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bibliography.bib
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@misc{weisstein_2018, title={Hamiltonian Cycle}, url={http://mathworld.wolfram.com/HamiltonianCycle.html}, journal={Hamiltonian Cycle}, publisher={http://mathworld.wolfram.com/HamiltonianCycle.html}, author={Weisstein, Eric}, year={2018}, month={Oct}}
@misc{geeksforgeeks_2018, title={Travelling Salesman Problem | Set 1 (Naive and Dynamic Programming)}, url={https://www.geeksforgeeks.org/travelling-salesman-problem-set-1/}, journal={GeeksforGeeks}, year={2018}, month={Sep}}
@misc{anir123_2017, title={How many Hamiltonian cycles are there in a complete graph $K_n$ ($n\geq 3$) Why?}, url={https://math.stackexchange.com/questions/249817/how-many-hamiltonian-cycles-are-there-in-a-complete-graph-k-n-n-geq-3-why}, journal={Mathematics Stack Exchange}, publisher={Mathematics Stack Exchange}, author={anir123}, year={2017}, month={Feb}}
@misc{geeksforgeeks_2018_2, title={NP-Completeness | Set 1 (Introduction)}, url={https://www.geeksforgeeks.org/np-completeness-set-1/}, journal={GeeksforGeeks}, publisher={GeeksforGeeks}, year={2018}, month={Sep}}
@book{cormen_leiserson_rivest_stein, place={Cambridge, Massachusetts}, edition={3}, title={{Introduction to Algorithms}}, publisher={The MIT Press}, author={Cormen, T. H. and Leiserson, C. E. and Rivest, R. L. and Stein, C.}}
@misc{problems_in_computer_science, url={http://www.cse.msu.edu/~torng/360Book/Problems/}, journal={Problems in Computer Science}}
@misc{rowell, title={{Know Thy Complexities!}}, url={http://bigocheatsheet.com/}, journal={Big-O Algorithm Complexity Cheat Sheet (Know Thy Complexities!) @ericdrowell}, author={Rowell, E.}}
@misc{black_tanenbaum_2017, title={{Dictionary of Algorithms and Data Structures}}, url={https://xlinux.nist.gov/dads/HTML/graph.html}, author={Black, P. E. and Tanenbaum, P. J.}, year={2019}, month={Feb}}
@misc{weisstein_2018_3, title={MathWorld--A Wolfram Web Resource}, url={http://mathworld.wolfram.com/AdjacentVertices.html}, journal={Adjacent Vertices}, author={Weisstein, Eric W}, year={2018}, month={Nov}}
@misc{complete_graphs, title={Mathonline}, url={http://mathonline.wikidot.com/complete-graphs}, journal={Complete Graphs}}
@misc{thompson, url={https://www.cs.cmu.edu/afs/cs/project/jair/pub/volume18/thompson03a-html/node6.html}, journal={Formal Definition}, author={Thompson, Cindi}}
@misc{cycle, title={Mathematics | Walks, Trails, Paths, Cycles and Circuits in Graph}, url={https://www.geeksforgeeks.org/mathematics-walks-trails-paths-cycles-and-circuits-in-graph/}, journal={GeeksforGeeks}, year={2018}, month={Jul}}
@book{harris_hirst_mossinghoff_2008, place={New York}, edition={2}, title={{Combinatorics and Graph Theory}}, publisher={Springer}, author={Harris, J. M. and Hirst, J. L. and Mossinghoff, M. J.}, year={2008}, editor={Axler, S. and Ribet, K.A.}}
@book{bondy_murty_1982, place={New York}, edition={5}, title={{Graph Theory With Applications}}, publisher={{Elsevier Science Publishing}}, author={Bondy, J. A. and Murty, U. S. R.}, year={1982}}
@misc{connected, title={Connected Graph}, url={http://mathworld.wolfram.com/ConnectedGraph.html}, journal={From MathWorld--A Wolfram Web Resource}, author={Weisstein, Eric W.}}
@misc{guichard_2018, title={{An Introduction to Combinatorics and Graph Theory}}, author={Guichard, D.}, year={2018}, month={Jul}, url= {https://www.whitman.edu/mathematics/cgt_online/cgt.pdf}}
@book{ray_2013, place={New Delhi}, title={{Graph Theory with Algorithms and its Applications: In Applied Science and Technology}}, publisher={Springer}, author={Ray, S. S.}, year={2013}}
@misc{weisstein_eric, title={Vertex Degree}, url={http://mathworld.wolfram.com/VertexDegree.html}, journal={From MathWorld--A Wolfram Web Resource}, author={Weisstein, E. W.}}
@misc{black_2009, title={optimization problem}, url={https://xlinux.nist.gov/dads/HTML/optimization.html}, journal={Dictionary of Algorithms and Data Structures}, author={Black, Paul E.}, year={2009}, month={Apr}}
@misc{hackerearth_blog, title={Shortest Path Algorithms}, url={https://www.hackerearth.com/practice/algorithms/graphs/shortest-path-algorithms/tutorial/}, journal={HackerEarth Blog}}
@misc{geeksforgeeks, title={Applications of Minimum Spanning Tree Problem}, url={https://www.geeksforgeeks.org/applications-of-minimum-spanning-tree/}, journal={GeeksforGeeks}}
@misc{adamchik_2009, title={{Algorithmic Complexity}}, url={https://www.cs.cmu.edu/~adamchik/15-121/lectures/Algorithmic Complexity/complexity.html}, author={Adamchik, V. S.}, year={2009}}
@misc{big_o_notation_explained, url={https://programming.guide/big-o-notation-explained.html}}
@misc{carter_1999, title={{Tractability of computation}}, url={https://csustan.csustan.edu/~tom/MISC/qc-article/node10.html}, author={Carter, T.}, year={1999}, month={May}}
@misc{encyclopædia_britannica, title={NP-complete problem}, url={https://www.britannica.com/science/NP-complete-problem\#ref97461}, journal={Encyclopædia Britannica}, publisher={Encyclopædia Britannica, inc.}}
@article{Sanchit,
author = {Goyal, S.},
year = {2010},
month = {Jan},
pages = {},
title = {{A Survey on Travelling Salesman Problem}}
}
@article{Krivelevich,
author = {Krivelevich, Michael},
year = {2011},
month = {11},
pages = {},
title = {On the number of Hamilton cycles in pseudo-random graphs},
volume = {19},
journal = {Electronic Journal of Combinatorics}
}
@misc{pettis, title={Analysis of Algorithms Advanced Programming/Practicum 15-200}, url={https://www.cs.cmu.edu/~pattis/15-1XX/15-200/lectures/aa/index.html}, journal={Scientology: The Thriving Cult of Greed and Power}, author={Pettis, Richard E.}}
@misc{kaveh_tehada_2013, title={{What is the definition of $P$, $NP$, $NP$-complete and $NP$-hard?}}, url={https://cs.stackexchange.com/questions/9556/what-is-the-definition-of-p-np-np-complete-and-np-hard}, publisher={Computer Science Stack Exchange}, author={Kaveh and Tehada}, year={2017}, month={Jul}}
@article{arora_agarwal_tanwar_2016, title={{Solving TSP using Genetic Algorithm and Nearest Neighbour Algorithm and their Comparison}}, volume={Vol.7}, url={https://pdfs.semanticscholar.org/9fc2/8fac2603cfda11da21033a58bbb5c7b75e09.pdf}, number={1}, journal={International Journal of Scientific \& Engineering Research}, author={Arora, K. and Agarwal, S. and Tanwar, R.}, year={2016}, month={Jan}, pages={1014--1018}}
@article{article,
author = {Rosenkrantz, Daniel and Edwin Stearns, Richard and M. Lewis II, Philip},
year = {1977},
month = {09},
pages = {563-581},
title = {An Analysis of Several Heuristics for the Traveling Salesman Problem},
volume = {6},
journal = {SIAM J. Comput.},
}
@article{khan_agrawal_2016, title={A COMPARITIVE STUDY OF NEAREST NEIGHBOUR ALGORITHM AND GENETIC ALGORITHM IN SOLVING TRAVELLING SALESMAN PROBLEM}, volume={03}, url={https://www.irjet.net/archives/V3/i5/IRJET-V3I550.pdf}, number={05}, journal={International Research Journal of Engineering and Technology (IRJET)}, author={Khan, Ajaz Ahmed and Agrawal, Himani}, year={2016}, month={May}, pages={234–238}}
@article{Rosenkrantz,
author = {Rosenkrantz, D. and Edwin Stearns, R. and M. Lewis II, P.},
year = {1977},
month = {Sep},
pages = {563--581},
title = {{An Analysis of Several Heuristics for the Traveling Salesman Problem}},
volume = {Vol. 6},
journal = {SIAM J. Comput.},
}
@book{vazirani_2003, place={New York}, edition={2}, title={{Approximation Algorithms}}, publisher={Springer}, author={Vazirani, V. V.}, year={2003}}
@misc{prim's_algorithm_1997, url={https://www8.cs.umu.se/kurser/TDBA77/VT06/algorithms/BOOK/BOOK2/NODE74.HTM}, year={1997}, month={Jun}}
@misc{prim's_algorithm, url={http://www.oxfordmathcenter.com/drupal7/node/685}, author={{The Oxford Math Center}}, title={{Prim's Algorithm}}}
@misc{greedy_algorithms, url={https://web.stanford.edu/class/archive/cs/cs161/cs161.1138/lectures/14/Small14.pdf}}
@book{dorigo_stutzle_thomas_2004, place={Cambridge, Massachusetts}, title={{Ant Colony Optimization}}, publisher={The MIT Press}, author={Dorigo, M. and Stützle, T.}, year={2004}}
@article{thrm_paper,
author = {Stützle, Thomas and Dorigo, Marco},
year = {2002},
month = {09},
pages = {358 - 365},
title = {A short convergence proof for a class of ACO algorithms},
volume = {6},
journal = {Evolutionary Computation, IEEE Transactions on},
doi = {10.1109/TEVC.2002.802444}
}
@article{article_rg,
author = {Dorigo, Marco and Birattari, Mauro and Stützle, Thomas},
year = {2006},
month = {12},
pages = {28-39},
title = {Ant Colony Optimization},
volume = {1},
journal = {Computational Intelligence Magazine, IEEE},
doi = {10.1109/MCI.2006.329691}
}
@article{dorigo_gambardella_1997,
author = {Dorigo, M. and Maria Gambardella, L.},
year = {1997},
month = {Feb},
pages = {73--81},
title = {{Ant Colonies for the Traveling Salesman Problem}},
volume = {Vol. 43},
journal = {Bio Systems},
}
@misc{reinelt, url={https://www.iwr.uni-heidelberg.de/groups/comopt/software/TSPLIB95/}, journal={TSPLIB}, publisher={Universität Heidelberg}, author={Reinelt, G.}}
@incollection{Matai10,
author = {Rajesh, M. and Surya, S. and Murari, L. M.},
title = {{Traveling Salesman Problem: an Overview of Applications, Formulations, and Solution Approaches}},
booktitle = {{Traveling Salesman Problem}},
publisher = {IntechOpen},
address = {Rijeka},
year = {2010},
editor = {Donald Davendra},
chapter = {1},
url = {https://doi.org/10.5772/12909}
}
@book{garey_johnson_1979, place={San Francisco}, title={{Computers and Intractability: A Guide to the Theory of NP-Completeness}}, publisher={W.H. Freeman and Company}, author={Garey, M. R. and Johnson, D. S.}, year={1979}}
@misc{chekuri_im_2011, title={{Approximation Algorithms}}, url={https://courses.engr.illinois.edu/cs598csc/sp2011/Lectures/lecture_2.pdf}, author={Chekuri, C. and Im, S.}, year={2011}, month={Jan}}