VincentWilliams

Since 2008 I have been attempting to solve the Computer Science problem: Does P equal NP? My approach has been to focus on finding a Polynomial Solution to the NP problem: Given a Graph G, what is the Maximum Independent Set for G? ( Wiki Link ) I am posting about this for a few reasons: Discussion about "P = NP?" I believe that P does equal NP, in the sense that there is a solution(s) to MIS and I believe that there is a faster way than Brute Force Method in order to return an answer. Sharing of my ideas I hope this helps anyone else seeking a solution to this problem to learn from my experiences Feedback from others that could lead to new understanding and ideas Listed below are my failed attempts at solving this problem: Cycle CountFor each Vertex V in the Graph G, count how many 3-Vertex Cycles V is a part of. Then choose V that has the smallest count, repeat until all vertices are either chosen or invalid. Edge Ranking SystemFor each Vertex V in the Graph G, assign it a percentage based on: (Number of Edges of V / Number of Vertices with the same Number of Edges). Then choose the vertex with the highest percentage. Repeat on the new Graph. Edge TrackingFor each Vertex V in the Graph G, mark V as chosen and all neighbors as invalid. Then count how many edges were lost throughout G. Reset G and move onto the next V, repeat. Once all vertices have been selected, choose the vertex that had the least amount of edges lost throughout G. Then repeat on the new G, until there are no more valid vertices. Reduce By CyclesFor each Vertex V in the Graph G, find the smallest cycle it is a part of and record it. Remove duplicate cycles from the record. Create new vertices based on the cycles and create edges between the new vertices if the two cycles share a vertex. With the new Graph, repeat finding the cycles for each vertex and creating new vertices and graphs. End once a Graph has no cycles in it. With this final Graph, choose the vertices with the smallest number of edges until each Vertex is chosen or invalid. Based on the Chosen Vertices, go to the Graph before this one and only choose Vertices based on smallest number of edges that were chosen in the Graph after this one. Repeat until no longer able to go back a Graph. Ratio of Cycles and Non-CyclesFor each Vertex V in the Graph G, count the number of 3-Vertex Cycles it is a part of and count how many neighbors that do not make a 3-Vertex Cycle with V. Then sort the vertices on Non-Cycles Increasing, then sort based on Cycles Increasing. Once sorted, choose the first Vertex and mark it Valid and all of its' neighbors Invalid. Then repeat the counting and sorting and choosing until all vertices are valid or invalid --- If you can say it, you can code it.