language agnostic - Determining edge weights given a list of walks in a graph -


These questions are in relation to the list of works done in the succession and the data set with the total time required to complete them. I am thinking that it would be possible to determine useful things about the length of the tasks, either as either or with some initial cavity based on the proper domain knowledge. I think graph theory will be a way of presenting this essence in essence, and there is a good understanding of things, but I am definitely unable to know whether I am on the right path. Apart from this, I think it is a very interesting question to crack, so we can go here:

  1. Is it possible to determine the weight of the edges in the guided weighted article Is there a list of walks in that graph? I recognize the quantity and quality of the sequence on the identified pathways, will direct the quality of any possible answer, but we estimate all possible movements and their length is given. If a definitive answer is not possible, then what type of things about the graph can be concluded ? How do you reach those findings?

  2. What if several possible moves with different lengths? Can you calculate a decent average (or other instance measurement) for each shore, which can be achieved enough ordering on different routes? How will some permutations break from the set of available data, affect the accuracy of calculations?

  3. After all, if you had a set of initial estimates in the form of load and those who used them had to be refined? Will it improve the efficiency of your cavities and how do you implement additional information?

EDIT: Explanation on the difficulties of a plain linear algebraic approach. Consider the following set of walks: 

  a = 5b = 4b + c = 5 a + b + c = 8

A matrix equation It is not possible to solve these values, but we still want to estimate the conditions. Some useful initial data may be available in Scenario 3, and in any case we can implement the knowledge of the real world - such that the length of work can not be negative. I would like to know if you have ideas about how we can make proper assessment. And we also know what we do not know - like when there is not enough data to tell one from B.

Linear algebra seems like an application.

You have a set of linear equations that you need to solve.

For example, if the length of the work is for T1, T2, T3 3 functions.

and you are given

T1 + T2 = 2 (Task 1 and 2 to 2 hours) T1 + T2 + T3 = 7 (all 3 works T2 = T3 = 6 (Tasks take 2 and 3 6 hours)

Resolution t1 = 1, t2 = 1, t3 = 5 < / Code>.

You can use any linear algebra technique (for example :) to solve them, which will tell you that there is no unique solution, no solution or no unlimited number of solutions (No other possibilities are possible).

If you think that linear equations do not have a solution, you can try to add a very small random number to some workload / coefficients of the matrix and try to solve it again. You can. (I believe that falls). Matrix is ​​notorious for the fundamentally changing behavior with small changes in values, so it will probably give you approximate approximate answer

Or maybe you can start a little sluggish work in each walk You can try (i.e. add more variables) and try to choose the solution of the new equations, where the sluggish function has some linear barriers (such as 0 & lt; S_i <0.0001 and s_i at least) Using techniques.


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