Network Decomposition and Maximum Independent Set Part Ⅰ:Theoretic Basis

IntroductionItisofsignificanttheoreticalmeaningtofindthemaximumindependentsetwithinanetwork .Thisisnotonlyrelatedtoclique ,nodecovering ,coloringandmatchingissues ,butalsoassociatedwithmanycombinatorialoptimization problems .In practicalapplications ,find…

Network Decomposition and Maximum Independent Set Part Ⅰ: Theoretic Basis

The structure and characteristics of a connected network are analyzed, and a special kind of sub-network, which can optimize the iteration processes, is discovered. Then, the sufficient and necessary conditions for obtaining the maximum independent set are deduced. It is found that the neighborhood of this sub-network possesses the similar characters, but both can never be allowed incorporated together. Particularly, it is identified that the network can be divided into two parts by a certain style, and then both of them can be transformed into a pair sets network, where the special sub-networks and their neighborhoods appear alternately distributed throughout the entire pair sets network. By use of this characteristic, the network decomposed enough without losing any solutions is obtained. All of these above will be able to make well ready for developing a much better algorithm with polynomial time bound for an odd network in the the application research part of this subject.