From 88dd7bf39193d54252fb562f0f7aedadea1e90ee Mon Sep 17 00:00:00 2001
From: Noah Zarro <noahzarro@gmail.com>
Date: Fri, 30 Jul 2021 14:28:26 +0200
Subject: [PATCH] until lesson 10

---
 README.md                           |   4 ++++
 images/communication_complexity.png | Bin 0 -> 81848 bytes
 images/diameter_synchronous.png     | Bin 0 -> 92902 bytes
 images/fooling_set.png              | Bin 0 -> 60194 bytes
 images/monochromatic.png            | Bin 0 -> 54095 bytes
 images/naive_diameter.png           | Bin 0 -> 42911 bytes
 summary.md                          |  26 +++++++++++++++++++++++++-
 7 files changed, 29 insertions(+), 1 deletion(-)
 create mode 100644 images/communication_complexity.png
 create mode 100644 images/diameter_synchronous.png
 create mode 100644 images/fooling_set.png
 create mode 100644 images/monochromatic.png
 create mode 100644 images/naive_diameter.png

diff --git a/README.md b/README.md
index c3dab41..8556615 100644
--- a/README.md
+++ b/README.md
@@ -148,6 +148,10 @@ A set where all nodes have the same value and each two nodes can span up a recta
 ## Communication Complexity
 To test equality of to bit strings of length $`k`$ (a function with a fooling set as solution set) $`\mathcal{O}(\log 2^k)`$ bits have to be exchanged. After this, the solution set can be narrowed down to a single value. If fewer bits get exchanged, the solution set can still be a fooling set, which is not monochromatic (same values anywhere) and is therefore ambiguous.
 
+
+# 10. Lecture
+
+TODO
 # 11. Lecture
 It covers the topic of wireless transport protocols to avoid collisions
 
diff --git a/images/communication_complexity.png b/images/communication_complexity.png
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diff --git a/summary.md b/summary.md
index c15bd6e..6971d31 100644
--- a/summary.md
+++ b/summary.md
@@ -69,5 +69,29 @@ rounds.
 |Merging Network|![merging_network](images/merging_network.png)<br>A merging network of width n merges two sorted input sequences of length n/2 each into one sorted sequence of length n.|$`1+2\log n`$|
 |Batcher Network|![batcher](images/batcher.png)<br>A sorting network (Algorithm 8.18) sorts an arbitrary sequence of n values.|$`O(\log^2n)`$|
 
+### Advanced
+|Name|Algorithm|Rounds|
+|---|---|---|
+|Naive Diameter Construction|![naive_diameter](images/naive_diameter.png)|$`O(D)`$|
+|APSP Diameter Construction|![diameter_synchronous](images/diameter_synchronous.png)|$`O(n)`$|
+|Borůvka's Algorithm|<ul><li>Start with empty spanning forest</li><li>Each fragment computes minimal outgoing edge</li><li>Fragments get merged over minimal outgoing edges, and they get added to the MST</li><li>Repeat</li></ul>|$`O(\log n)`$|
+
+### Definitions
+|Name|Definition|
+|---|---|
+|Communication Complexity|![communication_complexity](images/communication_complexity.png)|
+|Monochromatic|![monochromatic](images/monochromatic.png)|
+|Fooling Set|![](images/fooling_set.png)|
+
+## Structures
+- TODO: Local Model
+
+
+## Varia
+
+### Landauer Notation
+
+|Symbol|Meaning|
+|---|---|
+|$`f \in O(g)`$||
 
-## Structures
\ No newline at end of file
-- 
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