CostB1=V(A,S)×Size(A)=500×10=5,000 bytesCost sub cap B 1 end-sub equals cap V open paren cap A comma cap S close paren cross Size open paren cap A close paren equals 500 cross 10 equals 5 comma 000 bytes The reduced relation R′cap R prime

When solving distributed database system problems, keep these fundamental principles in mind:

: Always start by identifying the primary key. For vertical, check that every attribute appears at least once. For horizontal, ensure predicates are complete and mutually exclusive.

A semi-join ( R ⋉ S ) projects the join attributes of S and ships only those to the site of R , reducing the size of R before shipping it for the full join.

One of the first challenges in a distributed environment is deciding how to split data (fragmentation) and where to put it (allocation). Horizontal vs. Vertical Fragmentation

In a standard 2PC protocol, the Coordinator fails after sending "PREPARE" messages but before writing the final decision to the log. The participants have voted "YES" and are waiting. Why is this a problem? How does a 3-Phase Commit (3PC) solve it?

Now read_TS(D)=5, write_TS(D)=20. TS(T1)=10 < write_TS(D)=20 → reject (obsolete write).