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- 11:18, 15 February 2023 Reduction from OV to Diameter 2 vs 3 (hist | edit) [506 bytes] Admin (talk | contribs) (Created page with "FROM: OV TO: Diameter 2 vs 3 == Description == == Implications == If: to-time: $O(N^{({2}-\epsilon)})$ where $N = nd$ and $V,E = O(n)$<br/>Then: from-time: $O((nd)^{({2}-\epsilon)}) \leq n^{({2}-\epsilon)} poly(d)$ where {2} sets of $n$ $d$-dimensional vectors == Year == 2013 == Reference == L. Roditty and V. Vassilevska Williams. Fast approximation algorithms for the diameter and radius of sparse graphs. In STOC, pages 515–524, 2013. https://peop...")
- 11:18, 15 February 2023 Reduction from 3-OV to Diameter 3 vs 7 (hist | edit) [469 bytes] Admin (talk | contribs) (Created page with "FROM: 3-OV TO: Diameter 3 vs 7 == Description == == Implications == If: to-time: $O(N^{({3}/{2}-\epsilon)}$ where $N=n^{2} d^{2}$ and $\epsilon > {0}$<br/>Then: from-time: $n^{3-{2}\epsilon} poly(d)$ == Year == 2018 == Reference == Arturs Backurs, Liam Roditty, Gilad Segal, Virginia Vassilevska Williams, and Nicole Wein. Towards tight approximation bounds for graph diameter and eccentricities. https://dl.acm.org/doi/pdf/10.1145/3188745.3188950")
- 11:18, 15 February 2023 Reduction from CNF-SAT to k-OV (hist | edit) [466 bytes] Admin (talk | contribs) (Created page with "FROM: CNF-SAT TO: k-OV == Description == == Implications == If: to-time: $N^{(k-\epsilon)} poly(m)$ where $m$-dimensional vectors, $k$-OV, $N$ vectors per set<br/>Then: from-time: ${2}^{(n-\epsilon')} \poly(m)$ where $\epsilon' = \epsilon/k > {0}$, $n$ variables, $m$ clauses == Year == 2005 == Reference == Ryan Williams. A new algorithm for optimal 2-constraint satisfaction and its implications. Theor. Comput. Sci., 348(2-3):357–365, 2005.")
- 11:18, 15 February 2023 Fagin (4NF Decomposition for Functional and Multivalued Dependency Sets 4NF Decomposition) (hist | edit) [350 bytes] Admin (talk | contribs) (Created page with "== Time Complexity == exponential == Space Complexity == exponential words (https://link.springer.com/article/10.1007/BF01934180) == Description == == Approximate? == Exact == Randomized? == No, deterministic == Model of Computation == Word RAM == Year == 1977 == Reference == https://dl.acm.org/doi/abs/10.1145/320557.320571")
- 11:18, 15 February 2023 Sciore (4NF Decomposition for Conflict-Free Dependency Sets 4NF Decomposition) (hist | edit) [285 bytes] Admin (talk | contribs) (Created page with "== Time Complexity == poly-time == Space Complexity == words () == Description == == Approximate? == Exact == Randomized? == No, deterministic == Model of Computation == Word RAM == Year == 1981 == Reference == https://dl.acm.org/doi/abs/10.1145/582318.582337")
- 11:18, 15 February 2023 Lien (4NF Decomposition for Conflict-Free Dependency Sets 4NF Decomposition) (hist | edit) [387 bytes] Admin (talk | contribs) (Created page with "== Time Complexity == $O(k^{2} n^{2})$ == Space Complexity == $O(k^{2})$ words (Derived: Uses an auxiliary array of size $k \times k$) == Description == Multiway Decomposition Algorithm == Approximate? == Exact == Randomized? == No, deterministic == Model of Computation == Word RAM == Year == 1982 == Reference == https://dl.acm.org/doi/abs/10.1145/319540.319546")
- 11:18, 15 February 2023 Grahne and Räihä (4NF Decomposition for Functional and Multivalued Dependency Sets 4NF Decomposition) (hist | edit) [360 bytes] Admin (talk | contribs) (Created page with "== Time Complexity == exponential == Space Complexity == exponential words (https://link.springer.com/article/10.1007/BF01934180) == Description == Synthesis Algorithm == Approximate? == Exact == Randomized? == No, deterministic == Model of Computation == Word RAM == Year == 1983 == Reference == https://www.vldb.org/conf/1983/P186.PDF")
- 11:18, 15 February 2023 Global Newton Method (n player games Nash Equilibria) (hist | edit) [307 bytes] Admin (talk | contribs) (Created page with "== Time Complexity == Unknown == Space Complexity == () == Description == == Approximate? == Approximate Approximation Factor: == Randomized? == Yes, == Model of Computation == == Year == 2008 == Reference == https://www.sciencedirect.com/science/article/pii/S0022053108000811")
- 11:18, 15 February 2023 Mixed Integer Programming (n player games Nash Equilibria) (hist | edit) [292 bytes] Admin (talk | contribs) (Created page with "== Time Complexity == Unknown == Space Complexity == () == Description == == Approximate? == Approximate Approximation Factor: == Randomized? == Yes, == Model of Computation == == Year == 2005 == Reference == https://www.aaai.org/Papers/AAAI/2005/AAAI05-078.pdf")
- 11:18, 15 February 2023 Support enumeration and search (n player games Nash Equilibria) (hist | edit) [293 bytes] Admin (talk | contribs) (Created page with "== Time Complexity == Unknown == Space Complexity == () == Description == == Approximate? == Approximate Approximation Factor: == Randomized? == Yes, == Model of Computation == == Year == 2004 == Reference == https://www.aaai.org/Library/AAAI/2004/aaai04-105.php")
- 11:18, 15 February 2023 Lipton, Markakis and Mehta method 2 (n player games Nash Equilibria) (hist | edit) [357 bytes] Admin (talk | contribs) (Created page with "== Time Complexity == $O(n^{ck^{2} log (k^{2}n)$/eps^2}) == Space Complexity == $O(k^{2}log^{2} n/eps^{2})$ words () == Description == == Approximate? == Approximate Approximation Factor: == Randomized? == Yes, == Model of Computation == Word RAM words == Year == 2003 == Reference == https://dl.acm.org/doi/10.1145/779928.779933")
- 11:18, 15 February 2023 Lipton, Markakis and Mehta method (2 player games Nash Equilibria) (hist | edit) [340 bytes] Admin (talk | contribs) (Created page with "== Time Complexity == $O(n^{c log n/eps^2})$ == Space Complexity == $O(log^{2} n/eps^{2})$ words () == Description == == Approximate? == Approximate Approximation Factor: == Randomized? == Yes, == Model of Computation == Word RAM words == Year == 2003 == Reference == https://dl.acm.org/doi/10.1145/779928.779933")
- 11:18, 15 February 2023 Treap ( Self-Balancing Trees Search) (hist | edit) [292 bytes] Admin (talk | contribs) (Created page with "== Time Complexity == $O(n)$ == Space Complexity == $O({1})$? words (^see above) == Description == == Approximate? == Exact == Randomized? == Yes, == Model of Computation == Word RAM == Year == 1989 == Reference == http://faculty.washington.edu/aragon/pubs/rst89.pdf")
- 11:18, 15 February 2023 Blum, Shelton, Koller (Graphical games, Multi-agent influence diagrams Nash Equilibria) (hist | edit) [396 bytes] Admin (talk | contribs) (Created page with "== Time Complexity == Unknown? == Space Complexity == words () == Description == == Approximate? == Approximate Approximation Factor: == Randomized? == Yes, == Model of Computation == Word RAM == Year == 2003 == Reference == https://www.semanticscholar.org/paper/A-Continuation-Method-for-Nash-Equilibria-in-Games-Blum-Shelton/4a3b80041922298db147debc2a2307bc4a5a42e9")
- 11:18, 15 February 2023 Tango Tree ( Self-Balancing Trees Search) (hist | edit) [303 bytes] Admin (talk | contribs) (Created page with "== Time Complexity == $O((k+{1})$log(log(n))) == Space Complexity == words () == Description == == Approximate? == Exact == Randomized? == No, deterministic == Model of Computation == Word RAM == Year == 2004 == Reference == http://erikdemaine.org/papers/Tango_SICOMP/paper.pdf")
- 11:18, 15 February 2023 Lemke-Howson Algorithm (2 player games Nash Equilibria) (hist | edit) [335 bytes] Admin (talk | contribs) (Created page with "== Time Complexity == Exponential == Space Complexity == $O(mn)$? words (I am not sure if this can be optimized?) == Description == == Approximate? == Approximate Approximation Factor: == Randomized? == Yes, == Model of Computation == Word RAM == Year == 1964 == Reference == https://doi.org/10.1137/0112033")
- 11:18, 15 February 2023 Scapegoat Tree ( Self-Balancing Trees Search) (hist | edit) [322 bytes] Admin (talk | contribs) (Created page with "== Time Complexity == $O(nlogn)$ == Space Complexity == $O({1})$? words (^see above) == Description == == Approximate? == Exact == Randomized? == No, deterministic == Model of Computation == Word RAM == Year == 1989 == Reference == https://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.138.4859")
- 11:18, 15 February 2023 Bayer, McCreight B-Tree ( Self-Balancing Trees Search) (hist | edit) [264 bytes] Admin (talk | contribs) (Created page with "== Time Complexity == $O(b*log(n)$/log(b))? == Space Complexity == $O({1})$ words (^see above) == Description == == Approximate? == Exact == Randomized? == No, deterministic == Model of Computation == Word RAM == Year == 1970 == Reference ==")
- 11:18, 15 February 2023 Tarjan Splay Tree ( Self-Balancing Trees Search) (hist | edit) [249 bytes] Admin (talk | contribs) (Created page with "== Time Complexity == $O(n)$ == Space Complexity == $O({1})$ words (^see above) == Description == == Approximate? == Exact == Randomized? == No, deterministic == Model of Computation == Word RAM == Year == 1985 == Reference ==")
- 11:18, 15 February 2023 Treap ( Self-Balancing Trees Deletion) (hist | edit) [292 bytes] Admin (talk | contribs) (Created page with "== Time Complexity == $O(n)$ == Space Complexity == $O({1})$? words (^see above) == Description == == Approximate? == Exact == Randomized? == Yes, == Model of Computation == Word RAM == Year == 1989 == Reference == http://faculty.washington.edu/aragon/pubs/rst89.pdf")
- 11:18, 15 February 2023 AVL Tree ( Self-Balancing Trees Search) (hist | edit) [353 bytes] Admin (talk | contribs) (Created page with "== Time Complexity == $O(logn)$ == Space Complexity == $O({1})$ words (Need to keep track of constant amount of info during search (i.e. which node we're on and what direction to go)) == Description == == Approximate? == Exact == Randomized? == No, deterministic == Model of Computation == Word RAM == Year == 1962 == Reference ==")
- 11:18, 15 February 2023 Scapegoat Tree ( Self-Balancing Trees Deletion) (hist | edit) [318 bytes] Admin (talk | contribs) (Created page with "== Time Complexity == $O(n)$ == Space Complexity == $O({1})$? words (^see above) == Description == == Approximate? == Exact == Randomized? == No, deterministic == Model of Computation == Word RAM == Year == 1989 == Reference == https://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.138.4859")
- 11:18, 15 February 2023 Bayer, McCreight B-Tree ( Self-Balancing Trees Deletion) (hist | edit) [299 bytes] Admin (talk | contribs) (Created page with "== Time Complexity == $O(b*log(n)$/log(b))? == Space Complexity == $O(b)$? words (^see above, but with branching factor involved) == Description == == Approximate? == Exact == Randomized? == No, deterministic == Model of Computation == Word RAM == Year == 1970 == Reference ==")
- 11:18, 15 February 2023 AVL Tree ( Self-Balancing Trees Deletion) (hist | edit) [252 bytes] Admin (talk | contribs) (Created page with "== Time Complexity == $O(logn)$ == Space Complexity == $O({1})$ words (^see above) == Description == == Approximate? == Exact == Randomized? == No, deterministic == Model of Computation == Word RAM == Year == 1962 == Reference ==")
- 11:18, 15 February 2023 Treap ( Self-Balancing Trees Insertion) (hist | edit) [292 bytes] Admin (talk | contribs) (Created page with "== Time Complexity == $O(n)$ == Space Complexity == $O({1})$? words (^see above) == Description == == Approximate? == Exact == Randomized? == Yes, == Model of Computation == Word RAM == Year == 1989 == Reference == http://faculty.washington.edu/aragon/pubs/rst89.pdf")
- 11:18, 15 February 2023 Scapegoat Tree ( Self-Balancing Trees Insertion) (hist | edit) [318 bytes] Admin (talk | contribs) (Created page with "== Time Complexity == $O(n)$ == Space Complexity == $O({1})$? words (^see above) == Description == == Approximate? == Exact == Randomized? == No, deterministic == Model of Computation == Word RAM == Year == 1989 == Reference == https://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.138.4859")
- 11:18, 15 February 2023 Tarjan Splay Tree ( Self-Balancing Trees Deletion) (hist | edit) [249 bytes] Admin (talk | contribs) (Created page with "== Time Complexity == $O(n)$ == Space Complexity == $O({1})$ words (^see above) == Description == == Approximate? == Exact == Randomized? == No, deterministic == Model of Computation == Word RAM == Year == 1985 == Reference ==")
- 11:18, 15 February 2023 Bayer, McCreight B-Tree ( Self-Balancing Trees Insertion) (hist | edit) [299 bytes] Admin (talk | contribs) (Created page with "== Time Complexity == $O(b*log(n)$/log(b))? == Space Complexity == $O(b)$? words (^see above, but with branching factor involved) == Description == == Approximate? == Exact == Randomized? == No, deterministic == Model of Computation == Word RAM == Year == 1970 == Reference ==")
- 11:18, 15 February 2023 Tarjan Splay Tree ( Self-Balancing Trees Insertion) (hist | edit) [249 bytes] Admin (talk | contribs) (Created page with "== Time Complexity == $O(n)$ == Space Complexity == $O({1})$ words (^see above) == Description == == Approximate? == Exact == Randomized? == No, deterministic == Model of Computation == Word RAM == Year == 1985 == Reference ==")
- 11:18, 15 February 2023 AVL Tree ( Self-Balancing Trees Insertion) (hist | edit) [359 bytes] Admin (talk | contribs) (Created page with "== Time Complexity == $O(logn)$ == Space Complexity == $O({1})$ words (Each node being changed requires constant auxiliary space to make changes; can reuse space across nodes being changed) == Description == == Approximate? == Exact == Randomized? == No, deterministic == Model of Computation == Word RAM == Year == 1962 == Reference ==")
- 11:18, 15 February 2023 Scapegoat Tree ( Self-Balancing Trees Creation) (hist | edit) [376 bytes] Admin (talk | contribs) (Created page with "== Time Complexity == $O(nlogn)$ == Space Complexity == $O(n)$ words (Need to keep track of intermediary stages of tree before outputting) == Description == == Approximate? == Exact == Randomized? == No, deterministic == Model of Computation == Word RAM == Year == 1989 == Reference == https://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.138.4859")
- 11:18, 15 February 2023 Treap ( Self-Balancing Trees Creation) (hist | edit) [350 bytes] Admin (talk | contribs) (Created page with "== Time Complexity == $O(nlogn)$ == Space Complexity == $O(n)$ words (Need to keep track of intermediary stages of tree before outputting) == Description == == Approximate? == Exact == Randomized? == Yes, == Model of Computation == Word RAM == Year == 1989 == Reference == http://faculty.washington.edu/aragon/pubs/rst89.pdf")
- 11:18, 15 February 2023 Tango Tree ( Self-Balancing Trees Creation) (hist | edit) [363 bytes] Admin (talk | contribs) (Created page with "== Time Complexity == $O(nlogn)$ == Space Complexity == $O(n)$ words (Need to keep track of intermediary stages of tree before outputting) == Description == == Approximate? == Exact == Randomized? == No, deterministic == Model of Computation == Word RAM == Year == 2004 == Reference == http://erikdemaine.org/papers/Tango_SICOMP/paper.pdf")
- 11:18, 15 February 2023 Babai 1980 (Graph Isomorphism, Bounded Vertex Valences Graph Isomorphism Problem) (hist | edit) [356 bytes] Admin (talk | contribs) (Created page with "== Time Complexity == \exp(n^{\frac{1}{2} + $O({1})$}) == Space Complexity == $O(n^{2})$ words (https://epubs.siam.org/doi/epdf/10.1137/0209018) == Description == == Approximate? == Exact == Randomized? == Yes, Las Vegas == Model of Computation == Word RAM == Year == 1980 == Reference == https://epubs.siam.org/doi/10.1137/0209018")
- 11:18, 15 February 2023 Babai 1980 (Graph Isomporhism, Trivalent Graphs Graph Isomorphism Problem) (hist | edit) [353 bytes] Admin (talk | contribs) (Created page with "== Time Complexity == \exp(cn^{\frac{1}{2}} \log n) == Space Complexity == $O(n^{2})$ words (https://epubs.siam.org/doi/epdf/10.1137/0209018) == Description == == Approximate? == Exact == Randomized? == Yes, Las Vegas == Model of Computation == Word RAM == Year == 1980 == Reference == https://epubs.siam.org/doi/10.1137/0209018")
- 11:18, 15 February 2023 Gronlund, Pettie (3-Clique Exact-Weight k-Clique Problem) (hist | edit) [315 bytes] Admin (talk | contribs) (Created page with "== Time Complexity == $O(n^{3}*(log log n)$^{2}/(log n)) == Space Complexity == words () == Description == == Approximate? == Exact == Randomized? == No, deterministic == Model of Computation == Word RAM == Year == 2014 == Reference == https://ieeexplore.ieee.org/abstract/document/6979047")
- 11:18, 15 February 2023 Nesetril, Poljak (k-Clique k-Clique Problem) (hist | edit) [440 bytes] Admin (talk | contribs) (Created page with "== Time Complexity == $O(n^(k-({3}-\omega)*floor(k/{3}))$ where omega is the exponent on matrix multiplication == Space Complexity == $O(n^({2}k/{3})$) ish words (matrix sizes) == Description == == Approximate? == Exact == Randomized? == No, deterministic == Model of Computation == Word RAM == Year == 1985 == Reference == https://dml.cz/bitstream/handle/10338.dmlcz/106381/CommentatMathUnivCarol_026-1985-2_22.pdf")
- 11:18, 15 February 2023 APSP algorithm (3-Clique Min-Weight k-Clique Problem) (hist | edit) [256 bytes] Admin (talk | contribs) (Created page with "== Time Complexity == $O(n^{3} / {2}^(log n)$^{0.5}) == Space Complexity == words () == Description == == Approximate? == Exact == Randomized? == No, deterministic == Model of Computation == Word RAM == Year == - == Reference == -")
- 11:18, 15 February 2023 Brute force enumeration (k-Clique k-Clique Problem) (hist | edit) [298 bytes] Admin (talk | contribs) (Created page with "== Time Complexity == $O(n^k)$ == Space Complexity == $O(k)$ auxiliary words (keeping track of which vertices we're looking at) == Description == == Approximate? == Exact == Randomized? == No, deterministic == Model of Computation == Word RAM == Year == - == Reference == -")
- 11:18, 15 February 2023 Reduction to Chan, Williams (k-OV Orthogonal Vectors) (hist | edit) [315 bytes] Admin (talk | contribs) (Created page with "== Time Complexity == $O(n^{(k-{1}/O(d/log(n)))})$ == Space Complexity == words () == Description == == Approximate? == Exact == Randomized? == No, deterministic == Model of Computation == Word RAM == Year == 2016 == Reference == https://epubs.siam.org/doi/abs/10.1137/1.9781611974331.ch87")
- 11:18, 15 February 2023 Chan, Williams (OV Orthogonal Vectors) (hist | edit) [317 bytes] Admin (talk | contribs) (Created page with "== Time Complexity == $O(n^{({2}-{1}/O(d/log(n)))})$ == Space Complexity == words () == Description == == Approximate? == Exact == Randomized? == No, deterministic == Model of Computation == Word RAM == Year == 2016 == Reference == https://epubs.siam.org/doi/abs/10.1137/1.9781611974331.ch87")
- 11:18, 15 February 2023 Abboud, Williams, Yu (OV Orthogonal Vectors) (hist | edit) [314 bytes] Admin (talk | contribs) (Created page with "== Time Complexity == $O(n^{({2}-{1}/O(d/log(n)))})$ == Space Complexity == words () == Description == == Approximate? == Exact == Randomized? == Yes, Monte Carlo == Model of Computation == Word RAM == Year == 2015 == Reference == https://epubs.siam.org/doi/abs/10.1137/1.9781611973730.17")
- 11:18, 15 February 2023 Reduction to Abboud, Williams, Yu (k-OV Orthogonal Vectors) (hist | edit) [312 bytes] Admin (talk | contribs) (Created page with "== Time Complexity == $O(n^{(k-{1}/O(d/log(n)))})$ == Space Complexity == words () == Description == == Approximate? == Exact == Randomized? == Yes, Monte Carlo == Model of Computation == Word RAM == Year == 2015 == Reference == https://epubs.siam.org/doi/abs/10.1137/1.9781611973730.17")
- 11:18, 15 February 2023 Exhaustive search (Minimum Wiener Connector problem Wiener Index) (hist | edit) [337 bytes] Admin (talk | contribs) (Created page with "== Time Complexity == {2}^($O(n)$) == Space Complexity == $O(n)$ auxiliary words (Keeps track of current subset being checked, minimum subset, and O(1) Wiener indices) == Description == == Approximate? == Exact == Randomized? == No, deterministic == Model of Computation == Word RAM == Year == 2015 == Reference ==")
- 11:18, 15 February 2023 Exhaustive search (k-OV Orthogonal Vectors) (hist | edit) [299 bytes] Admin (talk | contribs) (Created page with "== Time Complexity == $O(d*n^k)$ == Space Complexity == $O(k)$ auxiliary words (keeping track of which vectors we're looking at) == Description == == Approximate? == Exact == Randomized? == No, deterministic == Model of Computation == Word RAM == Year == - == Reference == -")
- 11:18, 15 February 2023 Wen (2-dimensional Maximum subarray problem) (hist | edit) [309 bytes] Admin (talk | contribs) (Created page with "== Time Complexity == $O(log n)$ == Space Complexity == words () == Description == == Approximate? == Exact == Randomized? == No, deterministic == Model of Computation == EREW PRAM == Year == 1995 == Reference == https://www.sciencedirect.com/science/article/abs/pii/016781919400063G")
- 11:18, 15 February 2023 KALYAN PERUMALLA and NARSINGH DEO (2-dimensional Maximum subarray problem) (hist | edit) [322 bytes] Admin (talk | contribs) (Created page with "== Time Complexity == $O(log n)$ == Space Complexity == words () == Description == == Approximate? == Exact == Randomized? == No, deterministic == Model of Computation == CREW PRAM == Year == 1995 == Reference == https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.24.1291&rep=rep1&type=pdf")
- 11:18, 15 February 2023 Takaoka (2-dimensional Maximum subarray problem) (hist | edit) [350 bytes] Admin (talk | contribs) (Created page with "== Time Complexity == $O(n^{3} * ((log log n)$/(log n))^({1}/{2})) == Space Complexity == words () == Description == == Approximate? == Exact == Randomized? == No, deterministic == Model of Computation == Word RAM == Year == 2002 == Reference == https://www.sciencedirect.com/science/article/pii/S1571066104003135?via%3Dihub")
- 11:18, 15 February 2023 Tamaki, Tokuyama (exact) (2-dimensional Maximum subarray problem) (hist | edit) [320 bytes] Admin (talk | contribs) (Created page with "== Time Complexity == $O(n^{3} * ((log log n)$/(log n))^({1}/{2})) == Space Complexity == words () == Description == == Approximate? == Exact == Randomized? == No, deterministic == Model of Computation == Word RAM == Year == 1998 == Reference == https://dl.acm.org/doi/pdf/10.5555/314613.314823")
- 11:18, 15 February 2023 Tamaki, Tokuyama (approximate) (2-dimensional Maximum subarray problem) (hist | edit) [357 bytes] Admin (talk | contribs) (Created page with "== Time Complexity == $O(n^(omega)$ * (-log(epsilon))/epsilon) == Space Complexity == words () == Description == == Approximate? == Approximate Approximation Factor: (1-epsilon) == Randomized? == No, deterministic == Model of Computation == Word RAM == Year == 1998 == Reference == https://dl.acm.org/doi/pdf/10.5555/314613.314823")