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P对NP的世界

Polynomial时间和指数时间的比赛

 
 
 

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What is the mystery of the P=?NP  

2010-01-11 09:13:30|  分类: 图论中NP问题 |  标签: |举报 |字号 订阅

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In my view, the major reason is that the problem become more complex when more restriction are given.  In an other word,  if an algorithm can  solve a problem  in polynomial time, it is always low efficiently after problem is restricted. Such as perfect matching is known easy and the restricted perfect matching is always hard.  So people like to believe that P =/= NP.
In addition, it is known that if one algorithm can solve a known NP-complete problem in polynomial time, then all NP problems can be solved efficient.  Some researchers have declared some algorithms to solve the NP-complete problem in polynomial time. Therefore P=NP is possible corrected.
However it could not sure that a determine algorithm can solve all NP problems in polynomial time.  Certainly, TM is a machine instead of a simple algorithm. Therefore, P=?NP is mystery for general researcher.

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