Lmst

Trying to tame the NP-complete beast — writing a paper about my algorithm for solving the Hamiltonian cycle #graphs #hamiltoncycle #npcomplete #graphalgorithms #computerscience #heuristics #optimization #research #computationalcomplexity #hacking #latex

Dual-monitor desk setup with code and research paper on screen, colorful mechanical keyboard, and a focused work atmosphere.

🚀 Excited to announce my 5th course, Network Algorithms and Approximations! 🎓 Explore NP-complete problems (Set Cover, Unique Coverage, etc.), approximation techniques, and applications in data science, neural nets, & network optimization.

📺 First lecture: https://youtu.be/Tnm-8xieqB4
🎥 Weekly uploads: Wednesdays at 7 PM EDT. Playlist: https://youtube.com/playlist?list=PLx7SjCaKZzEIeJxOlTuXveAE5eY7WOYB9

Plus, all 4 previous courses (Game Theory, Algorithms, Lower Bounds, Data Science) are online! 🌐 https://youtube.com/@hajiaghayi

#NetworkDesign #Optimization #NPComplete #Algorithms #DataScience #NeuralNets

In our effort to put courses online, we continue lectures on Algorithmic Lower Bound Course. Now you can watch

Lesson 4-11: Algorithmic Lower Bounds by Mohammad Hajiaghayi - NP-Completeness and Beyond

(FEEL FREE TO SUBSCRIBE TO YOUTUBE @hajiaghayi FOR FUTURE LESSONS Premiering on WEDNESDAYS)

https://youtu.be/VZyffnAb1r0 (Lesson 4: 3-Partition Problem & Proving NP-Hardness)

https://youtu.be/4fCD9_1eQw0 (Lesson 5: Puzzle Problem NP-Hardness & 3-Partition)

https://youtu.be/FIyEj72-UJQ (Lesson 6: 3-SAT Problem & Proving NP-Hardness)

https://youtu.be/tbSJzaKx2pA (Lesson 7: Puzzle Problem NP-Hardness via 3-SAT)

https://youtu.be/voRVebBsh94 (Lesson 8: Fine-grained Subcubic Complexity: Part 1)

https://youtu.be/gRURSM6QARo (Lesson 9: Fine-grained Subcubic Complexity: Part 2)

https://youtu.be/qPw82bTAXkc (Lesson 10: Fine-grained Subquadratic Complexity 1)

https://youtu.be/C6j4avVkI7U (Lesson 11: Fine-grained Subquadratic Complexity 2)

#AlorithmicComplexity,

#HardnessExploration,

#NP,

#PSPACE,

#NPComplete,

#LogSpace,

#ExponentialComplexity,

#ParallelComputation,

#PvsNP,

#NPSPACE,

#NonDeterministicSpace, hashtag

#CommunicationComplexity, hashtag

#GeometricProblems,

#AlgorithmDesign,

#ComputationalComplexity,

#TheoreticalComputerScience,

#AlgorithmicLowerBounds

For comprehensive handwritten lecture notes on this course, visit the instructor's website:

http://www.cs.umd.edu/~hajiagha/
The course textbook "Computational Intractability: A Guide to Algorithmic Lower Bounds" by Demaine, Gasarch, and Hajiaghayi is available for free at:

https://hardness.mit.edu/

#BingChat (precise) has concluded that P=NP

I asked it to write a Python script that when given a graph where there are no more than 5 edges for every vertex, it returns the length of the longest path that visits each vertex no more than once. Then lifted the edge count restriction.

In both cases it claimed polynomial time complexity to solve an NP-hard problem

#ComputerScience #complexity #PequalsNP #NPhard #NPcomplete #python #GraphTheory

$Sure! Here is the modified version of the script that can handle graphs with any number of edges per vertex: ```python def longest_path(graph): def dfs(vertex, visited, path): nonlocal max_path visited.add(vertex) path.append(vertex) max_path = max(max_path, len(path)) for neighbor in graph[vertex]: if neighbor not in visited: dfs(neighbor, visited, path) path.pop() visited.remove(vertex) max_path = 0 for vertex in graph: dfs(vertex, set(), []) return max_path # Example usage graph = { 'A': ['B', 'C', 'D', 'E', 'F', 'G'], 'B': ['A', 'C', 'D', 'E', 'F', 'G'], 'C': ['A', 'B', 'D', 'E', 'F', 'G'], 'D': ['A', 'B', 'C', 'E', 'F', 'G'], 'E': ['A', 'B', 'C', 'D', 'F', 'G'], 'F': ['A', 'B', 'C', 'D', 'E', 'G'], 'G': ['A', 'B', 'C', 'D', 'E', 'F'] } print(longest_path(graph)) # 7 ``` This version of the script is identical to the previous version, except that it does not have any restrictions on the number of edges per vertex. The `longest_path` function still performs a depth-first search starting from each vertex in the graph and uses the `dfs` function to recursively explore all unvisited neighbors of each vertex. The time complexity of this version of the function is still `O(V*(V+E))`, where `V` is the number of vertices and `E` is the number of edges in the input graph.$

There will be a completely useless science in the following years: learning to make effective prompts for chatGPT. Am I missing something? What do you learn from a correct prompt? Is finding the right prompt for chatGPT another #NPcomplete problem?

[Up and Atom] on the unsolved problem of whether NP-Complete problems can be decided in polynomial time
https://youtu.be/ctwX--JEzSA
#mathematics #ComputerScience #computability #ComplexityTheory #NPComplete

#Kingdomino is #NPComplete...

https://arxiv.org/abs/1909.02849

#NPComplete

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