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POUnbiased (random?) selection algorithm
 

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    <p><strong>The problem:</strong> There are X number of properties, all floats between 0 and 1.<br> Choosing a property has a constant cost of C. (as opposed to leaving it at 0)<br> The cost of a property is proportional to its value (be it exponential or linear) How would I go making an unbiased (randomized?) selection of a subset of properties given a budget B?</p> <p>Lets say the "cost" function is something like the following: (exponential version)<br></p> <pre><code>cost = C*sgn(x) + ke^(ax) 0 &lt;= x &lt;= 1 Constants: C, k, a </code></pre> <p>My first thought was some kind of optimization problem, but there's really nothing to maximize/minimize. I guess you could view it as finding a solution as close as possible to B. That doesn't really make sense though, since I'm not looking for the "best" solution, any solution close enough to B would do.</p> <p>I then started looking at random sampling which seems like the most similar problem. I've found something called random weighted sampling which looks promising, but I'm not sure how the "budget" would fit in.</p> <p>I'm not looking for something very exact or that guarantees independent results. Perhaps I am over complicating this? At this stage I'm just looking for something quick and dirty that can be implemented in Java or a similar language.</p> <p><strong>Edit:</strong> I followed the advice below and posted the question at <a href="https://math.stackexchange.com/questions/64914/unbiased-random-selection-algorithm">here</a> at math.stackexchange.com. I think I made it a lot more clear over there what I'm trying to achieve</p>
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    1. COThe problem is not clear to me. Do you want the random selection not regard the cost? Then just do a random shuffling, and then from the first element select all until you are inside the budget.
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    2. COIt should regard the cost. Basically I want it too choose some of the properties with various "strength", creating a balance between the strength of the properties (due to exponentially higher costs), and between the amount of properties (due to the constant cost of a property). A selection can contain a few strong properties or a lot of weak ones, or anything in between. Hope that makes sense.
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    3. COWhy not draw samples from the desired distribution, and if the sample is too expensive (doesn't fit in your budget) simply discard it and draw a new sample.
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