P vs. NP Millennium PROBLEM

Suppose that you are organizing housing accommodations for a group of four hundred university students. Space is limited and only one hundred of the students will receive places in the dormitory. To complicate matters, the Dean has provided you with a list of pairs of incompatible students, and requested that no pair from this list appear in your final choice. This is an example of what computer scientists call an NP-problem, since it is easy to check if a given choice of one hundred students proposed by a coworker is satisfactory (i.e., no pair from taken from your coworker's list also appears on the list from the Dean's office), however the task of generating such a list from scratch seems to be so hard as to be completely impractical. Indeed, the total number of ways of choosing one hundred students from the four hundred applicants is greater than the number of atoms in the known universe! Thus no future civilization could ever hope to build a supercomputer capable of solving the problem by brute force; that is, by checking every possible combination of 100 students. However, this apparent difficulty may only reflect the lack of ingenuity of your programmer. In fact, one of the outstanding problems in computer science is determining whether questions exist whose answer can be quickly checked, but which require an impossibly long time to solve by any direct procedure. Problems like the one listed above certainly seem to be of this kind, but so far no one has managed to prove that any of them really are so hard as they appear, i.e., that there really is no feasible way to generate an answer with the help of a computer. Stephen Cook and Leonid Levin formulated the P (i.e., easy to find) versus NP (i.e., easy to check) problem independently in 1971.

Proposed P vs. NP SOLUTION

EFL has demonstrated the following sample setup and solution for the Millennium Math Problem of P vs. NP.  The P vs. NP solution has been formulated and currently functions in an Excel spreadsheet to show the versatility and flexibility of the solution format.  The P vs. NP solution is performed in three phases:

SAMPLE of the P vs. NP SOLUTION:

• Data/information INPUT         
• Optimized Model SETUP
• Optimized Solution OUTPUT 

Not only do we believe that we have solved the P vs. NP Millennium problem, but we have shown a sample of the additional solution of the next-step problem using the P vs. NP solution.  This additional solution involves practical applications using weighted or preferred factors, such as constraints of male with female, smoking with non-smoking, grade point averages, etc. in determining room assignments.  Also, a few examples of how this same technology can be expanded to potential uses in business and medicine, such as allocation of hotel rooms, hospital rooms, and organ donation assignments.  The next-step problem solution is also performed in three phases:

SAMPLE of ADDITIONAL SOLUTION Using the P vs. NP SOLUTION:

The above input and output pages are ONLY samples of interactive Excel spreadsheets that can have new input data entered and then re-optimized at a touch of a keystroke.  Currently, there are certain data sets that will not run on these spreadsheets (e.g. some data sets may have up to 399 incompatible students, but the current spreadsheets only handle up to 4 incompatible students).  These limitations are easily overcome by minor software code changes.  The current spreadsheets demostrate valid P vs. NP solution principles and can easily modified to adapt to extreme data sets.

Interested to find out more Information--Please Contact Us at: contact@exactflowlogic.com