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» Lower bounds on the obstacle number of graphs
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117
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JGT
2010
113views more  JGT 2010»
15 years 6 days ago
Crossing numbers of imbalanced graphs
The crossing number, cr(G), of a graph G is the least number of crossing points in any drawing of G in the plane. According to the Crossing Lemma of Ajtai, Chv´atal, Newborn, Sze...
János Pach, József Solymosi, G&aacut...
FOCS
2006
IEEE
15 years 7 months ago
On the Quantum Query Complexity of Local Search in Two and Three Dimensions
The quantum query complexity of searching for local optima has been a subject of much interest in the recent literature. For the d-dimensional grid graphs, the complexity has been...
Xiaoming Sun, Andrew Chi-Chih Yao
135
Voted
COCOON
2007
Springer
15 years 8 months ago
On the Number of Cycles in Planar Graphs
We investigate the maximum number of simple cycles and the maximum number of Hamiltonian cycles in a planar graph G with n vertices. Using the transfer matrix method we construct a...
Kevin Buchin, Christian Knauer, Klaus Kriegel, And...
STOC
1995
ACM
115views Algorithms» more  STOC 1995»
15 years 5 months ago
Geometric lower bounds for parametric matroid optimization
We relate the sequence of minimum bases of a matroid with linearly varying weights to three problems from combinatorial geometry: k-sets, lower envelopes of line segments, and con...
David Eppstein
SODA
2004
ACM
87views Algorithms» more  SODA 2004»
15 years 3 months ago
Optimal space lower bounds for all frequency moments
We prove that any one-pass streaming algorithm which ( , )-approximates the kth frequency moment Fk, for any real k = 1 and any = 1 m , must use 1 2 bits of space, where m is th...
David P. Woodruff