# Permutation-based parallel-by-serial calculation of resistance in a circuit

We have employed a computational method for identifying order of receipt of signals from senders based on a telecommunications and/or EE technique. However, we would like to find out which permutation-based technique in EE this stems from.

The technical report states the following:

“The approach is similar to computing resistance in a circuit, which is a parallel-by-serial procedure. The parallel conductivities from all preceding components to a target component are all summed, within a permuted ordering of components, to determine the phase conductivity of the permutation, and then the order conductivity is formulated by cascading all the phase conductivities.”

Note, all the components have to be the same type, maybe resistors or capacitors, but differ by varying rating of their units (10 Ohms, 20 Ohms, 30 Ohms, ..., 500 Ohms). However, you don't know their ratings, but rather, only a label like 1,2,3,4,5. During the calculation, the order of all of the components in the circuit are permuted(shuffled), and all the resistance up to a target is calculated – but each component is once the target.

The application of this calculation would be employed for numerous e.g. circuit boards, where the goal for each board would be to determine if order 7-->3-->1-->2-->5-->6-->4 resulted in the greatest resistance. Another board might have components with labels 12, 3, 55, 13, 92, and 105 (which in truth have different ratings, but you don't know what the ratings are). Overall, you are trying to determine for each board what order of labels results in the greatest resistance. Then over several hundred boards you can develop a picture of what the order is for labels which results in the greatest resistance (on average).

Is there a standard permutation-based technique in EE to find resistance in a circuit that is both serial and parallel?

• I think the answer is probably "no"... Assuming you have no EE experience: Basic lumped-constant circuit analysis does not use any of the kind of stochastic random rearrangement of components you seem to be implying. In CompE/math terminology, a circuit is a graph of nodes (where each node has a voltage and KCL applies) and each edge is a component (e.g. resistor). KVL applies around each complete loop/mesh. Ohm's Law constrains the relation of current and voltage. Solving this system of equations yields all node voltages and mesh currents. No need to perform any permutation. – MarkU Jul 23 '16 at 3:44
• The first part of your question and the text you're quoting from are pure technobabble -- they use a lot of technical terms without saying anything specific. They're equivalent to saying, "I created this fancy turkey dinner with all of the trimmings by 'cooking'." Well, duh! You need to be a lot more specific about the system(s) you are describing. – Dave Tweed Jul 23 '16 at 12:23
• Thanks - very helpful. We were basically saying, we need to figure out exactly what the authors are talking about. Sounds like there's not a permutation-based anything for determining resistance in a circuit. – user117542 Jul 23 '16 at 17:48