Why does Dumbledore wait until Half-Blood Prince to start hunting Horcruxes?

Voldemort attempts, and fails to kill Harry. People are said to think he's still alive

-> http://ift.tt/1EwbQYA <-

Dumbedolre appears to be highly intelligent wizard. Surely he must have have understood why Voldemort didn't die - because of the conversation he had about Horcruxes. We know that Dumbedolre knew about this conversation, or at least the part that V asked about the magical item "Horcrux".

Only knowing about this conversation would not be much of a proof that he actually created one. But then Voldemort appears to be some form of alive in the Philosopher's Stone.

So... after the events of Philosopher's Stone, Dumbledore knows 2 things for sure :

1. Voldemort is still alive

2. Voldemort has asked about Horcruxes one of the Hogwarts teachers

Dumbledore is known for his guesses. He must have guessed that V has at least ONE horcrux.

So my question is, why did he wait the events up to Harry's 6th year to actually start hunting it ?