From b01015b343cf976696ae8548929648f1cafe53cf Mon Sep 17 00:00:00 2001 From: Noah Zarro <noahzarro@gmail.com> Date: Mon, 26 Jul 2021 16:14:32 +0200 Subject: [PATCH] added algorithms of 1 and 2 --- README.md | 3 +++ images/6_color.png | Bin 0 -> 129264 bytes images/bellman_ford_bfs.png | Bin 0 -> 81924 bytes images/dijkstra_bfs.png | Bin 0 -> 167499 bytes images/echo.png | Bin 0 -> 32541 bytes images/flooding.png | Bin 0 -> 61548 bytes images/ghs.png | Bin 0 -> 194607 bytes images/greedy_sequential.png | Bin 0 -> 62290 bytes images/reduce.png | Bin 0 -> 141155 bytes images/shift_down.png | Bin 0 -> 58023 bytes images/six_2_three.png | Bin 0 -> 85291 bytes images/slow_tree_coloring.png | Bin 0 -> 96087 bytes summary.md | 40 ++++++++++++++++++++++++++++++++++ 13 files changed, 43 insertions(+) create mode 100644 images/6_color.png create mode 100644 images/bellman_ford_bfs.png create mode 100644 images/dijkstra_bfs.png create mode 100644 images/echo.png create mode 100644 images/flooding.png create mode 100644 images/ghs.png create mode 100644 images/greedy_sequential.png create mode 100644 images/reduce.png create mode 100644 images/shift_down.png create mode 100644 images/six_2_three.png create mode 100644 images/slow_tree_coloring.png create mode 100644 summary.md diff --git a/README.md b/README.md index 99ca3eb..5c2d971 100644 --- a/README.md +++ b/README.md @@ -46,6 +46,9 @@ To further reduce the colors needed to $`\Delta+1`$, the colors are grouped into If one iteration is complete, the remaining colors are regrouped again in the same way, but now there are only half as many groups. This is done until only one group is left. +# 4. Lecture + + # 5. 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distance between any two nodes in the graph + +## Theorems +- 1.13: $`\Chi(Tree)\leq2`$ + +## Algorithms + +### Coloring + +|Name|Algorithm|Round Complexity|Colors| +|---|---|---|---| +|Greedy Sequential||$`O(n)`$|$`\Delta+1`$| +|Reduce||$`O(n)`$|$`\Delta+1`$| +|Slow Tree Coloring||$`O(Tree Height)`$|$`2`$| +|6-Color||$`O(\log*(n))`$|$`6`$| +|Six-2-Three||$`O(1)`$|$`3`$| + +### Trees + +|Name|Algorithm|Round Complexity|Message Complexity| +|---|---|---|---| +|Flooding||$`O(n)`$|$`O(m)`$| +|Echo||$`O(n)`$|$`O(n)`$| +|Dijkstra BFS||$`O(D^2)`$|$`O(m+nD)`$| +|Bellman-Ford BFS||$`O(D)`$|$`O(nm)`$| +|GHS MST||$`O(n\log n)`$|$`O(m\log n)`$| + +## Structures \ No newline at end of file -- GitLab