Rules: Relative Clause Reduction

1. In defining clauses, we can omit the relative pronoun in the position of object.
The boy who / whom / that you don’t like much wants to talk to you.
The boy you don’t like much wants to talk to you.
Note: In non-defining sentences you neither omit the relative pronoun nor use “that”.
My mother, who / whom that you met yesterday, wants to talk to you.
My mother you met yesterday…

2. We can use participles when reducing the sentence.
a) Present Participle Ving (simultaneous)
We stood on the bridge which connects the two halves of the city.
We stood on the bridge connecting the two halves of the city.(Present Participle)
b) Past Participle V3 or being V3 (passive simultaneous)
Two boy who was attacked by a dog was taken to hospital.
Two boy attacked by a dog was taken to hospital. (Past Participle)
c) Perfect Participle having V3 (active-explaining sth.happened before the others)
The girl who has asked a question is very clever.
The girl having asked a question is very clever.(Perfect Participle)
d) Perfect passive participle having been V3 (passive-explaining sth happened before the others)
The teacher who has been asked a question is very clever.
The teacher having been asked a question is very clever.(Perfect passive participle)

3. If “To be” verb is used after a relative pronoun we can omit “Relative Pronoun + To be”.
The car which is parked next to mine is very expensive.
The car parked next to mine is very expensive.
Hamlet,which was written by Shakespeare sometime in the early 1600s, is among the classics.
Hamlet, written by Shakespeare sometime in the early 1600s, is among the classics.

4. When the verb “have” meaning possession, we can omit relative pronoun and “have” and use with(+) or without(-).
Students who have enough knowledge and skills will be admitted.
Students with enough knowledge and skills will be admitted.
People who don’t have their ID cards can not get in.
People without their ID cards can not get in.

5. We can use infinitive “to” in the cases below.
1. The only…to
2. Superlative…to
3. The first, last, second, next…to
John is the only person who understands me.
John is the only person to understand me.
Tom is the most handsome boy who came in this school.
Tom is the most handsome boy to come in this school.
Jack is the first person who has handed in this exam.
Jack is the first person to have handed in this exam.

source : http://www.grammarbank.com/reduced-relative-clauses.html