Exact-3D-Matching: Given a set $S$ and a collection of three-element subsets of $S$, called triples, is there a sub-collection of disjoint triples that exactly cover $S$?
Given a set $S$ of $3n$ integers, can it be partitioned into $n$ disjoint three-element subsets, such that every subsets has exactly the same sum?
It is known that the
3-Partition problem can be proved to be NP-complete by reducing the NP-complete
Exact-3D-Matching problem to it. And the NP-completeness of the
Exact-3D-Matching problem is proved by reducing the
3SAT problem to it (both are given in the book Computers and Intractability: A Guide to the Theory of NP-Completeness).
Problem: My problem is:
How to prove the NP-completeness of the
Exact-3D-Matchingproblem by reducing the
3-Partitionproblem to it?
I have found neither papers nor lecture notes on it.