Oral History Data Organization

You are helping scientists analyze oral history data they have
collected by interviewing members of a village.

From these interviews they have learned about a set of n people (all
are dead now) whom we will denote P1, P2, ... Pn. The have also
collected facts about when these people lived relative to one another.
Each fact has one of the following two forms:
For some i and j, person Pi died before person Pj was born, or
For some i and j, the life spans of Pi and Pj overlapped at least
partially.

Naturally they are not sure that all these facts are correct.
What they would like you to determine is whether the data they have
collected is at least internally consistent, in the sense that there
could have existed a set of people for which all the facts they have
learned simultaneously hold.

An efficient algorithm is proposed to do this: either it produces
proposed dates of birth and death for each of the n people so that all
the facts hold true, or it reports (correctly) that no such dates
can exist. That is the facts collected by the scientists are not
internally consistent.