Breadth First Search visits every vertex and every edge of a graph.

So, its time complexity is:

$O(V+E)$

Therefore,

$(A)-(II)$

Rabin-Karp Algorithm compares the pattern of length $m$ with possible positions in the text.

In the worst case, it may take:

$\theta((n-m+1)m)$

Therefore,

$(B)-(III)$

Depth-First Search also visits every vertex and every edge.

So, its running time is:

$\theta(V+E)$

Therefore,

$(C)-(I)$

Heap sort has worst case time complexity:

$O(n\log n)$

Therefore,

$(D)-(V)$

Quick sort has worst case time complexity:

$O(n^2)$

This happens when partitioning is highly unbalanced.

Therefore,

$(E)-(IV)$

Final matching is:

$(A)-(II), (B)-(III), (C)-(I), (D)-(V), (E)-(IV)$