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» The three dimensions of proofs
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COMPGEOM
1996
ACM
15 years 4 months ago
New Lower Bounds for Convex Hull Problems in Odd Dimensions
We show that in the worst case, (ndd=2e;1 +n logn) sidedness queries are required to determine whether the convex hull of n points in IRd is simplicial, or to determine the number ...
Jeff Erickson
CORR
2006
Springer
89views Education» more  CORR 2006»
14 years 12 months ago
Finite-State Dimension and Real Arithmetic
We use entropy rates and Schur concavity to prove that, for every integer k 2, every nonzero rational number q, and every real number , the base-k expansions of , q + , and q all...
David Doty, Jack H. Lutz, Satyadev Nandakumar
CORR
2006
Springer
120views Education» more  CORR 2006»
14 years 12 months ago
Improved Bounds and Schemes for the Declustering Problem
Abstract. The declustering problem is to allocate given data on parallel working storage devices in such a manner that typical requests find their data evenly distributed among the...
Benjamin Doerr, Nils Hebbinghaus, Sören Werth
GD
2004
Springer
15 years 5 months ago
The Three Dimensional Logic Engine
We consider the following graph embedding question: given a graph G, is it possible to map its vertices to points in 3D such that G is isomorphic to the mutual nearest neighbor gra...
Matthew Kitching, Sue Whitesides
DM
1999
65views more  DM 1999»
14 years 11 months ago
Finite three dimensional partial orders which are not sphere orders
Abstract. Given a partially ordered set P = (X; P ), a function F which assigns to each x 2 X a set F (x) so that x y in P if and only if F (x) F (y) is called an inclusion represe...
Stefan Felsner, Peter C. Fishburn, William T. Trot...