Newman's theorem via Carathéodory
Yaqiao Li, Ali Mohammad Lavasani, Mehran Shakerinava
Abstract
We give a streamlined short proof of Newman's theorem in communication complexity by applying the classical and the approximate Carathéodory's theorems.
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Newman's theorem via Carathéodory
Abstract
We give a streamlined short proof of Newman's theorem in communication complexity by applying the classical and the approximate Carathéodory's theorems.
Paper Structure (3 theorems, 2 equations)
This paper contains 3 theorems, 2 equations.
Key Result
Proposition 1
Let $S \subseteq \mathbb{R}^n$. Every $x \in conv(S)$ can be written as a convex combination of at most $n+1$ points from $S$.
Theorems & Definitions (4)
- Proposition 1: Carathéodory, CaraCara2
- Proposition 2: Approximate Carathéodory, Cara_approx_1
- Theorem 1: Newman, Newman
- proof