Subset sum - probability of solution existence

Asked Sep 30 '17 at 22:25

Active Oct 01 '17 at 00:42

Viewed 277 times

We have a set of integers in which there may be numbers from $-n$ to $n$ (excluding of course zero).

The set contains $2\cdot k$ numbers ($2 \cdot k < n$).

We assume that the numbers are random and the probability of random numbers is equal.

What is theoretically the chance of a solution existence to solve a subset sum problem for this set of numbers?

-- Edit:

Number of positive numbers in set is equal number of negative numbers (this is $k$).

edited Oct 01 '17 at 00:42

asked Sep 30 '17 at 22:25

Aurelio

It would help if you would tell us what a subset sum problem is. – Gerry Myerson Oct 01 '17 at 05:18
Question: Is there a subset of a set whose sum of elements sums to 0? https://en.wikipedia.org/wiki/Subset_sum_problem – Aurelio Oct 01 '17 at 06:13
I suspect there's no simple answer as a function of $k$ and $n$. Some special cases are easy, e.g., $k=1$. – Gerry Myerson Oct 01 '17 at 11:46

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