1. Distributed Application Partitioning
ECE 556 Final Project
Brad Colvin

2. Problem Overview
Optimally allocating the components of a distributed program over several machines.
Communication between machines is assumed to be the major factor in application performance
Can be represented by a graph
NP-hard for case of 3 or more terminals
Can be thought of as a partitioning problem

3. Collapse the graph Given G = {N, E, M} N is the set of Nodes
E is the set of Edges
M is the set of machine nodes

4. Dominant Edge Take node n and its heaviest edge e
Edges a1,a2,…ar with opposite end nodes not in M
Edges b1,b2,…bk with opposite end nodes in M
If w(e) >= Sum(w(ai)) + Max(w(b1),…,w(bk))
Then the min-cut does not contain e
So e can be collapsed

5. Machine Cut
Let machine cut Mi be the set of all edges between a machine mi and non-machine nodes N
Let Wi be the sum of the weight of all edges in the machine cut Mi
Wi’s are sorted so W1>=W2>=…
Any edge that has a weight greater than W2 cannot be part of the min-cut

6. Zeroing
Assume that node n has edges to each of the m machines in M with weights w1<=w2<=…<=wm
Reducing the weights of each of the m edges from n to machines M by w1 doesn’t change the assignment of nodes for the min-cut
It reduces the cost of the minimum cut by (m-1)w1

7. Order of Application
If the previous 3 techniques are repeatedly applied on a graph until none of them are applicable
Then the resulting reduced graph is independent of the order of application of the techniques

8. Output List of nodes collapsed into each of the machine nodes
Weight of edges connecting the machine nodes

9. Credits
Main Paper: Graph Cutting Algorithms for Distributed Applications Partitioning
Graphs from: Fast Optimally-Preserving Graph Reduction for Dynamics-Based Partitioning of Distributed Object Applications
Authors: Karin Hogstedt, Doug Kimelman, VT Rajan, Tova Roth, and Mark Wegman