python - How to order/sort a 2D table of dependencies -


i'm curious if there higher level theory/approaches/algorithm solving problem have.

i'm working on network routing problem (a proprietary radio network). way of example, have network of 5 devices. each device, can measure how can hear other devices. 0th root node interesting source. in table form, might end like:

    _0_ _1_ _2_ _3_ _4_ 1 | 21   -  42  55   0 2 |  0  63   -  18  20 3 | 20   0   0   -   0 4 |  0   0  13   0   -

each row indicates how device can hear other 5 sources. want sort them each device gets best sum signals preceding elements. simple case, ordering might 1, 3, 2, 4. 3, 1, 2, 4. in fact, second better because 1 can hear both 0 , 3. 3, 2, 1, 4 work well.

i'm trying determine kind of algorithm can use order these. there's bit of traveling salesmen it, , don't need "best" sort. pretty sort. need scale 9 devices 10 sources.

any thoughts, help, nudges, tips, hints appreciated.

this problem can modeled minimum feedback arc set problem, np-hard problem. original graph complete directed graph, weight of each edge (v0, v1) being signal strength v0 v1. after computing maximum feedback arc set, topological sort give ordering has maximum total signal.


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