CS622 Page 1

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Mesh Network Design

• Backbone network design goals
• Direct path between source and destination.
• Well-utilized components
• Use high speed lines to achieve economy of scale.
• These goals are self-contradictory.

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Examples of Bad DesignToo Many Direct Links
Nodes with High Degree

• 45 node network with cost264,411/month

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Design with Only High Speed Links

• Warning sign high average number of hops

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2-Level Design (96,777)

• Pick heavy traffic nodes as interior nodes of
  the tree.

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More Reliable Design

• Instead of tree, interior nodes form a
  2-connected graph.

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A Different Interior Topology

• Reduce cost from 112,587?108,724

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Add More Backbone Nodes

• 103,107 cost reduced.

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Even Lower Cost Design

• 101,806

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Algorithm Complexity and Design Space Size

• Even if a subset of designs can be identified we
  are still dealing with big design space.
• Here the number in D is based on 2 c(45,2)

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Mentor Algorithm KKG91

• Assume single link type with capacity C.
• Choose backbone sites. (Also called Threshold
  Cluster Algorithm)
• Calculate the normalized weight NW(Ni)W(Ni)/C
• Choose sites with NW(Ni) gt WPARM (threshold)
• Group end sites around a backbone site, x, based
  onCost(x, Ni)/MAXCOST lt RPARM.Where MAXCOSTMax
  i,j Cost(Ni, Nj)
• If there are sites not covered in groups, compute
  merit(n)1/2(MaxDistCtr-distCtrn)/MaxDistCtr
  1/2(Weightn/WeightMax)Here
  andCenter of Mass (xctr, yctr) defined by
• Sort the merit functions. The node with largest
  merit get picked asbackbone node. Group end
  node around it. Repeat until all nodes are
  covered in groups.

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Mid Stage of Threshold Cluster Algorithm

• Big Squares are Backbone nodes.

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Final Stage of Threshold Clustering

• Based on merit(), three backbone nodes are picked.

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Mentor Algorithm Steps 2-3

• Pick median node (root node of the network) with
  smallest Moment()
• Build a restricted Prim-Dijkstra tree rooted at
  median.Here only backbone nodes can be the
  interior nodes of the tree.
• Sequencing Node Pair Prepare adding additional
  direct links to the tree.
• Use the tree to list node pair in sequenceThe
  node pair with longer path will list first
• Choose home node H for each node pair (Ni,Nj) (H
  and Nx are intermediate nodes along the path)
  that satisfies Cost(Ni, H)Cost(H,Nj)lt Cost(Ni,
  Nx)Cost(Nx,Nj).

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Restricted Prim-Dijkstra Tree

• Note that there is an end node that violate the
  constraint.

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Sequencing Node Pairs
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Mentor Algorithm Step 5

• Decide which node pairs deserve direct links.
• Start with the top node pair (N1,N2) in the
  sequence.
• Calculate the utilization uTraf(N1,N2)/(nC)wher
  e nceil(Traf(N1,N2)/C).
• If ugtutilmin, add direct link between N1 and N2.
• If ult utilmin, add Traf(N1,N2) to Traf(N1,H) and
  Traf(H,N2). Here H is the home of (N1,N2).
• Remove (N1,N2) from the sequence and repeat Step
  5 again until all node pairs are processed.

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Complexity of Mentor Algorithm

• The three basic steps backbone selection, tree
  building, and direct link addition are all O(n2).
• It can be executed pretty fast.
• Typically we will generate a set of designs based
  on the same threshold parameter, e.g., different
  a in the restricted Prim-Dijkstra tree, or
  different node pair sequence (note that the
  sequence are not unique).
• We then pick the best design from the set.

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Example of Mentor Algorithm Result

• 15 sites, 5 backbone nodes

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Mentor Algorithm Design 2

• 221,590, same 5 backbone nodes, with lower
  utilmin0.7

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Mentor Algorithm Design 3

• Same 5 backbone nodes but with different tree.
  209,220.

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Cost of Designs vs. a and utilmin

• A0.1 and 1-utilmin0.1 is the best value.

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Cost vs. Size of Backbone