DOCSLIB.ORG

Detecting Cycles in Graphql Schemas

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text

Load more

Linköping University | Department of Computer and Information Science Bachelor thesis, 16 ECTS | Computer Engineering 2019 | LIU-IDA/LITH-EX-G--19/001--SE Detecting Cycles in GraphQL Schemas Jonas Lind Kieron Soames Supervisor : Patrick Lambrix Examiner : Olaf Hartig Linköpings universitet SE–581 83 Linköping +46 13 28 10 00 , www.liu.se Upphovsrätt Detta dokument hålls tillgängligt på Internet – eller dess framtida ersättare – under 25 år från publiceringsdatum under förutsättning att inga extraordinära omständigheter uppstår. Tillgång till dokumentet innebär tillstånd för var och en att läsa, ladda ner, skriva ut enstaka kopior för enskilt bruk och att använda det oförändrat för ickekommersiell forskning och för undervisning. Överföring av upphovsrätten vid en senare tidpunkt kan inte upphäva detta tillstånd. All annan användning av dokumentet kräver upphovsmannens medgivande. För att garantera äktheten, säkerheten och tillgängligheten finns lösningar av teknisk och admin- istrativ art. Upphovsmannens ideella rätt innefattar rätt att bli nämnd som upphovsman i den omfattning som god sed kräver vid användning av dokumentet på ovan beskrivna sätt samt skydd mot att dokumentet ändras eller presenteras i sådan form eller i sådant sam- manhang som är kränkande för upphovsmannens litterära eller konstnärliga anseende eller egenart. För ytterligare information om Linköping University Electronic Press se förlagets hemsida http://www.ep.liu.se/. Copyright The publishers will keep this document online on the Internet – or its possible replacement – for a period of 25 years starting from the date of publication barring exceptional circum- stances. The online availability of the document implies permanent permission for anyone to read, to download, or to print out single copies for his/hers own use and to use it unchanged for non-commercial research and educational purpose. Subsequent transfers of copyright cannot revoke this permission. All other uses of the document are conditional upon the con- sent of the copyright owner. The publisher has taken technical and administrative measures to assure authenticity, security and accessibility. According to intellectual property law the author has the right to be mentioned when his/her work is accessed as described above and to be protected against infringement. For additional information about the Linköping Uni- versity Electronic Press and its procedures for publication and for assurance of document integrity, please refer to its www home page: http://www.ep.liu.se/. c Jonas Lind Kieron Soames Abstract GraphQL is a database handling API created by Facebook, that provides an effective al- ternative to REST-style architectures. GraphQL provides the ability for a client to spec- ify exactly what data it wishes to receive. A problem with GraphQL is that the freedom of creating customized requests allows data to be included several times in the response, growing the response’s size exponentially. The thesis contributes to the field of GraphQL analysis by studying the prevalence of simple cycles in GraphQL schemas. We have im- plemented a locally-run tool and webtool using Tarjan’s and Johnson’s algorithms, that parses the schemas, creates a directed graph and enumerates all simple cycles in the graph. A collection of schemas was analysed with the tool to collect empirical data. It was found that 39.73 % of the total 2094 schemas contained at least one simple cycle, with the average number of cycles per schema being 4. The runtime was found to be on average 11 mil- liseconds, most of which consisted of the time for parsing the schemas. It was found that 44 out of the considered schemas could not be enumerated due to containing a staggering amount of simple cycles. It can be concluded that it is possible to test schemas for cyclicity and enumerate all simple cycles in a given schema efficiently. Acknowledgments We would like to thank Olaf Hartig, for the support and opportunity to take part in your research, we hope you find the results as interesting as we did. Another huge thank you goes out to Yun Wan Kim from Toronto for providing the collection of GraphQL schemas. We would also want to thank all friends and family that have supported us in our studies and the writing of this thesis. Finally, thank you to our opponents Daniel Dzabic and Jacob Mårtensson for the insightful critique, and for your patience. iv Contents Abstract iii Acknowledgments iv Contents v List of Figures vii List of Tables viii 1 Introduction 1 1.1 Background . 2 1.2 Motivation . 2 1.3 Research questions . 3 1.4 Delimitations . 3 2 Theory 4 2.1 GraphQL . 4 2.2 Graph Theory . 7 2.3 Algorithms . 8 3 Method 18 3.1 Issues to be addressed . 18 3.2 Comparing the algorithms . 18 3.3 Creating the cycle detecting tool . 19 3.4 Web application . 21 3.5 Testing the implementation . 23 3.6 Empirical evaluation . 23 4 Results 24 4.1 Adjustments of the schema converter . 24 4.2 Runtime . 24 4.3 Distribution of Types . 25 4.4 Cycles and SCCs in schemas . 25 5 Discussion 33 5.1 Implementation . 33 5.2 Cycles in schemas . 34 5.3 Evaluation of the Method . 35 6 Conclusion 36 6.1 The work in a wider context . 36 6.2 Future work . 36 v Bibliography 37 A Appendix 38 A.1 Git repositories . 38 vi List of Figures 2.1 An example of some of the more important GraphQL schema types. 5 2.2 An example of a GraphQL query and the expected result. 7 2.3 The graph illustrated is an example of a directed multigraph. The edges are illus- trated as arrows and are unidirectional, leading from a vertex to another. 7 2.4 An example of a directed multigraph that contains multiple SCC’s. ......... 8 2.5 An example SCC that contains 2 cycles (1 Ñ 2 Ñ 3 Ñ 1 and 2 Ñ 4 Ñ 5 Ñ 2). 13 2.6 An example illustration the operation of the Weinblatt algorithm. 16 3.1 An example of a GraphQL schema. This schema is the schema for the graph shown in Figure 2.4 . 20 3.2 An illustration of how the data is structured when converted to a graph. 21 4.1 Average and median runtime of the cycle detection tool for the collection of schemas. Note that none of the edge case schemas are represented in this graph. 25 4.2 Runtime for each schema (without the edge case schemas), where the time is di- vided into the three phases of the cycle detection tool. 26 4.3 The average distribution of vertex types in graphs. 26 4.4 Proportion of schemas that contained cycles versus those that did not. 27 4.5 The distribution of cycles in non-edge case schemas. Only the schemas that con- tain cycles are included. 28 4.6 a) The distribution of cycles compared to the number of edges in schemas. b) The distribution of cycles compared to the number of vertices in schemas. 29 4.7 The distribution of cycles compared to the ratio between edges and vertices in schemas. 30 4.8 The amount of cycles in schemas compared to the size of the largest SCC in each schema. 30 4.9 Screenshot of the web application before the user have entered a GraphQL schema to be evaluated. 31 4.10 Screenshot of the web application after the user entered a schema. The application evaluated the schema and produced a directed graph and all simple cycles are presented to the user in the leftmost text-area. 32 A.1 An illustration of the general layout of the git repositories, branches, forks and how they are connected for the web application as well as for the locally run tool. 39 vii List of Tables 4.1 Average vertices, edges, average connectivity and the average size of the largest SCC in evaluated schemas, clustered by the number of cycles contained in the schemas. 28 viii 1 Introduction Data transfers in a client-to-server relationship have been around since the first websites started to emerge in the 1990s. However, the way clients and servers communicate has been a topic of discussion and research for a long time. In the early 2000s the Representational State Transfer (REST) architectural style, coined by Fielding [4], started to become the most prevalent solution to how developers allowed clients to access websites and is the most com- mon solution right up to the current day. REST-style architectures gave website developers powerful tools that would allow users to request, send or modify data from the server by sending GET, POST, PUT or DELETE requests over the predefined paths. Using a REST-style architecture would allow a client visiting a website to be provided with the information the client needed, when the client needed it. The client is also allowed to interact with the website in more ways than just retrieving information. For example, a client could enter a username and a password into a form to be able to create a profile on a website with persistent data of the client’s information. However, as web services started to increase in scope and with the rise of social me- dia web applications, the amount of data that is sent to and from modern web servers in- creased drastically. The increase in data traffic would illuminate the limitations of using a REST style architecture, since it uses predefined static paths from the client to the server. In a REST style architecture, a datapoint is a node from which data can be received, e.g. www.website.com/datapoint-name where datapoint-name is one of the many datapoints that a website potentially could have.
Recommended publications
  • 11Th International Conference for Internet Technology and Secured Transactions

    11Th International Conference for Internet Technology and Secured Transactions

    Analysis of PRNGs with Large State Spaces and Structural Improvements Gabriele Spenger, Jörg Keller Faculty of Mathematics and Computer Science FernUniversität in Hagen 58084 Hagen, Germany [email protected], [email protected] Abstract usually been subject for a lot of scientific work trying to find any kinds of weaknesses before their standardization. But there are also occasions where the The security of cryptographic functions such as standards do not provide the right tools for an pseudo random number generators (PRNGs) can application. One example is the application on low cost usually not be mathematically proven. Instead, RFID transmitters, which only allow a very low statistical properties of the generator are commonly complexity of the algorithms due to the cost restraints evaluated using standardized test batteries on a (the cost is mostly driven by the required chip area [1]). limited number of output values. This paper In these cases, it might be required to use a non- demonstrates that valuable additional information standardized algorithm. This implies the danger of about the properties of the algorithm can be gathered choosing an algorithm that does not provide the by analyzing the state space. As the state space for necessary security. practical use cases is usually huge, two approaches Besides the algorithms themselves also a couple of are presented to make this analysis manageable. methods for the assessment of the suitability of Results for a practical application of these cryptographic functions have been standardized. approaches to the algorithms AKARI and A5/1 are Examples for methods for assessing the security of provided, giving new insights about the suitability of PRNGs are the Marsaglia suite of Tests of these PRNGs for security applications.
  • Using Map Service API for Driving Cycle Detection for Wearable GPS Data: Preprint

    Using Map Service API for Driving Cycle Detection for Wearable GPS Data: Preprint

    Using Map Service API for Driving Cycle Detection for Wearable GPS Data Preprint Lei Zhu and Jeffrey Gonder National Renewable Energy Laboratory To be presented at Transportation Research Board (TRB) 97th Annual Meeting Washington, DC January 7-11, 2018 NREL is a national laboratory of the U.S. Department of Energy Office of Energy Efficiency & Renewable Energy Operated by the Alliance for Sustainable Energy, LLC This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications. Conference Paper NREL/CP-5400-70474 December 2017 Contract No. DE-AC36-08GO28308 NOTICE The submitted manuscript has been offered by an employee of the Alliance for Sustainable Energy, LLC (Alliance), a contractor of the US Government under Contract No. DE-AC36-08GO28308. Accordingly, the US Government and Alliance retain a nonexclusive royalty-free license to publish or reproduce the published form of this contribution, or allow others to do so, for US Government purposes. This report was prepared as an account of work sponsored by an agency of the United States government. Neither the United States government nor any agency thereof, nor any of their employees, makes any warranty, express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately owned rights. Reference herein to any specific commercial product, process, or service by trade name, trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, or favoring by the United States government or any agency thereof.
  • Modèle Document

    Modèle Document

    AVISO DT CorSSH and DT SLA Product Handbook Reference: CLS-DOS-NT-08.341 Nomenclature: - Issue: 2 rev 0 Date: October 2012 Aviso Altimetry 8-10 rue Hermès, 31520 Ramonville St Agne, France – [email protected] DT CorSSH and DT SLA Product Handbook CLS-DOS-NT-08.341 Iss :2.9 - date : 28/02/2012 - Nomenclature: - i.1 Chronology Issues: Issue: Date: Reason for change: 1.0 2005/07/18 1st issue 1.1 2005/11/08 Processing of ERS-2 data 1.2 2005/10/17 Processing of GFO data 1.3 2008/06/10 New standards for corrections and models for Jason-1 1.4 2008/08/07 New standards for corrections and models for Envisat after cycle 65. 1.5 2008/12/18 New standards for corrections and models for Jason-1 GDR-C. 1.6 2010/03/05 New standards for Jason-2 1.7 2010/06/08 New standards for corrections and/or models Processing of ERS-1 data 1.8 2011/04/14 Correction of table 2 1.9 2012/02/28 Specification of the reading routines for SLA files only 2.0 2012/10/16 New geodetic orbit for Jason-1 (c≥500) New version D for Jason-2 (c≥146) D : page deleted I : page inserted M : page modified DT CorSSH and DT SLA Product Handbook CLS-DOS-NT-08.341 Iss :2.9 - date : 28/02/2012 - Nomenclature: - i.2 List of Acronyms: ATP Along Track Product Aviso Archiving, Validation and Interpretation of Satellite Oceanographic data Cersat Centre ERS d’Archivage et de Traitement CLS Collecte, Localisation, Satellites CMA Centre Multimissions Altimetriques Cnes Centre National d’Etudes Spatiales CorSSH Corrected Sea Surface Height Doris Doppler Orbitography and Radiopositioning Integrated
  • Exact Learning of Sequences from Queries and Trackers

    Exact Learning of Sequences from Queries and Trackers

    UNIVERSITY OF CALIFORNIA, IRVINE Exact Learning of Sequences from Queries and Trackers DISSERTATION submitted in partial satisfaction of the requirements for the degree of DOCTOR OF PHILOSOPHY in Computer Science by Pedro Ascens~ao Ferreira Matias Dissertation Committee: Distinguished Professor Michael T. Goodrich, Chair Distinguished Professor David Eppstein Professor Sandy Irani 2021 Chapter 2 c 2020 Springer Chapter 4 c 2021 Springer All other materials c 2021 Pedro Ascens~aoFerreira Matias DEDICATION To my parents Margarida and Lu´ıs,to my sister Ana and to my brother Luisito, for the encouragement in choosing my own path, and for always being there. { Senhorzinho Doutorzinho ii TABLE OF CONTENTS Page COVER DEDICATION ii TABLE OF CONTENTS iii LIST OF FIGURES v ACKNOWLEDGMENTS vii VITA ix ABSTRACT OF THE DISSERTATION xii 1 Introduction 1 1.1 Learning Strings . .3 1.2 Learning Paths in a Graph . .4 1.3 Literature Overview on Exact Learning and Other Learning Models . .5 2 Learning Strings 12 2.1 Introduction . 12 2.1.1 Related Work . 14 2.1.2 Our Results . 18 2.1.3 Preliminaries . 19 2.2 Substring Queries . 20 2.2.1 Uncorrupted Periodic Strings of Known Size . 22 2.2.2 Uncorrupted Periodic Strings of Unknown Size . 25 2.2.3 Corrupted Periodic Strings . 30 2.3 Subsequence Queries . 36 2.4 Jumbled-index Queries . 39 2.5 Conclusion and Open Questions . 46 3 Learning Paths in Planar Graphs 48 3.1 Introduction . 48 3.1.1 Related Work . 50 3.1.2 Definitions . 52 iii 3.2 Approximation algorithm . 53 3.2.1 Lower bound on OPT .........................
  • USE and MAINTENANCE MANUAL

    USE and MAINTENANCE MANUAL

    USE and MAINTENANCE MANUAL -Steam sterilizer- FOREWORD This manual must be considered an integral part of the sterilizer, and must always be available to users. The manual must always accompany the sterilizer, even if it is sold to another user. All operators are responsible for reading this manual and for strictly complying with the instructions and information it provides. COMINOX is not liable for any damage to people, things, or the sterilizer itself in the event that the operator fails to comply with the conditions described in the manual. These instructions are confidential and the customer may not disclose any information to third parties. Further, this documentation and its attachments may not be tampered with or modified, copied, or ceded to third parties without authorization from COMINOX. 2 Table of contents TABLE OF CONTENTS TABLE OF CONTENTS ........................................................................................................................ 3 Reference index .............................................................................................................................. 6 Graphic representation of references Mod. 18 ......................................................................... 7 Graphic representation of references Mod. 24 ......................................................................... 8 INTRODUCTION .............................................................................................................................. 11 GENERAL SUPPLY CONDITIONS .......................................................................................................
  • 1 Abelian Group 266 Absolute Value 307 Addition Mod P 427 Additive

    1 Abelian Group 266 Absolute Value 307 Addition Mod P 427 Additive

    1 abelian group 266 certificate authority 280 absolute value 307 certificate of primality 405 addition mod P 427 characteristic equation 341, 347 additive identity 293, 497 characteristic of field 313 additive inverse 293 cheating xvi, 279, 280 adjoin root 425, 469 Chebycheff’s inequality 93 Advanced Encryption Standard Chebycheff’s theorem 193 (AES) 100, 106, 159 Chinese Remainder Theorem 214 affine cipher 13 chosen-plaintext attack xviii, 4, 14, algorithm xix, 150 141, 178 anagram 43, 98 cipher xvii Arithmetica key exchange 183 ciphertext xvii, 2 Artin group 185 ciphertext-only attack xviii, 4, 14, 142 ASCII xix classic block interleaver 56 asymmetric cipher xviii, 160 classical cipher xviii asynchronous cipher 99 code xvii Atlantic City algorithm 153 code-book attack 105 attack xviii common divisor 110 authentication 189, 288 common modulus attack 169 common multiple 110 baby-step giant-step 432 common words 32 Bell’s theorem 187 complex analysis 452 bijective 14, 486 complexity 149 binary search 489 composite function 487 binomial coefficient 19, 90, 200 compositeness test 264 birthday paradox 28, 389 composition of permutations 48 bit operation 149 compression permutation 102 block chaining 105 conditional probability 27 block cipher 98, 139 confusion 99, 101 block interleaver 56 congruence 130, 216 Blum integer 164 congruence class 130, 424 Blum–Blum–Shub generator 337 congruential generator 333 braid group 184 conjugacy problem 184 broadcast attack 170 contact method 44 brute force attack 3, 14 convolution product 237 bubble sort 490 coprime
  • Cuckoo Cycle: a Memory Bound Graph-Theoretic Proof-Of-Work

    Cuckoo Cycle: a Memory Bound Graph-Theoretic Proof-Of-Work

    Cuckoo Cycle: a memory bound graph-theoretic proof-of-work John Tromp December 31, 2014 Abstract We introduce the first graph-theoretic proof-of-work system, based on finding small cycles or other structures in large random graphs. Such problems are trivially verifiable and arbitrarily scalable, presumably requiring memory linear in graph size to solve efficiently. Our cycle finding algorithm uses one bit per edge, and up to one bit per node. Runtime is linear in graph size and dominated by random access latency, ideal properties for a memory bound proof-of-work. We exhibit two alternative algorithms that allow for a memory-time trade-off (TMTO)|decreased memory usage, by a factor k, coupled with increased runtime, by a factor Ω(k). The constant implied in Ω() gives a notion of memory-hardness, which is shown to be dependent on cycle length, guiding the latter's choice. Our algorithms are shown to parallelize reasonably well. 1 Introduction A proof-of-work (PoW) system allows a verifier to check with negligible effort that a prover has expended a large amount of computational effort. Originally introduced as a spam fighting measure, where the effort is the price paid by an email sender for demanding the recipient's attention, they now form one of the cornerstones of crypto currencies. As proof-of-work for new blocks of transactions, Bitcoin [1] adopted Adam Back's hashcash [2]. Hashcash entails finding a nonce value such that application of a cryptographic hash function to this nonce and the rest of the block header, results in a number below a target threshold1.
  • User's Manual

    User's Manual

    FCModeler User’s Manual Version 1.0 September 2002 Written by Zach Cox Julie Dickerson Adam Tomjack Copyright Julie Dickerson, Iowa State University 2002 Table of Contents 1 Introduction to FCModeler .....................................................................................................1 2 Setting Up FCModeler............................................................................................................ 1 2.1 Setting up the FCModelerConfig File............................................................................. 1 2.2 Running FCModeler....................................................................................................... 1 3 Sources of Input ...................................................................................................................... 1 3.1 Graph XML Files............................................................................................................ 1 3.1.1 XML Format ........................................................................................................... 1 3.1.2 Example of a Complete XML File.......................................................................... 5 3.1.3 Opening a Graph XML File.................................................................................... 6 3.1.4 Saving a Graph XML File....................................................................................... 7 3.1.5 Saving a JPEG Image of the Graph ........................................................................ 8 3.2 MySQL Database...........................................................................................................
  • Graph Algorithms: the Core of Graph Analytics

    Graph Algorithms: the Core of Graph Analytics

    Graph Algorithms: The Core of Graph Analytics Melli Annamalai and Ryota Yamanaka, Product Management, Oracle August 27, 2020 AskTOM Office Hours: Graph Database and Analytics • Welcome to our AskTOM Graph Office Hours series! We’re back with new product updates, use cases, demos and technical tips https://asktom.oracle.com/pls/apex/asktom.search?oh=3084 • Sessions will be held about once a month • Subscribe at the page above for updates on upcoming session topics & dates And submit feedback, questions, topic requests, and view past session recordings • Note: Spatial now has a new Office Hours series for location analysis & mapping features in Oracle Database: https://asktom.oracle.com/pls/apex/asktom.search?oh=7761 2 Copyright © 2020, Oracle and/or its affiliates Safe harbor statement The following is intended to outline our general product direction. It is intended for information purposes only, and may not be incorporated into any contract. It is not a commitment to deliver any material, code, or functionality, and should not be relied upon in making purchasing decisions. The development, release, timing, and pricing of any features or functionality described for Oracle’s products may change and remains at the sole discretion of Oracle Corporation. 3 Copyright © 2020, Oracle and/or its affiliates Agenda 1. Introduction to Graph Algorithms Melli 2. Graph Algorithms Use Cases Melli 3. Running Graph Algorithms Ryota 4. Scalability in Graph Analytics Ryota Melli Ryota Nashua, New Hampshire, USA Bangkok, Thailand @AnnamalaiMelli @ryotaymnk
  • Pollard's Rho Method

    Pollard's Rho Method

    Computational Number Theory and Algebra June 20, 2012 Lecture 18 Lecturers: Markus Bl¨aser,Chandan Saha Scribe: Chandan Saha In the last class, we have discussed the Pollard-Strassen's integer factoring algorithm that has a run- ning time of O~(s(N)1=2) bit operations, where s(N) is the smallest prime factor of the input (composite) number N. This algorithm has a space complexity of O~(s(N)1=2) bits. In today's class, we will discuss a heuristic, randomized algorithm - namely, Pollard's rho method, whose `believed' expected time complexity is O~(s(N)1=2) bit operations, and which uses only O~(1) space! Although, a rigorous analysis of Pollard's rho method is still open, in practice it is observed that Pollard's rho method is more efficient than Pollard- Strassen factoring algorithm (partly because of the low memory usage of the former). Today, we will cover the following topics: • Pollard's rho method, and • Introduction to smooth numbers. 1 Pollard's rho method Let N be a number that is neither a prime nor a perfect power, and p the smallest prime factor of N. If we pick numbers x0; x1; x2;::: from ZN uniformly, independently at random then after at most p + 1 such pickings we have (for the first time) two numbers xi; xs with i < s such that xi = xs mod p. Since N is not a perfect power, there is another prime factor q > p of N. Since the numbers xi and xs are randomly chosen from ZN , by the Chinese remaindering theorem, xi 6= xs mod q with probability 1 − 1=q even under the condition that xi = xs mod p.
  • I/O Efficient Accepting Cycle Detection*

    I/O Efficient Accepting Cycle Detection*

    I/O Efficient Accepting Cycle Detection? J. Barnat, L. Brim, P. Simeˇcekˇ Department of Computer Science, Faculty of Informatics Masaryk University Brno, Czech Republic Abstract. We show how to adapt an existing non-DFS-based accepting cycle detection algorithm OWCTY [10, 15, 29] to the I/O efficient setting and compare its I/O efficiency and practical performance to the existing I/O efficient LTL model checking approach of Edelkamp and Jabbar [14]. The new algorithm exhibits similar I/O complexity with respect to the size of the graph while it avoids quadratic increase in the size of the graph. Therefore, the number of I/O operations performed is significantly lower and the algorithm exhibits better practical performance. 1 Introduction Model checking became one of the standard technique for verification of hard- ware and software systems even though the class of systems that can be fully verified is fairly limited due to the well known state explosion problem [12]. The automata-theoretic approach [33] to model checking finite-state systems against linear-time temporal logic (LTL) reduces to the detection of reachable accepting cycles in a directed graph. Due to the state explosion problem, the graph tends to be extremely large and its size poses real limitations to the verification process. Many more-or-less successful techniques have been introduced [12] to reduce the size of the graph advancing thus the frontier of still tractable systems. Never- theless, for real-life industrial systems these techniques are not efficient enough to fit the data into the main memory. An alternative solution is to increase the computational resources available to the verification process.
  • Spread Spectrum Based Statistically Distributed

    Spread Spectrum Based Statistically Distributed

    BIJIT - BVICAM’s International Journal of Information Technology Bharati Vidyapeeth’s Institute of Computer Applications and Management (BVICAM), New Delhi (INDIA) A Methodology to Find the Cycle in a Directed GraphUsing Linked List Shubham Rungta1, Samiksha Srivastava2, Uday Shankar Yadav3and Rohit Rastogi4 Submitted in July 2013, Accepted in September 2014 Abstract - In computer science, cycle detection is the Here f(x) is the function and [x: x is 1, 2, 3, 4, 5, 6, y… in algorithmic problem of finding a cycle in a sequence of sequence, where y is 2, 3, 4, 5, and 6 in sequence and is iterated functionvalues. The analysis of cycles in network has repeated], here cycle exists because x repeats the value 2, 3, 4, different application in the design and development in 5, 6 repeatedly. This paper proposes a SUS’s cycle detection communication systems such as the investigation of algorithm to detect cycles and to find number of cycles in any topological features and consideration of reliability and fault directed graph whether it is simple or multi digraph. This tolerance. There are various problems related to the analysis algorithm is also helpful in fetching out the number of cycles in of cycles in network among which the most important one is the whole graph. the detection of cycles in graph. In this paper, we proposed SUS_dcycle method which is a detection algorithm for 2.0 EARLIER WORKS IN THIS FIELD detecting cycle in a directed graph, with the help of linked list 2.1 Floyd's cycle-finding algorithm, also called the "tortoise in order to discover new lists in run time.