On the Duality Feature of NP Complete Problems and Their Opt-Solutions
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NP Complete (abbreviated as NPC) problems, standing at the crux of deciding whether P=NP, are among hardest problems in computer science and other related areas. Observing that NPC problems have different natures, they can be further classified. We show that the classification of NPC problems may depend on their natures, reduction methods, exact algorithms, and the boundary between P and NP. We propose a new perspective: both P problems and NPC problems have the duality feature in terms of computational complexity of asymptotic efficiency of algorithms. We then introduce near optimal solutions...
NP Complete (abbreviated as NPC) problems, standing at the crux of deciding whether P=NP, are among hardest problems in computer science and other related areas. Observing that NPC problems have different natures, they can be further classified. We show that the classification of NPC problems may depend on their natures, reduction methods, exact algorithms, and the boundary between P and NP. We propose a new perspective: both P problems and NPC problems have the duality feature in terms of computational complexity of asymptotic efficiency of algorithms. We then introduce near optimal solutions to some NPC problems such as Traveling Salesman Problems (TSP), Boolean Satisfiability Problems (SAT), Scheduling algorithms in Cloud data centers and Bigdata process platforms. These solutions may shine light on other NPC problems and their applications.
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