Titlebook: Discrete and Computational Geometry; Japanese Conference, Jin Akiyama,Mikio Kano Conference proceedings 2003 Springer-Verlag Berlin Heidelb

難聽的聲音

Comparing Hypergraphs by Areas of Hyperedges Drawn on a Convex Polygon,dges .?∈?. such that . contains at least one node from each of {., ..., .???1}, {., ..., .???1} and {., ..., .???1, 0, ..., .???1 }. We show that for two hypergraphs . and .′ on ., the following two conditions are equivalent.

Armada

整體

On Partitioning a Cake,es. It is known [4, 5, 9] that any two masses have convex .-partition for .=(1/3,1/3,1/3). We prove the existence of convex .-partitions for any .=(.,.,1-2.), 0<.<1/3. We also provide an infinite family of . each of which does not guarantee a convex .-partition of a cake.

FRONT

Succinct Data Structures for Approximating Convex Functions with Applications,. Our data structures are succinct using only .((1/.)log.(.)) bits of storage. We show that this is optimal by providing a matching lower bound showing that any data structure providing such an .-approximation requires at least Ω((1/.)log.(.)) bits of storage.