János Pach, Rom Pinchasi, Micha Sharir
COLT
2008
Springer
13 years 9 months ago
Almost Tight Upper Bound for Finding Fourier Coefficients of Bounded Pseudo- Boolean Functions
A pseudo-Boolean function is a real-valued function defined on {0, 1}n . A k-bounded function is a pseudo-Boolean function that can be expressed as a sum of subfunctions each of w...
Sung-Soon Choi, Kyomin Jung, Jeong Han Kim