Algorithms for Mining Tuples of Data on huge sample space
For Apriori, you do not need to have tuples or vectors. It can be implemented with very different data types. The common data type is a sorted item list, which could as well look like 1 13 712 1928 123945 191823476 stored as 6 integers. This is essentially equivalent to a sparse binary vector and often very memory efficient. Plus, APRIORI is actually designed to run on data sets too large for your main memory!
Scalability of APRIORI is a mixture of the number of transactions and the number of items. Depending of how they are, you might prefer different data structures and algorithms.
I read that Apriori algorithm is used to fetch association rules from the dataset like a set of tuples. It helps us to find the most frequent 1-itemsets, 2-itemsets and so-on. My problem is bit different. I have a dataset, which is a set of tuples, each of varying size - as follows :
(1, 234, 56, 32)
(25, 4575, 575, 464, 234, 32)
. . . different size tuples
The domain for entries is huge, which means that I cannot have a binary vector for each tuple, that tells me if item 'x' is present in tuple. Hence, I do not see Apriori algorithm fitting here.
My target is to answer questions like :

Give me the ranked list of 5 numbers, that occur with 234 most of the time
Give me the top 5 subsets of size 'k' that occur most frequently together

Requirements : Exact representation of numbers in output (not approximate), Domain of numbers can be thought of as 1 to 1 billion. 
I have planned to use the simple counting methods, if no standard algorithm fits here. But, if you guys know about some algorithm that can help me, please let me know