Final answer:
The question involves discussing the advantages and disadvantages of nested-loop and merge-join algorithms and executing a merge-join on given relations, which cannot be done due to lack of data.
Step-by-step explanation:
The question at hand involves database management concepts, specifically relating to the implementation of natural join operations between two relations in a database. The request is two-fold. The first part discusses the advantages and disadvantages of nested-loop join and merge-join algorithms, without assuming any ordering of relations.
The second part requires executing a merge-join algorithm on given populated relations "r" and "s" to demonstrate the process. Regrettably, since the populated contents of relations "r" and "s" were not provided, I cannot perform a merge-join algorithm on them.
However, I can discuss the theory behind each join method.
Advantages of a nested-loop join include its straightforward implementation and not requiring the input relations to be sorted. It is particularly efficient if one of the relations is very small.
Disadvantages are that it can be very inefficient for large datasets as it requires a loop within a loop, resulting in potentially quadratic time complexity.
The merge-join algorithm is efficient if both relations are sorted on the join key. Advantages of merge-join include better performance than nested-loop join for large, sorted datasets since it requires only a single pass through each dataset. Disadvantages include the necessity for the input data to be sorted, which can be an added cost if they are not already sorted.