6500
Since it is unlikely that there exists a polynomial time solution for any of these hard problems -LRB- unless P = NP and P #P = P -RRB- , our results highlight and justify the need for developing polynomial time approximations for these computations .
 used for: polynomial time solution, hard problems; used for: polynomial time approximations, computations
Given options, please tell me the relationships of all the listed entity pairs.Output format is "relation1: word1, word2; relation2: word3, word4". 
Option: conjunction, feature of, hyponym of, used for, part of, compare, evaluate for 
Text: {0} 
 Entity Pairs:  polynomial time solution, hard problems; polynomial time approximations, computations 
Answer:
 used for: polynomial time solution, hard problems; used for: polynomial time approximations, computations