Intelligent scheduling
Solving the Hamiltonian path problem with a light-based computer
Natural Computing: an international journal
Computational Complexity: A Conceptual Perspective
Computational Complexity: A Conceptual Perspective
Quantum approaches to graph colouring
Theoretical Computer Science
Solving the subset-sum problem with a light-based device
Natural Computing: an international journal
An Optical Wavelength-Based Solution to the 3-SAT Problem
OSC '09 Proceedings of the 2nd International Workshop on Optical SuperComputing
Lower bounds on the complexity of the wavelength-based machine
UCNC'12 Proceedings of the 11th international conference on Unconventional Computation and Natural Computation
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The graph 3-colorability problem is a decision problem in graph theory which asks if it is possible to assign a color to each vertex of a given graph using at most three colors, satisfying the condition that every two adjacent vertices have different colors. It has been proved that the graph 3-colorability problem belongs to NP-complete class of problems which no polynomial resources solution is found for them yet. In this paper, a novel optical solution to the graph 3-colorability problem is provided. In this solution, polynomial number of black filters are created in preprocessing phase each of which has exponential size and requires exponential time to be created. After preprocessing phase, the provided solution takes O(n + m) time to decide if a given graph is 3-colorable or not, where the given graph has n vertices and m edges.