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Commit 4507cbc4 authored by zarron's avatar zarron
Browse files

fixed fooling set

parent ce29738a
......@@ -137,7 +137,7 @@ Every node calculates its maximum radius by flooding echo. The largest radius is
As the naïve approach, but each node only starts the flooding if it receives the pebble. The pebble is forwarded in a BFS way and pauses at each token one round to ensure that the flooding messages do not overlap. It has round complexity of $`\mathcal{O}(n) + \mathcal{O}(D) = \mathcal{O}(n)`$
## Fooling Sets
A matrix which has the same entries on two opposite corners, but another entry in either one of the remaining corners. It is defined recursively, i.e. it consists itself out of fooling sets
A set where all nodes have the same value and each two nodes can span up a rectangle, where one of the edges has a different value than the nodes in the fooling set.
## 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.
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