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» The three dimensions of proofs
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COMPGEOM
1996
ACM
15 years 1 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 9 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 9 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 3 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 9 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...