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Randomised enumeration of small witnesses using a decision oracle [article]

Kitty Meeks
2018 arXiv   pre-print
The enumeration algorithm also gives rise to an efficient algorithm to count the total number of witnesses when this number is small.  ...  If the decision version of the problem is solved by a randomised algorithm which may return false negatives, then the same method allows us to output a list of witnesses in which any given witness will  ...  However, we can seek to do much better than this when the number of witnesses is small by making use of a decision oracle.  ... 
arXiv:1509.05572v4 fatcat:vbjy6c45tfgvnmkzejfsptb7le

Randomised Enumeration of Small Witnesses Using a Decision Oracle

Kitty Meeks
2018 Algorithmica  
This also gives rise to an efficient algorithm to count the total number of witnesses when this number is small.  ...  of witnesses and f is a computable function.  ...  , there is a randomised algorithm which is guaranteed to enumerate all witnesses and whose expected number of oracle calls is at most 2 O(k) log 2 n · N , where N is the total number of witnesses.  ... 
doi:10.1007/s00453-018-0404-y fatcat:xztv56xxibh2phqg746wrbbt3m

The challenges of unbounded treewidth in parameterised subgraph counting problems

Kitty Meeks
2016 Discrete Applied Mathematics  
problems, and between exact counting, approximate counting and the corresponding decision problems. 1 This result has previously been used along the same lines in different settings by a number of authors  ...  The paper also gives a thorough survey of known results on this subject and the methods used, as well as discussing the relationships both between multicolour and uncoloured versions of subgraph counting  ...  We obtain an approximation to N using a simple random sampling algorithm.  ... 
doi:10.1016/j.dam.2015.06.019 fatcat:utjeznnsxfd45oozdipbxe5xyu

The challenges of unbounded treewidth in parameterised subgraph counting problems [article]

Kitty Meeks
2015 arXiv   pre-print
problems, and between exact counting, approximate counting and the corresponding decision problems.  ...  The paper also gives a thorough survey of known results on this subject and the methods used, as well as discussing the relationships both between multicolour and uncoloured versions of subgraph counting  ...  We obtain an approximation to N using a simple random sampling algorithm.  ... 
arXiv:1402.5857v2 fatcat:e2qzddfidbe73airuxbpmi4lwm

Detecting and Counting Small Subgraphs, and Evaluating a Parameterized Tutte Polynomial: Lower Bounds via Toroidal Grids and Cayley Graph Expanders [article]

Marc Roth, Johannes Schmitt, Philip Wellnitz
2021 arXiv   pre-print
Specifically, we study the parameterized complexity of 𝙴𝚍𝚐𝚎𝚂𝚞𝚋(Φ) and of its counting problem #𝙴𝚍𝚐𝚎𝚂𝚞𝚋(Φ) with respect to both approximate and exact counting.  ...  This allows us to establish hardness of exact counting using the Complexity Monotonicity framework due to Curticapean, Dell and Marx (STOC'17).  ...  We thank Johannes Lengler and Holger Dell for helpful discussions on early drafts of this work.  ... 
arXiv:2011.03433v2 fatcat:7aauf7xejvfx5atw3n7s6sefsa

Exact and Approximate Pattern Counting in Degenerate Graphs: New Algorithms, Hardness Results, and Complexity Dichotomies [article]

Marco Bressan, Marc Roth
2021 arXiv   pre-print
We study the problems of counting the homomorphisms, counting the copies, and counting the induced copies of a k-vertex graph H in a d-degenerate n-vertex graph G.  ...  Those lower bounds for exact counting are complemented with new algorithms for approximate counting of subgraphs and induced subgraphs in degenerate graphs.  ...  Roth is grateful to Lior Gishboliner for introducing him to pattern counting in degenerate graphs.  ... 
arXiv:2103.05588v2 fatcat:pqq53dd72rdjzpc4unymf3igki

Foundations of Online Structure Theory II: The Operator Approach [article]

Rod Downey, Alexander Melnikov, Keng Meng Ng
2021 arXiv   pre-print
We suggest a unifying approach using operators where we allow the input to be a countable object of an arbitrary complexity.  ...  We introduce a framework for online structure theory. Our approach generalises notions arising independently in several areas of computability theory and complexity theory.  ...  a fast Cauchy sequence for f (x) using χ as an oracle.  ... 
arXiv:2007.07401v4 fatcat:abmc5m2g3zhq5f5gdjk37hvxmi

Homology Computation of Large Point Clouds using Quantum Annealing [article]

Raouf Dridi, Hedayat Alghassi
2016 arXiv   pre-print
It uses quantum annealing to compute a clique covering of the graph and then uses this cover to construct a Mayer-Vietoris complex.  ...  The pipeline takes as input a graph approximating the given point cloud.  ...  Oberoi and P. Ronagh for helpful discussions on the topic, and M. Bucyk for proof reading the manuscript.  ... 
arXiv:1512.09328v3 fatcat:pvx6jnwtkvds3lbrv4d6iif5le

Quantum Complexity: restrictions on algorithms and architectures [article]

Daniel James Shepherd
2010 arXiv   pre-print
A dissertation submitted to the University of Bristol in accordance with the requirements of the degree of Doctor of Philosophy (PhD) in the Faculty of Engineering, Department of Computer Science, July  ...  This n s is counting a number of rows, and should not be confused with the n used earlier for counting a number of columns.)  ...  (Note also that oracle use is sometimes employed not with a decision language but with an entire function, possibly probabilistic.  ... 
arXiv:1005.1425v1 fatcat:iusngjiypfgxzlezpnz5yiyarq

Machine Learning Testing: Survey, Landscapes and Horizons [article]

Jie M. Zhang University College London, Nanyang Technological University)
2019 arXiv   pre-print
This paper provides a comprehensive survey of Machine Learning Testing (ML testing) research.  ...  ., correctness, robustness, and fairness), testing components (e.g., the data, learning program, and framework), testing workflow (e.g., test generation and test evaluation), and application scenarios  ...  ACKNOWLEDGEMENT Before submitting, we sent the paper to those whom we cited, to check our comments for accuracy and omission.  ... 
arXiv:1906.10742v2 fatcat:p5c54cy4pjc5flzm7shybk3qxe

Computational Complexity of the Ground State Energy Density Problem [article]

James D. Watson, Toby S. Cubitt
2021 arXiv   pre-print
We formulate this rigorously as a function problem, in which we request an estimate of the ground state energy density to some specified precision; and as an equivalent promise problem, 𝖦𝖲𝖤𝖣, in which  ...  We show that for classical, translationally invariant, nearest neighbour Hamiltonians on a 2D square lattice, 𝖯^𝖭𝖤𝖤𝖷𝖯⊆𝖤𝖷𝖯^𝖦𝖲𝖤𝖣⊆𝖤𝖷𝖯^𝖭𝖤𝖷𝖯, and for quantum Hamiltonians 𝖯^𝖭𝖤𝖤𝖷𝖯⊆𝖤𝖷𝖯  ...  Acknowledgements The authors would like to recognise useful discussions with J. Lockhart, S. Gharibian, and J. Sullivan.  ... 
arXiv:2107.05060v1 fatcat:5nvhdl6f2ndsvorirbss75t2vy

Seeing Things in Random-Dot Videos [article]

Thomas Dagès, Michael Lindenbaum, Alfred M. Bruckstein
2020 arXiv   pre-print
and video data, leads us to see in it a simple computational Gestalt model of human perception with only two parameters: the time integration and the visual angle for candidate shapes to be detected.  ...  The algorithm not only manages to handle such signals but the striking similarity in its performance to the perception by human observers, as witnessed by a series of psychophysical experiments on image  ...  It consists in randomly sampling two points as candidates for a line and count the number of inliers and define that as the score of the sample.  ... 
arXiv:1907.12195v2 fatcat:i634k7bmcnaq3ozit2qtdrmbyq

Tutorials on Testing Neural Networks [article]

Nicolas Berthier and Youcheng Sun and Wei Huang and Yanghao Zhang and Wenjie Ruan and Xiaowei Huang
2021 arXiv   pre-print
The tools developed from this research are now collected, and publicly released, in a GitHub repository: , with the BSD 3-Clause licence.  ...  This tutorial is to go through the major functionalities of the tools with a few running examples, to exhibit how the developed techniques work, what the results are, and how to interpret them.  ...  Oracle To vet a new input as legitimate (i.e., su ciently close to a reference input), and check whether it is correctly classi ed by N , the oracle relies on a given norm and, optionally, on a (series  ... 
arXiv:2108.01734v1 fatcat:aa5yb4ipurcgndfnnwy2yt63wy

Deploying Search Based Software Engineering with Sapienz at Facebook [chapter]

Nadia Alshahwan, Xinbo Gao, Mark Harman, Yue Jia, Ke Mao, Alexander Mols, Taijin Tei, Ilya Zorin
2018 Lecture Notes in Computer Science  
in and uptake of SBSE (and hybridisations of SBSE) as a result.  ...  used daily by hundreds of millions of people around the globe.  ...  Thanks to all our colleagues at Facebook and in the scientific research, open source and developer communities for their support, both technical and non-technical, that has allowed us to so-rapidly deploy  ... 
doi:10.1007/978-3-319-99241-9_1 fatcat:h5gev4472fe5jnrgkspnfwzx6e

Introduction to the Theory of Complexity

V. J. Rayward-Smith
1995 Journal of the Operational Research Society  
A partition P of A is given by P = {{1, 3, 8}, {5, 16, 50}, {12, 25}}. Pairs, n-tuples and relations Given two elements x and y, let us denote the ordered pair of x and y with x, y .  ...  In the following chapters, we shall use the term 'relation' to denote both the set of ordered pairs R and the predicate associated with it.  ...  Acknowledgements This book originated from a course on Algorithms and Complexity given at the University of Rome 'La Sapienza' by D.P. Bovet and P. Crescenzi since 1986.  ... 
doi:10.1057/jors.1995.211 fatcat:rx2m7i3vyreaflkxrbmuh5kbhu
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