1. Trending Topics Are NOT Always The Most Popular Things People Are

Weird, huh?
But for a topic to become a trend, it actually has to meet several criteria beyond just being “popular:”

► It has to have no foul language in it.
► It has to be popular with a lot of people in a short period of time—it has to “peak” in popularity.
► Total tweets AND the total number of people tweeting BOTH matter. But unless there are tweets from a lot of people—what Twitter calls “widespread popularity“—total tweets will NOT matter.

A hashtag? is composed of keywords and the ?#? symbol which will mark different topics in a tweet and bring them all together in one thread.

These are useful in categorizing discussions and helping Twitter users find conversations that they are truly interested in. If you plan to come up with an effective hashtag, you have to understand the basic guidelines. Dedication is important in making a hashtag popular and well-received; so with relevance to the general public. The hashtags may be present in any part of the tweet so long as it is preceded by the # sign. Read about the do's and don't's of hashtags.

What is a trend?

Trends are not just words, phrases or hashtags that are used a lot, or the trends box would look the same every day and always feature ‘and’, ‘if’, ‘the’ and ‘Justin Bieber’. Twitter says its trends are ‘determined by an algorithm’ and that they identify ‘topics that are immediately popular’.

When topics gain above average mentions in a short period of time, they can become trends. If there are not many topics achieving this (for example at non-peak times) then it becomes easier to create a trend. This may go some way to explain how Jeremy Paxman’s beardmanaged to trend and subsequently caused a media storm.

There is, of course, a level of unknown as Twitter doesn’t want the system to be cheated.

How many tweets?

I am thinking of below algorithm, but not sure if there is a better algorithm.

Assuming Twitter uses last 24 hours (wild guess) of hashtags frequencies of tweets to compute the trending topics. To get the top 100 (let's say) trending topics, a MapReduce job can be run and top 100 values can be picked. This can be further optimized by maintaining hourly aggregates of hashtags.

But, I am not sure if it makes sense to compute all the hashtags frequencies (probably millions) just to find the top 100 trending topics. Probably, there is a better way. 

Similar problem also arises in finding search query trends of Google searches and its probably harder too.