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Make Flatting Example more readable and understandable
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@hayatoito
hayatoito committed Mar 4, 2016
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Expand Up @@ -337,7 +337,7 @@ <h3>Slots</h3>
<h2>Slotting Algorithm</h2>

<p>
The <dfn>slotting algorithm</dfn> <strong>must</strong> be used to determine the <a>assigned slot</a> for each node and <strong>must</strong> be <a data-lt="processing equivalence">equivalent</a> to processing the following steps:
The <dfn>slotting algorithm</dfn> <strong>must</strong> be used to determine the <a>assigned slot</a> of each node and <strong>must</strong> be <a data-lt="processing equivalence">equivalent</a> to processing the following steps:
</p>

<div class="algorithm">
Expand Down Expand Up @@ -382,7 +382,7 @@ <h2>Slotting Algorithm</h2>
<h2>Assigned Nodes Algorithm</h2>

<p>
The <dfn>get assigned nodes algorithm</dfn> <strong>must</strong> be used to determine the <dfn>assigned nodes</dfn> for a <a>slot</a> and <strong>must</strong> be <a data-lt="processing equivalence">equivalent</a> to processing the following steps:
The <dfn>get assigned nodes algorithm</dfn> <strong>must</strong> be used to determine the <dfn>assigned nodes</dfn> of a <a>slot</a> and <strong>must</strong> be <a data-lt="processing equivalence">equivalent</a> to processing the following steps:
</p>

<div class="algorithm">
Expand Down Expand Up @@ -419,7 +419,7 @@ <h2>Assigned Nodes Algorithm</h2>
<h2>Distributed Nodes Algorithm</h2>

<p>
The <dfn>get distributed nodes algorithm</dfn> <strong>must</strong> be used to determine the <dfn>distributed nodes</dfn> for a <a>slot</a> and <strong>must</strong> be <a data-lt="processing equivalence">equivalent</a> to processing the following steps:
The <dfn>get distributed nodes algorithm</dfn> <strong>must</strong> be used to determine the <dfn>distributed nodes</dfn> of a <a>slot</a> and <strong>must</strong> be <a data-lt="processing equivalence">equivalent</a> to processing the following steps:
</p>

<div class="algorithm">
Expand Down Expand Up @@ -577,15 +577,15 @@ <h3>Flattening Example</h3>
</table>

<p>
Suppose that an assigned slot for each node, if it exists, is:
Suppose that an <a>assigned slot</a> of each node, if it exists, is:
</p>

<ul>
<li>(D => L) (You can read this as <strong>"D is assigned to L</strong>")</li>
<li>(F => L)</li>
<li>(H => O)</li>
<li>(O => T)</li>
<li>(P => T)</li>
<li>D: => L (You can read this as <strong>"D is assigned to L</strong>")</li>
<li>F: => L</li>
<li>H: => O</li>
<li>O: => T</li>
<li>P: => T</li>
</ul>

<figure>
Expand All @@ -594,7 +594,7 @@ <h3>Flattening Example</h3>
</figure>

<p>
Then, the distributed nodes for each slot will be:
Then, the <a>assigned nodes</a> and the <a>distributed nodes</a> of each slot will be:
</p>

<table>
Expand All @@ -604,8 +604,9 @@ <h3>Flattening Example</h3>
<th>Root node is: </th>
<th>Hosted by:</th>
<th>Composed of: (in tree order)</th>
<th>Assigned Slot for a node</th>
<th>Distributed nodes for a slot</th>
<th><a>Assigned slot</a> of each node</th>
<th><a>Assigned nodes</a> of each slot</th>
<th><a>Distributed nodes</a> of each slot</th>
</tr>
</thead>
<tbody>
Expand All @@ -614,33 +615,68 @@ <h3>Flattening Example</h3>
<td>A</td>
<td>-</td>
<td>A, B, C, D, E, F, G, H, I</td>
<td>(D => L), (F => L), (H => O)</td>
<td>
<ul>
<li>D: => L</li>
<li>F: => L</li>
<li>H: => O</li>
</ul>
</td>
<td>-</td>
<td>-</td>
</tr>
<tr>
<td>shadow tree 1</td>
<td>J</td>
<td>C</td>
<td>J, K, L, M, N, O, P, Q</td>
<td>(O => T), (P => T)</td>
<td>L <= [D, F], M <= [], O <= [H]</td>
<td>
<ul>
<li>O: => T</li>
<li>P: => T</li>
</ul>
</td>
<td>
<ul>
<li>L: [D, F]</li>
<li>M: []</li>
<li>O: [H]</li>
</ul>
</td>
<td>
<ul>
<li>L: [D, F]</li>
<li>M: []</li>
<li>O: [H]</li>
</ul>
</td>
</tr>
<tr>
<td>shadow tree 2</td>
<td>R</td>
<td>N</td>
<td>R, S, T</td>
<td>-</td>
<td>T <= [H, P] </td>
<td>
<ul>
<li>T: [O, P]</li>
</ul>
</td>
<td>
<ul>
<li>T: [H, P]
</li>
</ul>
</td>
</tr>
</tbody>
</table>

<ul class="note">
<li>More than one nodes can be assigned to the same slot. e.g. (D => L), (F => L)</li>
<li>A slot can be assigned to an other slot, e.g. (O => T)</li>
<li>More than one nodes can be assigned to the same slot. e.g. D: => L, F: => L</li>
<li>A slot can be assigned to an other slot, e.g. O: => T</li>
<li>
The distributed nodes for T are [H, P]. That aren't [O, P].
The <a>distributed nodes</a> of T are [H, P]. That aren't [O, P].
A slot is never a member of distributed nodes of an other slot.
If a slot <var>A</var> is assigned to an other slot <var>B</var>, the distributed nodes for <var>A</var> are appended to the distributed nodes for <var>B</var>,
instead of <var>A</var> itself, as per the <a>get distributed nodes algorithm</a>.
Expand Down

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