This has been taken from a tutorial by Zeth Willie. I can't recommend his tutorials enough, seriously go check them out. He has a wonderful way of explaining things and he really goes in depth into topics.

He explains that this particular way of attaching an object to a curve is a less chunky way than the more well known 'attach to motion path'.

• Create a curve, you will probably need to rebuild curve so that the U value goes between 0 and 1. Pretty useful for later.
• Make an empty pointOnCurveInfo node using 'shadingNode -asUtility pointOnCurveInfo -n "myName". Obviously name it whatever you want.
• Open connection editor. Load the shape node of the curve into the left and the pointOnCurveInfo node into the right.
• Connect worldSpace to inputCurve.
• Then load up the pointOnCurveInfo into the left and the object you're trying to attach intot he right side.
• Connect result.position to translate.

Voila.

For some reason, Maya makes an addDoubleLinear when you attach an object to a motion path, and it connects it in a way that causes a cyclic dependency. You don't actually need this addDoubleLinear node.
To get rid of it you can shift+MMD the motion path node and the node of the object that's attached to the motion path, this will open up the Connection Editor. On the motion path node side, expand 'allCoordinates' and on the constrained node expand 'translate'. Now connect the 'xCoordinate' from the left to the 'translateX' on the right. Do the same for Y and Z. Now you can delete the addDoubleLinear node.

Make sure to remove unused influences, limit max influences and prune small influences to improve rig performance.

The profiler can locate performance bottlenecks in your scene by recording and demonstrating in a graph the amount of time that each process consumes.