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I'm engineer, not mathematician, so excuse me for wrong terminology, but I hope you'll understand the problem. Example situation: I have N electronic components. Each of them has reactance and susceptance components and they are different, but we know them.

$X = \{x_1, x_2, x_3...x_n\}$

$B = \{b_1, b_2, b_3...b_n\}$

One time I've measured reactance and susceptance of ONLY SEVERAL serially connected components, and achieve this

$X_{full} = x_a + x_b + ... + x_i$

$B_{full} = b_a + b_b + ... + b_i$

Is there methods, except of exhaustive search, to find WHICH devices are in the chain? Also, problem is more complicated because we knows not exact values of components, but with some deviation $x_n \pm \Delta x $, and also full sum is $X_{full} \pm \Delta X $. I hope you get the point with this simplified example. Ideal case when I get such result "probability of combination 1,3,5 is 90%, 2,4,6 is 80% etc..."

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  • $\begingroup$ "Subset-sum problem" (q.v.) asks whether a given number $X$ is the sum of a subset of the given numbers $\{\,x_1,x_2,\dots,x_n\,\}$. No algorithm significantly better than exhaustive search is known. There is much literature to be found by websearch. $\endgroup$
    – Gerry Myerson
    Commented May 29, 2016 at 13:19
  • $\begingroup$ @GerryMyerson Thank for your reply! But how to be with inaccurate values of resistance? $\endgroup$
    – artsin
    Commented May 29, 2016 at 18:01
  • $\begingroup$ As I wrote, there is much literature on the subset-sum problem. I would encourage you to have a look at it. I don't know whether your exact problem is there, but it might be, or the tools with which to tackle it might be. $\endgroup$
    – Gerry Myerson
    Commented May 29, 2016 at 22:46
  • $\begingroup$ If you view each component as an interval of ratios (x/B) where the interval represents the uncertainty in actual values, the target value will be a mediant sum (x/y mediant z/w is (x+y)/(z+w) and lies between the two) of values coming from the intervals, and the best you can conclude is that some components may have a higher than target ratio and some a lower than target ratio. Even knowing X_full and B_full and i does not help much when i is large. Can you get X and B for some subcircuits? Gerhard "Maybe Break Into Smaller Problems" Paseman, 2016.05.29. $\endgroup$
    – Gerhard Paseman
    Commented May 29, 2016 at 23:52

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