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Minimum set of constraints required to located a point within a timeline

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$begingroup$

I have a very specific problem, applicable to my own use-case of what I am trying to do and I was wondering if anyone can help me come up with, or point me directions towards how can I go about solving it. Or whether there is a simple mathematical model I can apply to solve the problem.

Given a fixed timeline, or time represented on a numberline extending far into the future upto a particular value, and extending into the past with a particular value, I need to be able to find the minimum set of constraints that are able to locate a particular point (within a particular accuracy) that lies at an unknown point on the timeline.

This is the solution that I currently have:

As shown in the diagram above, I initially add two constraints:
C1: x = X - 5 and y = Y where Y is some time in the future uptil where I am trying to find my point, lets assume its 25 in this case. This is a known numeric initial value. Similarly, the second constraint is y = X+5 and and x = 25 or any value in the past. Based on where the point is located, it will reject the first constraint, or the second, or both, or accept both. In all equations, 5 is the minimum accuracy to which I want to locate the point. This helps us make the following table:

In step 2, if I want to explore Case 2, I move further to the left, and define another set of constraints similar to the previous one.

This allows me to come up with a general equation for the number of constraints required (given that I add two at each step):

5 + 5*2 (n - 1)

where n = number of iterations.

So, if I wanted an accuracy uptil 25 to the left, I would need exactly n = 3 iterations and therefore a total of 6 constraints.

The question I have is that, even though I am adding two constraints at each step (coz that seems to be the minimum number I can add to be able to locate the point), is there any other way to arrive at the minimum number of constraints, or whether there is a mathematical model that would help me solve it for the minimum number of constraints required given that I want to locate a point within an accuracy of 5. I've thought of Linear Programming, but linear programming doesn't really help me with coming up with the minimum set of constraints.

optimization constraints

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0

$begingroup$

I have a very specific problem, applicable to my own use-case of what I am trying to do and I was wondering if anyone can help me come up with, or point me directions towards how can I go about solving it. Or whether there is a simple mathematical model I can apply to solve the problem.

Given a fixed timeline, or time represented on a numberline extending far into the future upto a particular value, and extending into the past with a particular value, I need to be able to find the minimum set of constraints that are able to locate a particular point (within a particular accuracy) that lies at an unknown point on the timeline.

This is the solution that I currently have:

As shown in the diagram above, I initially add two constraints:
C1: x = X - 5 and y = Y where Y is some time in the future uptil where I am trying to find my point, lets assume its 25 in this case. This is a known numeric initial value. Similarly, the second constraint is y = X+5 and and x = 25 or any value in the past. Based on where the point is located, it will reject the first constraint, or the second, or both, or accept both. In all equations, 5 is the minimum accuracy to which I want to locate the point. This helps us make the following table:

In step 2, if I want to explore Case 2, I move further to the left, and define another set of constraints similar to the previous one.

This allows me to come up with a general equation for the number of constraints required (given that I add two at each step):

5 + 5*2 (n - 1)

where n = number of iterations.

So, if I wanted an accuracy uptil 25 to the left, I would need exactly n = 3 iterations and therefore a total of 6 constraints.

The question I have is that, even though I am adding two constraints at each step (coz that seems to be the minimum number I can add to be able to locate the point), is there any other way to arrive at the minimum number of constraints, or whether there is a mathematical model that would help me solve it for the minimum number of constraints required given that I want to locate a point within an accuracy of 5. I've thought of Linear Programming, but linear programming doesn't really help me with coming up with the minimum set of constraints.

optimization constraints

share|cite|improve this question

asked yesterday

QPTRQPTR

15219

$endgroup$

add a comment | 

$begingroup$

I have a very specific problem, applicable to my own use-case of what I am trying to do and I was wondering if anyone can help me come up with, or point me directions towards how can I go about solving it. Or whether there is a simple mathematical model I can apply to solve the problem.

Given a fixed timeline, or time represented on a numberline extending far into the future upto a particular value, and extending into the past with a particular value, I need to be able to find the minimum set of constraints that are able to locate a particular point (within a particular accuracy) that lies at an unknown point on the timeline.

This is the solution that I currently have:

As shown in the diagram above, I initially add two constraints:
C1: x = X - 5 and y = Y where Y is some time in the future uptil where I am trying to find my point, lets assume its 25 in this case. This is a known numeric initial value. Similarly, the second constraint is y = X+5 and and x = 25 or any value in the past. Based on where the point is located, it will reject the first constraint, or the second, or both, or accept both. In all equations, 5 is the minimum accuracy to which I want to locate the point. This helps us make the following table:

In step 2, if I want to explore Case 2, I move further to the left, and define another set of constraints similar to the previous one.

This allows me to come up with a general equation for the number of constraints required (given that I add two at each step):

5 + 5*2 (n - 1)

where n = number of iterations.

So, if I wanted an accuracy uptil 25 to the left, I would need exactly n = 3 iterations and therefore a total of 6 constraints.

The question I have is that, even though I am adding two constraints at each step (coz that seems to be the minimum number I can add to be able to locate the point), is there any other way to arrive at the minimum number of constraints, or whether there is a mathematical model that would help me solve it for the minimum number of constraints required given that I want to locate a point within an accuracy of 5. I've thought of Linear Programming, but linear programming doesn't really help me with coming up with the minimum set of constraints.

optimization constraints

share|cite|improve this question

asked yesterday

QPTRQPTR

15219

$endgroup$

share|cite|improve this question

asked yesterday

QPTRQPTR

15219

share|cite|improve this question

asked yesterday

QPTRQPTR

15219

asked yesterday

QPTRQPTR

15219

asked yesterday

QPTRQPTR

15219