The maximization problem of the 3-way number partitioning reads as follows: given $n$ positive integers, partition them into 3 subsets such that the smallest sum is as large as possible. It is known to be NP-hard, but does it have an FPTAS?
I found answers for some related problems:
- There is no FPTAS for MSSP (Multiple Subset Sum Problem) unless P=NP - https://epubs.siam.org/doi/abs/10.1137/S1052623498348481?journalCode=sjope8
- There is an FPTAS for 2-way number partitioning - https://www.sciencedirect.com/science/article/pii/S0022000003000060
- There is no FPTAS for 3-partition, since it is strongly NP-hard - https://en.wikipedia.org/wiki/3-partition_problem
- There is a PTAS for 3-way number partitioning - https://en.wikipedia.org/wiki/Multiway_number_partitioning
Is there any FPTAS for 3-way number partitioning?