Automatski - Solution to NP-Complete Graph Coloring

NP-COMPLETE GRAPH COLORING
SOLUTION & BREAKING RSA 2048
Automatski Solutions
http://www.automatski.com
E: Aditya@automatski.com , Founder & CEO
M:+91-9986574181
© Automatski Solutions 2017. All Rights Reserved.

AUTOMATSKI’S EFFORTS
(LAST 25 YEARS)
1. 25+ years of Fundamental Research
2. Solved 50-100 of the Toughest
Problems on the Planet considered
unsolvable in a 1000 years given the
current state of Human Capability
and Technology
3. Including 7 NP-Complete + 4 NP-
Hard Problems
4. Broke RSA 2048
5. … in 1990’s

AUTOMATSKI HISTORY &
TIMELINE

GRAPH COLORING
 Graph Coloring is NP-Complete. Even 3-colouring is NP-complete.
 What’s the colouring problem on graphs? Given a graph G(V, E), the colouring
problem asks for an assignment of k colours to the vertices c : V → {1, 2, ..., k}. We
say that a colouring is proper if adjacent vertices receives different colours: ∀(u, v) ∈ E
: c(u) 6= c(v).
 The minimum colouring problem asks for the smallest k to properly colour G.
 The k-colouring problem asks whether G can be properly coloured using at most k
colours.
 We can Reduce Graph Coloring to K-SAT
 Also we can Reduce K-SAT to Graph Coloring
 Meaning? Cancer Drug, AGI, NLP, Robotics, Environment, Finance, & RSA can be
Broken.

WHERE ARE WE
GOING WITH ALL
THIS?

ORDER OF
ALGORITHMS
 Exponential => O( 2 ^ N ), O ( 3 ^ N ), O ( a ^ N) …
 Polynomial => O ( N ^ 2 ), O ( N ^ 3), O ( N ^ 5 ) …
 Logarithmic => O ( Log( N ) )…

MACHINES USED
 Development of Solution
 Machine #1
 AMD FX-6300 (6-Core), 32GB RAM
 Eight Year Old Machine
 Physical
 Testing of Parallelization & Concurrency
 Machine #2
 AWS EC2 m4.16xlarge ($3.2/hr)
 64 Core, 256 GB RAM
 Virtual Machine
 Machine #3
 AWS EC2 x1.32xlarge ($13.4/hr)
 128 Core, 1952 GB RAM
 Virtual Machine

BEFORE THE
A Message from our CFO!!!

MESSAGE FROM THE CFO!!!
 We are looking for Research & Development Grants
 Between
 $1m to $100m
 $1m will help us with the Research
 $100m will help us develop Path Breaking Solutions for over 10+ Domains using the
Breakthrough with a Big Bang.

AUTOMATSKI FUNDAMENTAL
RESEARCH
 Fundamental Research at Automatski has been working for the last 20-25+ years on
solving the toughest problems on the Planet.
 We have solved 7 NP-Complete Problems and 4 NP-Hard Problems, including the N-
Queens Completion Millennium Problem.
 We are applying them towards breakthroughs in 50+ Technology Domains
 These problems are considered unsolvable in a 1000 years given the current state of
Human Technology and Capability

SOLVED PROBLEMS
 N-Queens Completion
(Millennium Puzzle) Clay
Math Institute
 3-Sat/k-Sat
 Knapsack***
 Longest Common
Subsequence
 Travelling Salesman
Problem***
 3DM/nDM
 Graph Coloring -
Chromatic Number
 Linear Programming
 Integer Programming
 Mixed Integer
Programming
 Quadratic Programming
 Universal Expression
Programming
 Global Optimum in Hyper
Dimensional Space
 K-Means Clustering
 Universal Clustering
Algorithm
 Universal Constraint
Programming/Scheduling
 Integer Factorization***
 Prime Number Test***
 Universal Regression
 Non-Linear Random
Number Generation
 Automatic Theorem Proving
 Universal Experience
 Universal Heuristics
 Consciousness, Mind, Brain
 Genomics
 Billion & Trillion Actor Nano
Second Framework
 Universal Multi-Scale Simulations
 Internet Scale Rule Engine
 Internet Scale Workflow Engine
 Perfect Finance/Markets
 Perfect Environment
 Compromised All Cryptography
(RSA-2048, Elliptic Curve etc.)
 Post Quantum Cryptography
 Logarithmic Gradient Descent
Convergence
 Blackbox Function
Cracking/Reversal
 Hash Reversal (Incl. SHA-
256/512, LanMan etc.)
 NP-Complete Machine Learning
Algorithms (Clustering,
Regression, Classification)
 NP-Complete Deep Learning
Algorithms (ALL)
 Artificial General Intelligence
 Robotics (Simulations + RAD)***
 Universal Emotions
 Universal IQ
 Universal Creativity

FUND OUR RESEARCH
Together we can build the foundations of a better world

THE DEMO!

WHAT JUST HAPPENED?
 The cromatic number for The Hadwiger-Nelson problem is 5. Please download the 5 color
solution to 1585 problem from the link further later in this presentation.
 Aubrey de Grey "Amateur mathematician PARTIALLY solves 60-year-old problem"
https://phys.org/news/2018-04-amateur-mathematician-partially-year-old-problem.html he
basically eliminated 4 from the possibility of solutions. We solved the problem in entirety.
 We solved the problem in a single thread in 2 seconds on an 6 core/thread AMD FX6300
processor w/ 32GB Ram without using any GPGPU for processing.
 Finding the Chromatic Number in a Graph Coloring Problem is Proven to be NP-
Complete. It is one of the 7 NP-Complete + 4 NP Hard problems we have solved till now.
Including breaking RSA 2048 cryptography and the N-Queens Completion Millennium
Puzzle ( https://www.youtube.com/watch?v=kHk1xUEXep4&t=2s ) in polynomial time.
 The foremost attribute of such problems is that they are impossible to solve. But if anyone
gives a solution, it can be verified easily in polynomial time. The solution has been
provided to everyone.

HADWIGER-NELSON
PROBLEM
 In geometric graph theory, the Hadwiger–Nelson problem, named after
Hugo Hadwiger and Edward Nelson, asks for the minimum number of
colors required to color the plane such that no two points at distance 1 from
each other have the same color.
 Relation to Finite Graphs
 The Hadwiger–Nelson problem is often called "finding the chromatic number of
the plane".
 By the de Bruijn–Erdős theorem, a result of de Bruijn & Erdős (1951), the
problem is equivalent (under the assumption of the axiom of choice) to that of
finding the largest possible chromatic number of a finite unit distance graph.
 Ref: http://michaelnielsen.org/polymath1/index.php?title=Hadwiger-
Nelson_problem
 The 1585 Unit Distance Graph

HENCE…
 RSA 2048 is Cracked!
 Yet Again!
 For the Nth time using N different schemes. Recall…
 P = NP !!!
 7 NP-Complete & 4 NP-Hard Problems Solved in Polynomial time
 N-Queens Completion etc. Including K-Means
 Quantum Computing
 Other Schemes…
 Integer Factorization
 K-SAT
 …
 You know the best part?
 Polynomial Order Solutions are great from a theoretical point of view but are rarely practically
feasible.
 Logarithmic Order Solutions to NP-Complete Problems will define the Future of Mankind.

AVAILABLE
CONFIGURATIONS
 1k Nodes (Entry Level)
 1m Nodes
 1bn Nodes
 1tn Nodes

FROM HERE…
 Fact: We have Already proved feasibility of cracking RSA 2048 in 10+ Proven ways in
Polynomial Time. We have now proven it in Logarithmic Time. We now have to crack
it. And that involves Encodings and Reductions from one form to another.
 In the future video’s you will see
 More Logarithmic Time Algorithms (Our best kept secrets)
 E.g. General Purpose Constrained Optimization Solvers
 Also a Deterministic Algorithm to Find the Global Optima in a Billion Dimensions/Variables.
 I’m sure you will find it very interesting!!!

DO YOU HAVE ANY IDEA?
 What we can do with all the things
Automatski is demo’ing?
 Even though we have just shown
everyone 3-4 out of a 100+
Inventions and Innovations?
 Can you put a $ value on it? How
much will it be? Millions? Billions?
Trillions???
 Any guesses? Wanna try???

NEXT STEPS FOR
PROSPECTIVE CUSTOMERS
 Please contact sales at info@automatski.com
 Send an email with the following information…
 What is the problem(s) you are trying to solve?
 Or Kind of Cryptography that needs to be Cracked?
 We will take it from there…
*** No Free Trials/Pilots/POCs Offered

WARNING!!!
 Don’t contact us asking for The Source Code
 Don’t contact us asking us to
 File Patents
 Make Public Disclosures of our Algorithm(s)
 Publish Academic Papers

SAMPLE PROBLEMS &
RESULTS
 The .Zip File Contains
1. Sample Problems
2. And their Solutions
 Download .Zip File here
 http://bit.ly/2OWTN9x
 Download this Presentation here
 http://bit.ly/2OnanPL

Automatski - Solution to NP-Complete Graph Coloring

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