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Example 1: Should we say this

The authors study the load balancing problem and present greedy algorithms for it.

or this

The authors study the load balancing problem and they present greedy algorithms for it.

Example 2: Should we say this

We design algorithms for the problem and then we show that these algorithms are efficient.

or this

We design algorithms for the problem and then show that these algorithms are efficient.

closed as primarily opinion-based by Dan Bron, Hellion, jimm101, user66974, tchrist Feb 25 '17 at 15:20

Many good questions generate some degree of opinion based on expert experience, but answers to this question will tend to be almost entirely based on opinions, rather than facts, references, or specific expertise. If this question can be reworded to fit the rules in the help center, please edit the question.

  • What does your research tell you? – AmE speaker Feb 22 '17 at 16:09
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Technically, both sentences are correct. However, because these are compound sentences, the rule of Conjunction Reduction would apply.

This rule basically says that a common feature of two coordinated sentences can be omitted from the second sentence. Citation

Therefore you should skip the second personal pronoun.

But, it should be noted that occasionally it would also be correct to include the second pronoun anyway, in order to add emphasis.

For example, this sentence uses the pronoun twice in order to add emphasis:

"I washed the dishes and I swept the floor so you need to do the mopping!"

It would be correct to say "I washed the dishes and swept the floor..." but that second "I" makes it clearer to the listener why she or he has to do the mopping!

This discussion on Compound Reduction is also worth reading:

I <verb> and am <rest of sentence>

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