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Optimal Partitioning Algorithm

This is an implementation in Java of an Optimal Partitioning Algorithm (MCOP algorithm by Wu et al.).

The algorithm takes a weighted graph as input which represents your application's operations/calculations as the nodes and the communication between them as the edges. Each node has two costs: the first is the cost of performing the operation locally (e.g. on the mobile phone) and the second is the cost of performing it elsewhere (e.g. in the cloud). The weight of the edges is the communication cost to the offloaded computation. It is assumed that the communication cost between operations in the same location are negligible.

The result contains information about the costs and reports which operations should be performed locally and which should be offloaded.

There are different cost models in order to choose what you want to optimize for (time, energy cost or a balance). You can also create your custom cost model if these do not satisfy your needs.

In order to avoid adding more work to an operation which is already already costly, we suggest that you create the graph once at application startup and update the edge costs if the network situation changes. The graph can be re-used for multiple calculations.

Create Input

In order to create the graph, start by creating Node objects and connect them via edges. An /unoffloadable/ node represents an operation which must be performed on the mobile device. There must be at least one such node; this is where the algorithm will start calculating.

These nodes will be the same ones returned by the algorithm, so we recommend that you give these variables a memorable name related to their goal, e.g. takePicture, applySepia, etc.

The units are abstract. The algorithm will work as long as you keep them consistent.

Offload.Node a, b, c, d, e, f;

//parameters:
//local cost, remote cost, isOffloadable (default: true)
a = new Offload.Node(0, 0, false);
b = new Offload.Node(4, 1);
c = new Offload.Node(8, 2);
d = new Offload.Node(8, 2, false);
e = new Offload.Node(4, 1);
f = new Offload.Node(8, 2);

//parameters:
//target node, transmission cost
a.setEdge(b, 10);
b.setEdge(c, 6);
c.setEdge(d, 5);
d.setEdge(e, 5);
e.setEdge(f, 4);

Calculate What to Offload

Once you have created the nodes and edges, create an Offload object, initializing it with the nodes. Choose a cost model and call Offload.optimize() with it. The CostModels class contains constructors for the models implemented by this package.

Offload Offload = new Offload(a, b, c, d, e, f);
Offload.Result result = Offload.optimize(CostModels.responseTime());

Some cost models need more information:

//parameters:
//energy consumption while computing, idling, transmitting, omega
result = Offload.optimize(CostModels.energyConsumption(0.9f, 0.3f, 1.3f));
result = Offload.optimize(CostModels.weightedTimeAndEnergy(0.9f, 0.3f, 1.3f, 1f));

Getting Results

The result object contains the results of what to offload and what to keep local. The local and remote sets contain the nodes you gave the Offload object in the constructor, so if you gave the nodes significant names, you can perform a check such as result.local.contains(applySepia).

//set of nodes which should be calculated locally
Set<Node> local = result.local;

//set of nodes which should be calculated remotely
Set<Node> remote = result.remote;

//cost of performing all computation locally
float originalCost = result.originalCost;

//cost when using the local/remote partitioning of this object
float cost = result.cost;

//saved costs relative to performing all computation locally, between 0 and 1.
//savings = 1 - (result.cost / result.originalCost)
float savings = result.savings;

Modify an Old Input and Update Edge Costs

It is possible to update the edge costs of an input, simply by using the same setEdge function between different optimize calls. This way you can reuse the same objects but only update the transmission costs if your app detects changes in the network situation.

Offload offload = new Offload(a, b, c, d, e, f);
Offload.Result result1 = Offload.optimize(CostModels.responseTime());
a.setEdge(b, 1);
Offload.Result result2 = Offload.optimize(CostModels.responseTime());

Implement a Custom Cost Model

If none of the provided cost models satisfy your needs, you can create your own by implementing the CostModel interface and passing it to Offload.optimize().

static class MyCostModel implements CostModel {
    public void setNodes(final Offload.Node[] nodes){
        ...//if access to nodes is necessary
    }

    public float localCost(float in){
        return in*...//for modifying the local costs
    }

    public float remoteCost(float in){
        return in*...//for modifying the remote costs
    }

    public float transmissionCost(float in){
        return in*...//for modifying the transmission costs
    }
}

Output in dot Format

We also provide a built-in way to create a string in dot-format which shows the graph before and/or after the optimization. The optimized graph will be colored – blue for locally computed and red for remotely computed. You can use tools which understand the dot-format to generate a graph; for example GraphViz which has the dot command and is likely available for your platform.

Offload offload = new Offload(a, b, c, d, e, f);
Offload.Result result = offload.optimize(CostModels.responseTime());
String dotformat = DotExporter.fromResult(result);

Or to get the dot string before optimization

String dotformat = DotExporter.fromNodes(a, b, c, d, e, f)