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Analogy with electrostatics

Posted by schreib on 27 Sep 2011 at 08:26 GMT

The SinkSource algorithm can be better understood using an analogy to electrostatics. The analogy can be extended to the weighted case, but we will state it without any weights.
Think of r(v) as the electrostatic potential at node v. The nodes of V+ are connected to a voltage of 1, and the nodes of V- are grounded to a voltage of 0. Then, r(u)-r(v) corresponds to the electric field between the two nodes, and S corresponds to the total electrical energy - the electrostatic configuration indeed minimizes the energy. The local equation at a node is the Gauss equation, that, because no charges are present, becomes the Laplace equation. The solution has the electric potential at each node equal the average of its neighbors, which is exactly the result presented here as eq. (1).

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