https://wiki.expertiza.ncsu.edu/index.php?action=history&feed=atom&title=CSC%2FECE_506_Spring_2011%2Fch12_arCSC/ECE 506 Spring 2011/ch12 ar - Revision history2026-04-27T07:38:37ZRevision history for this page on the wikiMediaWiki 1.41.0https://wiki.expertiza.ncsu.edu/index.php?title=CSC/ECE_506_Spring_2011/ch12_ar&diff=45248&oldid=prevAkrepask at 06:45, 22 April 20112011-04-22T06:45:25Z<p></p>
<a href="https://wiki.expertiza.ncsu.edu/index.php?title=CSC/ECE_506_Spring_2011/ch12_ar&diff=45248&oldid=45177">Show changes</a>Akrepaskhttps://wiki.expertiza.ncsu.edu/index.php?title=CSC/ECE_506_Spring_2011/ch12_ar&diff=45177&oldid=prevVrmanda at 01:09, 19 April 20112011-04-19T01:09:38Z<p></p>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>The tree has a hierarchical structure of nodes on the bottom and switching nodes at the upper levels. The tree experiences high traffic and high latency if the package must travel through the upper levels. Also because of the high connectivity, this topology has high average energy dissipation.[[#References|<sup>[8]</sup>]]</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>The tree has a hierarchical structure of nodes on the bottom and switching nodes at the upper levels. The tree experiences high traffic and high latency if the package must travel through the upper levels. Also because of the high connectivity, this topology has high average energy dissipation.[[#References|<sup>[8]</sup>]]</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div></p></div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div></p></div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><<del style="font-weight: bold; text-decoration: none;">br</del>></div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">In a k-ary Tree interconnection network with </ins><<ins style="font-weight: bold; text-decoration: none;">b</ins>><ins style="font-weight: bold; text-decoration: none;">p</b> nodes the degree of the nodes k+1 and the total number of links is k*(p-1). The bisection bandwidth of the network is 1 and the diameter of the network is 2*(log<sub>k</sub>p).</ins></div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><h2>Fat Tree</h2></div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><h2>Fat Tree</h2></div></td></tr>
</table>Vrmandahttps://wiki.expertiza.ncsu.edu/index.php?title=CSC/ECE_506_Spring_2011/ch12_ar&diff=45175&oldid=prevVrmanda at 01:05, 19 April 20112011-04-19T01:05:38Z<p></p>
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 01:05, 19 April 2011</td>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>In 1985, an MIT professor invented the fat tree to improve upon the normal “skinny” tree. To improve upon the “skinny” tree topology, the fat tree “fattens” up the links at the upper levels. This helps to alleviate the traffic at upper levels and to decrease the latency of the message. However, by fattening, it is meant that additional links are added to this area, which will increase the average energy dissipated by this topology. [[#References|<sup>[11]</sup>]]</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>In 1985, an MIT professor invented the fat tree to improve upon the normal “skinny” tree. To improve upon the “skinny” tree topology, the fat tree “fattens” up the links at the upper levels. This helps to alleviate the traffic at upper levels and to decrease the latency of the message. However, by fattening, it is meant that additional links are added to this area, which will increase the average energy dissipated by this topology. [[#References|<sup>[11]</sup>]]</div></td></tr>
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<tr><td colspan="2" class="diff-side-deleted"></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">In an interconnection network with k-ary Fat Tree implementation of </ins><<ins style="font-weight: bold; text-decoration: none;">b</ins>><ins style="font-weight: bold; text-decoration: none;">p</b> nodes, the degree of the network would be <b>'k+1'</b> and the total number of links would be k*(p-1). The diameter of the network would be 2*log<sub>k</sub>p, the bisection bandwidth of the network would be p/2.</ins></div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><h2>Butterfly</h2></div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><h2>Butterfly</h2></div></td></tr>
</table>Vrmandahttps://wiki.expertiza.ncsu.edu/index.php?title=CSC/ECE_506_Spring_2011/ch12_ar&diff=45172&oldid=prevVrmanda at 01:01, 19 April 20112011-04-19T01:01:37Z<p></p>
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 01:01, 19 April 2011</td>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Another attempt to increase the “skinny” tree structure was the butterfly structure. The butterfly structure is similar to the tree structure, but it replicates the switching node structure of the tree topology and connects them together so that there are equal links and routers at all levels. There are 2 problems with this topology. First of all, there is no path diversity in this topology. There is only one path from the root to a downstream node. This is not ideal incase the network is congested in a certain area, but available in another. There is no way for the network to rebalance the work. Second of all, there are some very long routes in this topology. This requires there to be repeaters in between the nodes, which will cause the physical area to implement the network to increase dramatically. [[#References|<sup>[12]</sup>]] </div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Another attempt to increase the “skinny” tree structure was the butterfly structure. The butterfly structure is similar to the tree structure, but it replicates the switching node structure of the tree topology and connects them together so that there are equal links and routers at all levels. There are 2 problems with this topology. First of all, there is no path diversity in this topology. There is only one path from the root to a downstream node. This is not ideal incase the network is congested in a certain area, but available in another. There is no way for the network to rebalance the work. Second of all, there are some very long routes in this topology. This requires there to be repeaters in between the nodes, which will cause the physical area to implement the network to increase dramatically. [[#References|<sup>[12]</sup>]] </div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div></p></div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div></p></div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><<del style="font-weight: bold; text-decoration: none;">br</del>></div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">In a butterfly interconnection network topology with </ins><<ins style="font-weight: bold; text-decoration: none;">b</ins>> <ins style="font-weight: bold; text-decoration: none;">p </b>nodes, the degree of the network would be 4 and the total number of links in the network would be 2*p(log<sub>2</sub>p). The diameter of the network is log<sub>2</sub>p. The bisection bandwidth of the network is p/2.</ins></div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><h1>Comparison of Network Topologies </h1></div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><h1>Comparison of Network Topologies </h1></div></td></tr>
</table>Vrmandahttps://wiki.expertiza.ncsu.edu/index.php?title=CSC/ECE_506_Spring_2011/ch12_ar&diff=45159&oldid=prevVrmanda at 00:48, 19 April 20112011-04-19T00:48:07Z<p></p>
<table style="background-color: #fff; color: #202122;" data-mw="interface">
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 00:48, 19 April 2011</td>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>The hypercube is essentially multiple cubes put together. This topology was developed in 1983. Originally there were no routers. The next hops were just programmed into each node. Today the hypercube topology is used by many companies including Intel. It is so attractive because of its small diameter. The nodes are numbered in such a way that every neighboring node is only one bit difference. This greatly increases the ability to route messages through the network. The biggest drawback of the topology is the lack of scalability. For example if the dimension size is increased by one, one link will need to be added to every node in the network. [[#References|<sup>[10]</sup>]]</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>The hypercube is essentially multiple cubes put together. This topology was developed in 1983. Originally there were no routers. The next hops were just programmed into each node. Today the hypercube topology is used by many companies including Intel. It is so attractive because of its small diameter. The nodes are numbered in such a way that every neighboring node is only one bit difference. This greatly increases the ability to route messages through the network. The biggest drawback of the topology is the lack of scalability. For example if the dimension size is increased by one, one link will need to be added to every node in the network. [[#References|<sup>[10]</sup>]]</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div></p></div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div></p></div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>In an interconnection network of <b>p</b> nodes with Hypercube topology, the degree of the network would be log<sub>2</sub>p</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>In an interconnection network of <b>p</b> nodes with Hypercube topology, the degree of the network would be log<sub>2</sub>p <ins style="font-weight: bold; text-decoration: none;">and the diameter of the network would also be log<sub>2</sub>p. The total number of links in the network would be (p/2)*log<sub>2</sub>p and the bisection bandwidth of the network would be p/2.</ins></div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><h2>2-D Torus</h2></div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><h2>2-D Torus</h2></div></td></tr>
</table>Vrmandahttps://wiki.expertiza.ncsu.edu/index.php?title=CSC/ECE_506_Spring_2011/ch12_ar&diff=45157&oldid=prevVrmanda at 00:45, 19 April 20112011-04-19T00:45:38Z<p></p>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>The hypercube is essentially multiple cubes put together. This topology was developed in 1983. Originally there were no routers. The next hops were just programmed into each node. Today the hypercube topology is used by many companies including Intel. It is so attractive because of its small diameter. The nodes are numbered in such a way that every neighboring node is only one bit difference. This greatly increases the ability to route messages through the network. The biggest drawback of the topology is the lack of scalability. For example if the dimension size is increased by one, one link will need to be added to every node in the network. [[#References|<sup>[10]</sup>]]</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>The hypercube is essentially multiple cubes put together. This topology was developed in 1983. Originally there were no routers. The next hops were just programmed into each node. Today the hypercube topology is used by many companies including Intel. It is so attractive because of its small diameter. The nodes are numbered in such a way that every neighboring node is only one bit difference. This greatly increases the ability to route messages through the network. The biggest drawback of the topology is the lack of scalability. For example if the dimension size is increased by one, one link will need to be added to every node in the network. [[#References|<sup>[10]</sup>]]</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div></p></div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div></p></div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><<del style="font-weight: bold; text-decoration: none;">br</del>></div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">In an interconnection network of </ins><<ins style="font-weight: bold; text-decoration: none;">b</ins>><ins style="font-weight: bold; text-decoration: none;">p</b> nodes with Hypercube topology, the degree of the network would be log<sub>2</sub>p</ins></div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><h2>2-D Torus</h2></div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><h2>2-D Torus</h2></div></td></tr>
</table>Vrmandahttps://wiki.expertiza.ncsu.edu/index.php?title=CSC/ECE_506_Spring_2011/ch12_ar&diff=45155&oldid=prevVrmanda at 00:38, 19 April 20112011-04-19T00:38:44Z<p></p>
<table style="background-color: #fff; color: #202122;" data-mw="interface">
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<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 00:38, 19 April 2011</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l48">Line 48:</td>
<td colspan="2" class="diff-lineno">Line 48:</td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>The 2-D mesh can be thought of as several linear arrays put together to form a 2-dimensional structure. Nodes that are not on the edge have 4 input or output links, or a '''degree''' of 4. This topology has reasonably low energy dissipation without compromising throughput. The area overhead for this topology is also rather low since a node is never farther than a clock cycle away, this means there is no need for repeater insertion in between the nodes. (the repeaters have a high area overhead, so using them causes the area of the topology to increase) [[#References|<sup>[8]</sup>]]</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>The 2-D mesh can be thought of as several linear arrays put together to form a 2-dimensional structure. Nodes that are not on the edge have 4 input or output links, or a '''degree''' of 4. This topology has reasonably low energy dissipation without compromising throughput. The area overhead for this topology is also rather low since a node is never farther than a clock cycle away, this means there is no need for repeater insertion in between the nodes. (the repeaters have a high area overhead, so using them causes the area of the topology to increase) [[#References|<sup>[8]</sup>]]</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div></p></div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div></p></div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><<del style="font-weight: bold; text-decoration: none;">br</del>></div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">In a 2-D Mesh interconnection network with </ins><<ins style="font-weight: bold; text-decoration: none;">b</ins>> <ins style="font-weight: bold; text-decoration: none;">p</b> nodes, the degree of the network would be 4 and the total number of links would be <b> 2*sqrt(p)(sqrt(p) -1) </b>. The diameter of the network would be 2*(sqrt(p) - 1). The bisection bandwidth of the interconnection is the total number of links divided by the diameter of the network, which would result to be sqrt(p).</ins></div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><h2>Cube</h2></div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><h2>Cube</h2></div></td></tr>
</table>Vrmandahttps://wiki.expertiza.ncsu.edu/index.php?title=CSC/ECE_506_Spring_2011/ch12_ar&diff=45153&oldid=prevVrmanda at 00:32, 19 April 20112011-04-19T00:32:51Z<p></p>
<table style="background-color: #fff; color: #202122;" data-mw="interface">
<col class="diff-marker" />
<col class="diff-content" />
<col class="diff-marker" />
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<tr class="diff-title" lang="en">
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 00:32, 19 April 2011</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l39">Line 39:</td>
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<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Similar structure as the linear array, except, the ending nodes connect to each other, establishing a circular structure. This topology will scale better since the longest distance between two nodes is cut in half, but it eventually ends up scaling poorly if enough nodes are added. The congestion will also be cut in half since there is now 2 options for packets to traverse.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Similar structure as the linear array, except, the ending nodes connect to each other, establishing a circular structure. This topology will scale better since the longest distance between two nodes is cut in half, but it eventually ends up scaling poorly if enough nodes are added. The congestion will also be cut in half since there is now 2 options for packets to traverse.</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div></p></div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div></p></div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div>In a Ring interconnection network with <b>p</b> nodes, the total number of links in the network would be <del style="font-weight: bold; text-decoration: none;"><p> </del>and the degree of the interconnection network is <b>2</b>. The maximum distance between nodes in the network would be the distance between nodes that are half way through the network, hence the diameter would be <b> p/2 </b>. The bisection bandwidth of the network of the interconnection would thus become 2.</div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div>In a Ring interconnection network with <b>p</b> nodes, the total number of links in the network would be and the degree of the interconnection network is <b>2</b>. The maximum distance between nodes in the network would be the distance between nodes that are half way through the network, hence the diameter would be <b> p/2 </b>. The bisection bandwidth of the network of the interconnection would thus become 2.</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><h2>2-D Mesh</h2></div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><h2>2-D Mesh</h2></div></td></tr>
</table>Vrmandahttps://wiki.expertiza.ncsu.edu/index.php?title=CSC/ECE_506_Spring_2011/ch12_ar&diff=45151&oldid=prevVrmanda at 00:32, 19 April 20112011-04-19T00:32:00Z<p></p>
<table style="background-color: #fff; color: #202122;" data-mw="interface">
<col class="diff-marker" />
<col class="diff-content" />
<col class="diff-marker" />
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<tr class="diff-title" lang="en">
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 00:32, 19 April 2011</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l39">Line 39:</td>
<td colspan="2" class="diff-lineno">Line 39:</td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Similar structure as the linear array, except, the ending nodes connect to each other, establishing a circular structure. This topology will scale better since the longest distance between two nodes is cut in half, but it eventually ends up scaling poorly if enough nodes are added. The congestion will also be cut in half since there is now 2 options for packets to traverse.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>Similar structure as the linear array, except, the ending nodes connect to each other, establishing a circular structure. This topology will scale better since the longest distance between two nodes is cut in half, but it eventually ends up scaling poorly if enough nodes are added. The congestion will also be cut in half since there is now 2 options for packets to traverse.</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div></p></div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div></p></div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><<del style="font-weight: bold; text-decoration: none;">br</del>></div></td><td class="diff-marker" data-marker="+"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #a3d3ff; vertical-align: top; white-space: pre-wrap;"><div><ins style="font-weight: bold; text-decoration: none;">In a Ring interconnection network with </ins><<ins style="font-weight: bold; text-decoration: none;">b</ins>><ins style="font-weight: bold; text-decoration: none;">p</b> nodes, the total number of links in the network would be <p> and the degree of the interconnection network is <b>2</b>. The maximum distance between nodes in the network would be the distance between nodes that are half way through the network, hence the diameter would be <b> p/2 </b>. The bisection bandwidth of the network of the interconnection would thus become 2.</ins></div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><h2>2-D Mesh</h2></div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div><h2>2-D Mesh</h2></div></td></tr>
</table>Vrmandahttps://wiki.expertiza.ncsu.edu/index.php?title=CSC/ECE_506_Spring_2011/ch12_ar&diff=45149&oldid=prevVrmanda at 00:26, 19 April 20112011-04-19T00:26:23Z<p></p>
<table style="background-color: #fff; color: #202122;" data-mw="interface">
<col class="diff-marker" />
<col class="diff-content" />
<col class="diff-marker" />
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<tr class="diff-title" lang="en">
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">← Older revision</td>
<td colspan="2" style="background-color: #fff; color: #202122; text-align: center;">Revision as of 00:26, 19 April 2011</td>
</tr><tr><td colspan="2" class="diff-lineno" id="mw-diff-left-l29">Line 29:</td>
<td colspan="2" class="diff-lineno">Line 29:</td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>The nodes are connected linearly as in an array. This type of topology is simple and low cost. However, it has several shortcoming. First of all, it does not scale well. The longest distance between two nodes, or the '''diameter''', is equivalent to the number of nodes. In addition to not scaling well, this topology can also result in high congestion. [[#References|<sup>[8]</sup>]]</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>The nodes are connected linearly as in an array. This type of topology is simple and low cost. However, it has several shortcoming. First of all, it does not scale well. The longest distance between two nodes, or the '''diameter''', is equivalent to the number of nodes. In addition to not scaling well, this topology can also result in high congestion. [[#References|<sup>[8]</sup>]]</div></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div></p></div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div></p></div></td></tr>
<tr><td class="diff-marker" data-marker="−"></td><td style="color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #ffe49c; vertical-align: top; white-space: pre-wrap;"><div><del style="font-weight: bold; text-decoration: none;"><br></del></div></td><td colspan="2" class="diff-side-added"></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><br></td></tr>
<tr><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>In a linear array interconnection network with '''p''' nodes, the total number of <b>links</b> would be <b> p-1 </b> and the <b>degree</b> of the network would be <b>2 </b>. The total link bandwidth is <b> p-1 </b> times the link bandwidth, but bisection bandwidth is equal to one link bandwidth. Since global communication must always travel through one link, bisection bandwidth summarizes the bandwidth characteristic of the network better than the aggregate bandwidth.</div></td><td class="diff-marker"></td><td style="background-color: #f8f9fa; color: #202122; font-size: 88%; border-style: solid; border-width: 1px 1px 1px 4px; border-radius: 0.33em; border-color: #eaecf0; vertical-align: top; white-space: pre-wrap;"><div>In a linear array interconnection network with '''p''' nodes, the total number of <b>links</b> would be <b> p-1 </b> and the <b>degree</b> of the network would be <b>2 </b>. The total link bandwidth is <b> p-1 </b> times the link bandwidth, but bisection bandwidth is equal to one link bandwidth. Since global communication must always travel through one link, bisection bandwidth summarizes the bandwidth characteristic of the network better than the aggregate bandwidth.</div></td></tr>
</table>Vrmanda