1. Algorithms for Executing query

A.External sorting
B.Sort strategy
C. Merge strategy
2. Algorithm for select operation
A. Methods and Implementation of join operation

1. Algorithms for executing queries, especially for sorting and merging, play an essential role in database management systems (DBMS). Let's look at each of the items you've mentioned in this context:

A. External Sorting: External sorting algorithms are used when the data to be sorted does not fit into the available main memory (RAM) and must instead be processed using external memory (e.g., disk storage). The classic example of this is External Merge Sort, where data is divided into manageable chunks that are sorted in memory and then written back to disk. These chunks are then merged into a final sorted order.

B. Sort Strategy: A sort strategy refers to the method chosen by the database to order data based on a query that requests a sorted output (e.g., using an ORDER BY clause). The database may use various internal and external sorting algorithms depending on the size of the data and the indices available. For smaller datasets that fit in memory, quicksort or heapsort might be used, whereas external merge sort might be used for larger datasets.

C. Merge Strategy: Merge strategy is often associated with merge join, which is a method of joining two tables. In the context of sorting, it can refer to how sorted runs are combined in external merge sort. In a merge join, both inputs must be sorted on the join key, and the algorithm successively reads the smallest element from each input and outputs matching rows to the result set.

2. Algorithm for select operation:

In the context of SQL and databases, the SELECT operation is about retrieving data from the database. When dealing with SELECT operations that require joins, several algorithms or methods can be used to implement join operations, including:

A. Nested Loop Join: This algorithm is the simplest form of join, where each row from one table (the outer loop) is compared to all rows from another table (the inner loop) to find matching rows based on the join predicate. This method can be inefficient for large datasets because it involves many comparisons.

B. Sort-Merge Join: This method requires each dataset to be sorted on the join key. Then, both datasets are scanned, and matching rows are combined into the result set. This approach is more efficient than nested loops for large, sorted datasets.

C. Hash Join: In a hash join, a hash table is built using the join attribute of the smaller table. The larger table is then scanned, and the hash table is probed to find matching rows based on the hash value of their join attributes. Hash join is highly efficient for equi-join operations and is typically the fastest join method for large, unindexed datasets.

D. Index Join: If one or both tables have an index on the join column(s), the database can use this index to efficiently find matching rows. This can be orders of magnitude faster than the other methods if an index exists and is applicable to the query, as it avoids full table scans.

The optimal selection of the join algorithm depends on many factors, including the size of the tables, the presence of indices, the type of join predicates, and the specific DBMS's cost-based optimizer's estimates and decisions.