This document is an introduction to basic graph theory. It defines what a graph is made up of (vertices and edges) and describes different types of graphs (directed vs undirected). It also defines common graph terminology. The document outlines different ways to represent graphs using adjacency matrices and lists. It then describes algorithms for traversing graphs, including breadth-first search (BFS) and depth-first search (DFS), and provides examples of applications for each type of search.
This document provides definitions and theorems related to graph theory. It begins with definitions of simple graphs, vertices, edges, degree, and the handshaking lemma. It then covers definitions and properties of paths, cycles, adjacency matrices, connectedness, Euler paths and circuits. The document also discusses Hamilton paths, planar graphs, trees, and other special types of graphs like complete graphs and bipartite graphs. It provides examples and proofs of many graph theory concepts and results.
Amortized analysis allows analyzing the average performance of a sequence of operations on a data structure, even if some operations are expensive. There are three main methods for amortized analysis: aggregate analysis, accounting method, and potential method.
The accounting method assigns differing amortized costs to operations. When the amortized cost is higher than actual cost, the difference is stored as credit. Later operations may use accumulated credits when their amortized cost is lower than actual cost.
The potential method associates potential energy with the data structure as a whole. The amortized cost of an operation is the actual cost plus the change in potential. If potential never decreases, the total amortized cost bounds the total
The document discusses Hamilton paths and circuits, which are paths or circuits in a graph that visit each vertex exactly once. It provides examples of graphs that do and do not have Hamilton paths/circuits. It also discusses the number of Hamilton circuits in complete graphs KN, which is (N-1)!. Complete graphs have the maximum possible number of edges between N vertices.
This document discusses various algorithm paradigms, including brute force, divide and conquer, backtracking, greedy, and dynamic programming. It provides examples of problems that each paradigm can help solve. The brute force paradigm tries all possible solutions, often being the most expensive approach. Divide and conquer breaks problems into identical subproblems, solves them recursively, and combines the solutions. Backtracking uses depth-first search to systematically try and eliminate possibilities. Greedy algorithms make locally optimal choices at each step to find a global optimal solution. Dynamic programming solves problems with overlapping subproblems by storing and looking up past solutions instead of recomputing them.
This document introduces graph theory and provides examples of graphs in the real world. It discusses how graphs are used to represent connections between objects and discusses some key graph concepts like nodes, edges, paths, and degrees. Real-world examples of graphs mentioned include social networks, maps, and the structure of the internet. The document also explains why graph theory is useful for modeling real-world networks and solving optimization problems.
Given two integer arrays val[0...n-1] and wt[0...n-1] that represents values and weights associated with n items respectively. Find out the maximum value subset of val[] such that sum of the weights of this subset is smaller than or equal to knapsack capacity W. Here the BRANCH AND BOUND ALGORITHM is discussed .
The pumping lemma states that for any regular language L, there exists an integer n such that any string x in L with length at least n can be divided into uvw such that: (1) x=uvw, (2) the length of uv is at most n, (3) v is not empty, and (4) for all i>=0, uviw is in L. This allows proving that a language is non-regular by finding a string that cannot be pumped.
This document describes the Bellman-Ford algorithm, a single-source shortest path algorithm that can detect negative edge cycles. It provides pseudocode for the algorithm, runs through an example, discusses the relaxation equation and time/space complexity. It also lists some applications of Bellman-Ford in routing protocols and mentions some references for more information.
The Bellman¨CFord algorithm is an algorithm that computes shortest paths from a single source vertex to all of the other vertices in a weighted digraph.
Elliptic curve cryptography uses elliptic curves over finite fields for public-key encryption. It offers the same security as other public-key cryptosystems using smaller key sizes. The points on an elliptic curve over a finite field form a finite abelian group which can be used for cryptographic operations like point addition. Point addition involves calculating the slope between two points and using it to find the x-coordinate of the sum point, while point doubling uses the tangent line to find the double of a point.
The document discusses graph traversal algorithms breadth-first search (BFS) and depth-first search (DFS). It provides examples of how BFS and DFS work, including pseudocode for algorithms. It also discusses applications of BFS such as finding shortest paths and detecting bipartitions. Applications of DFS include finding connected components and topological sorting.
These slides are about parallel sorting algorithms. In which four types of sorting algorithms are discussed with the comparison between their sequential and parallel ways. The four algorithms which are included are: Bubble sort, merge sort, Bitonic sort and Shear sort.
Linear probing inserts each key into the first empty slot found by incrementing the initial hash value. Quadratic probing calculates successive probe positions using a quadratic formula. Both techniques can resolve collisions but quadratic probing reduces clustering by spreading keys more uniformly across the table.
Cs6503 theory of computation november december 2015 be cse anna university q...appasami
?
This document contains a question paper for a Computer Science and Engineering examination with 15 questions covering various topics in theory of computation such as finite automata, regular expressions, context-free grammars, pushdown automata, Turing machines, and complexity theory. It provides definitions and problems related to determining if a language is regular, context-free, recursively enumerable, deciding membership of strings in a language, and analyzing time complexity of problems. The questions range from basic concepts to more advanced topics like the halting problem and Rice's theorem. The document aims to comprehensively test students' understanding of the theory of computation.
This document provides an introduction to the Master Theorem, which can be used to determine the asymptotic runtime of recursive algorithms. It presents the three main conditions of the Master Theorem and examples of applying it to solve recurrence relations. It also notes some pitfalls in using the Master Theorem and briefly introduces a fourth condition for cases where the non-recursive term is polylogarithmic rather than polynomial.
Simulated annealing is an optimization technique inspired by annealing in metallurgy. It can be used to find solutions to problems like the N-queens puzzle. The algorithm starts with a random solution and makes random changes to it. If a change decreases the cost function, it is accepted, but changes that increase cost may still be accepted probabilistically to avoid getting stuck in local minima. This probability decreases as the "temperature" decreases over time. The document provides an example applying simulated annealing to solve the 40 queens puzzle and discusses advantages like the ability to find global minima without restrictions on the cost function.
The Bellman¨CFord algorithm is an algorithm that computes shortest paths from a single source vertex to all of the other vertices in a weighted digraph. It is slower than Dijkstra's algorithm for the same problem, but more versatile, as it is capable of handling graphs in which some of the edge weights are negative numbers.
This document provides an introduction to theory of computation from Dr. Hussien Sharaf. It discusses how TC emerged from mathematicians' efforts to model machines that can think and do calculations. TC gives answers about capabilities and limitations of computing machines. It explains that TC consists of automata theory, computability theory, and complexity theory. The document also introduces some basic mathematical notations and terminology used in TC like sets, sequences, tuples, relations, functions, graphs, strings, and languages. It includes examples and exercises to illustrate these concepts.
This document discusses methods for solving the travelling salesman problem, specifically focusing on the Hungarian method. It provides an overview of the travelling salesman problem and describes several algorithms to solve it, including genetic algorithms, branch and bound, and dynamic programming. It then explains the Hungarian method in more detail, outlining the algorithm's steps to find an optimal assignment with minimum cost by drawing lines through rows and columns to cover zero entries in the cost matrix. The advantages of the Hungarian method for solving travelling salesman problems are highlighted, along with its time complexity of O(n^3).
This document contains a presentation on Breadth-First Search (BFS) given to students. The presentation includes:
- An introduction to BFS and its inventor Konrad Zuse.
- Definitions of key terms like graph, tree, vertex, level-order traversal.
- An example visualization of BFS on a graph with 14 steps.
- Pseudocode and a Java program implementing BFS.
- Applications of BFS like shortest paths, social networks, web crawlers.
- The time and space complexity of BFS is O(V+E) and O(V).
- A conclusion that BFS is an important algorithm that traverses
The document discusses English grammar, specifically conditional sentences using the subjunctive mood. It provides examples of different types of subjunctive constructions, including be-type, were-type, and conditional subjunctives. It examines subjunctive uses involving time frames that are contrary to past, present, or future facts. Key points include structures using "should" + verb, "wish", and conditional sentences introduced by "if" or "but for".
This document provides an overview of graph theory and some of its common algorithms. It discusses the history of graph theory and its applications in various fields like engineering. It defines basic graph terminology like nodes, edges, walks, paths and cycles. It also explains popular graph algorithms like Dijkstra's algorithm for finding shortest paths, Kruskal's and Prim's algorithms for finding minimum spanning trees, and graph partitioning algorithms. It provides pseudocode, examples and analysis of the time complexity for these algorithms.
In graph theory, a matching is a subset of a graph's edges such hat no two edges meet the same vertex. A matching is maximum if no other matching contains more edges. A trivial solution (exhaustive search) to the problem of finding a maximum matching has exponential complexity. We illustrate polynomial time solutions to the problem that were published between 1965 and 1991.
The document discusses various concepts related to trees and graphs including:
- Definitions of trees, rooted trees, subtrees, and tree traversal methods like preorder, inorder and postorder searches.
- Minimum spanning trees, algorithms to find them like Prim's and Kruskal's, and definitions of spanning trees.
- Definitions of graphs, types of graphs, Euler's formula, planar graphs, Hamiltonian graphs, and graph isomorphism.
The document discusses disjoint sets and operations on disjoint sets such as union and find. Disjoint sets are sets that do not have any common elements. The union of two disjoint sets combines all the elements of both sets. The find operation takes an element as input and returns the set that contains that element. Disjoint sets can be represented using a tree structure. Algorithms for union and find operations are presented, including weighted union and collapsing find techniques that improve the efficiency.
implementation of travelling salesman problem with complexity pptAntaraBhattacharya12
?
This document discusses the travelling salesman problem and its implementation using complexity analysis algorithms. It introduces the travelling salesman problem, which aims to find the shortest route for a salesman to visit each city once and return to the starting point. It describes using graphs and dynamic programming to model and solve the problem. An algorithm is presented that uses dynamic programming to solve the travelling salesman problem in polynomial time by breaking it down into subproblems. Applications including routing software for delivery vehicles are discussed.
This document discusses graph coverage criteria for software testing. It defines graphs, paths, and coverage terms used for modeling software structures. The key structural coverage criteria are node coverage, edge coverage, edge-pair coverage, and prime path coverage. Node coverage requires each node to be visited, while edge coverage requires each edge to be visited. Edge-pair coverage extends this to pairs of edges. Prime path coverage requires all unique prime paths in the graph to be toured, handling loops in a finite way.
Process to file Income Tax Return (ITR1) on www.itreturnsonline.comrollitservices
?
The document outlines the steps to register and file income tax returns online through the income tax e-filing portal. It involves registering with PAN details, filling personal details, selecting the assessment year and ITR form, entering income and deduction details from Form 16 and other sources, generating an XML file, uploading it to the income tax website, downloading and opening the acknowledgment file after verification. The acknowledgment copy needs to be signed and sent to the CPC office address by post for confirmation.
This document describes the Bellman-Ford algorithm, a single-source shortest path algorithm that can detect negative edge cycles. It provides pseudocode for the algorithm, runs through an example, discusses the relaxation equation and time/space complexity. It also lists some applications of Bellman-Ford in routing protocols and mentions some references for more information.
The Bellman¨CFord algorithm is an algorithm that computes shortest paths from a single source vertex to all of the other vertices in a weighted digraph.
Elliptic curve cryptography uses elliptic curves over finite fields for public-key encryption. It offers the same security as other public-key cryptosystems using smaller key sizes. The points on an elliptic curve over a finite field form a finite abelian group which can be used for cryptographic operations like point addition. Point addition involves calculating the slope between two points and using it to find the x-coordinate of the sum point, while point doubling uses the tangent line to find the double of a point.
The document discusses graph traversal algorithms breadth-first search (BFS) and depth-first search (DFS). It provides examples of how BFS and DFS work, including pseudocode for algorithms. It also discusses applications of BFS such as finding shortest paths and detecting bipartitions. Applications of DFS include finding connected components and topological sorting.
These slides are about parallel sorting algorithms. In which four types of sorting algorithms are discussed with the comparison between their sequential and parallel ways. The four algorithms which are included are: Bubble sort, merge sort, Bitonic sort and Shear sort.
Linear probing inserts each key into the first empty slot found by incrementing the initial hash value. Quadratic probing calculates successive probe positions using a quadratic formula. Both techniques can resolve collisions but quadratic probing reduces clustering by spreading keys more uniformly across the table.
Cs6503 theory of computation november december 2015 be cse anna university q...appasami
?
This document contains a question paper for a Computer Science and Engineering examination with 15 questions covering various topics in theory of computation such as finite automata, regular expressions, context-free grammars, pushdown automata, Turing machines, and complexity theory. It provides definitions and problems related to determining if a language is regular, context-free, recursively enumerable, deciding membership of strings in a language, and analyzing time complexity of problems. The questions range from basic concepts to more advanced topics like the halting problem and Rice's theorem. The document aims to comprehensively test students' understanding of the theory of computation.
This document provides an introduction to the Master Theorem, which can be used to determine the asymptotic runtime of recursive algorithms. It presents the three main conditions of the Master Theorem and examples of applying it to solve recurrence relations. It also notes some pitfalls in using the Master Theorem and briefly introduces a fourth condition for cases where the non-recursive term is polylogarithmic rather than polynomial.
Simulated annealing is an optimization technique inspired by annealing in metallurgy. It can be used to find solutions to problems like the N-queens puzzle. The algorithm starts with a random solution and makes random changes to it. If a change decreases the cost function, it is accepted, but changes that increase cost may still be accepted probabilistically to avoid getting stuck in local minima. This probability decreases as the "temperature" decreases over time. The document provides an example applying simulated annealing to solve the 40 queens puzzle and discusses advantages like the ability to find global minima without restrictions on the cost function.
The Bellman¨CFord algorithm is an algorithm that computes shortest paths from a single source vertex to all of the other vertices in a weighted digraph. It is slower than Dijkstra's algorithm for the same problem, but more versatile, as it is capable of handling graphs in which some of the edge weights are negative numbers.
This document provides an introduction to theory of computation from Dr. Hussien Sharaf. It discusses how TC emerged from mathematicians' efforts to model machines that can think and do calculations. TC gives answers about capabilities and limitations of computing machines. It explains that TC consists of automata theory, computability theory, and complexity theory. The document also introduces some basic mathematical notations and terminology used in TC like sets, sequences, tuples, relations, functions, graphs, strings, and languages. It includes examples and exercises to illustrate these concepts.
This document discusses methods for solving the travelling salesman problem, specifically focusing on the Hungarian method. It provides an overview of the travelling salesman problem and describes several algorithms to solve it, including genetic algorithms, branch and bound, and dynamic programming. It then explains the Hungarian method in more detail, outlining the algorithm's steps to find an optimal assignment with minimum cost by drawing lines through rows and columns to cover zero entries in the cost matrix. The advantages of the Hungarian method for solving travelling salesman problems are highlighted, along with its time complexity of O(n^3).
This document contains a presentation on Breadth-First Search (BFS) given to students. The presentation includes:
- An introduction to BFS and its inventor Konrad Zuse.
- Definitions of key terms like graph, tree, vertex, level-order traversal.
- An example visualization of BFS on a graph with 14 steps.
- Pseudocode and a Java program implementing BFS.
- Applications of BFS like shortest paths, social networks, web crawlers.
- The time and space complexity of BFS is O(V+E) and O(V).
- A conclusion that BFS is an important algorithm that traverses
The document discusses English grammar, specifically conditional sentences using the subjunctive mood. It provides examples of different types of subjunctive constructions, including be-type, were-type, and conditional subjunctives. It examines subjunctive uses involving time frames that are contrary to past, present, or future facts. Key points include structures using "should" + verb, "wish", and conditional sentences introduced by "if" or "but for".
This document provides an overview of graph theory and some of its common algorithms. It discusses the history of graph theory and its applications in various fields like engineering. It defines basic graph terminology like nodes, edges, walks, paths and cycles. It also explains popular graph algorithms like Dijkstra's algorithm for finding shortest paths, Kruskal's and Prim's algorithms for finding minimum spanning trees, and graph partitioning algorithms. It provides pseudocode, examples and analysis of the time complexity for these algorithms.
In graph theory, a matching is a subset of a graph's edges such hat no two edges meet the same vertex. A matching is maximum if no other matching contains more edges. A trivial solution (exhaustive search) to the problem of finding a maximum matching has exponential complexity. We illustrate polynomial time solutions to the problem that were published between 1965 and 1991.
The document discusses various concepts related to trees and graphs including:
- Definitions of trees, rooted trees, subtrees, and tree traversal methods like preorder, inorder and postorder searches.
- Minimum spanning trees, algorithms to find them like Prim's and Kruskal's, and definitions of spanning trees.
- Definitions of graphs, types of graphs, Euler's formula, planar graphs, Hamiltonian graphs, and graph isomorphism.
The document discusses disjoint sets and operations on disjoint sets such as union and find. Disjoint sets are sets that do not have any common elements. The union of two disjoint sets combines all the elements of both sets. The find operation takes an element as input and returns the set that contains that element. Disjoint sets can be represented using a tree structure. Algorithms for union and find operations are presented, including weighted union and collapsing find techniques that improve the efficiency.
implementation of travelling salesman problem with complexity pptAntaraBhattacharya12
?
This document discusses the travelling salesman problem and its implementation using complexity analysis algorithms. It introduces the travelling salesman problem, which aims to find the shortest route for a salesman to visit each city once and return to the starting point. It describes using graphs and dynamic programming to model and solve the problem. An algorithm is presented that uses dynamic programming to solve the travelling salesman problem in polynomial time by breaking it down into subproblems. Applications including routing software for delivery vehicles are discussed.
This document discusses graph coverage criteria for software testing. It defines graphs, paths, and coverage terms used for modeling software structures. The key structural coverage criteria are node coverage, edge coverage, edge-pair coverage, and prime path coverage. Node coverage requires each node to be visited, while edge coverage requires each edge to be visited. Edge-pair coverage extends this to pairs of edges. Prime path coverage requires all unique prime paths in the graph to be toured, handling loops in a finite way.
Process to file Income Tax Return (ITR1) on www.itreturnsonline.comrollitservices
?
The document outlines the steps to register and file income tax returns online through the income tax e-filing portal. It involves registering with PAN details, filling personal details, selecting the assessment year and ITR form, entering income and deduction details from Form 16 and other sources, generating an XML file, uploading it to the income tax website, downloading and opening the acknowledgment file after verification. The acknowledgment copy needs to be signed and sent to the CPC office address by post for confirmation.
The document provides instructions for unblocking an ePass2003 token by downloading and installing an admin password plug-in file. It involves inserting the token, downloading the driver file from a website, extracting the downloaded file, running the admin password plug-in setup, clicking the triangle icon to unblock the token, and entering the default SO PIN and a new user PIN of at least 8 characters when prompted.
Exchange rates between currencies are determined by supply and demand in currency markets. The supply of foreign currencies like the US dollar comes from exporters receiving foreign currency, remittances from citizens working abroad, and foreign investment in the domestic economy. The demand for foreign currencies comes from importers needing foreign currency, remittances sent abroad, and domestic investment overseas. The RBI can influence exchange rates by buying or selling foreign reserves, but it aims to only smooth volatility and not interfere with market rates.
This document discusses key concepts about the normal distribution and z-scores, including:
- Approximately 68%, 95%, and 99% of scores in a normal distribution fall within 1, 2, and 3 standard deviations of the mean, respectively.
- A z-score describes how many standard deviations a raw score is above or below the mean, and allows comparison of scores from different distributions.
- The normal curve table lists percentages of scores associated with different z-scores and can be used to find percentages of scores above or below a given value.
LO1 Be able to determine own responsibilities and performance
Own responsibilities: personal responsibility; direct and indirect relationships and adaptability, decision-making processes and skills; ability to learn and develop within the work role; employment legislation, ethics, employment rights and responsibilities Performance objectives: setting and monitoring performance objectives Individual appraisal systems: uses of performance appraisals eg salary levels and bonus payments, promotion strengths and weaknesses, training needs; communication; appraisal criteria eg production data, personnel data, judgemental data; rating methods eg ranking, paired comparison, checklist, management by objectives Motivation and performance: application and appraisal of motivational theories and techniques, rewards and incentives, manager¡¯s role, self-motivational factors
The document discusses education and healthcare during the Mughal/Muslim era in India. It states that under Muslim rule, the government recognized its responsibility to provide for citizens and functioned as a welfare state by establishing many hospitals, medical colleges and funding healthcare. It also notes that both the government and wealthy individuals built educational institutions and supported scholars. The document outlines the educational institutions, subjects taught and prominent figures that advanced learning during several Muslim dynasties from the Slave dynasty to the Mughals. It provides praise from colonial-era writers about the high quality and widespread nature of education in India under Muslim rule.
Custom Molds, Inc. was founded in 1987 and originally focused on custom mold fabrication but has since expanded into plastic parts manufacturing. The changing sales mix has created bottlenecks and quality issues. Alternatives were presented: continue as is, discontinue molds, or restructure. Clear recommendations included improving lead times through better scheduling and layout, eliminating a machinist, and revising the layout. Detailed next steps are to implement recommendations and continue process improvement.
Information shared by M.Ali Lahore for the benefits of society. Get positive feedback after reading and serve the human being just through knowledge/money.You will get reward here and hereafter.Its depends upon you how you will use information for sake of ALLAH.You will be responsible for doing wrongs otherwise ALLAH have created human being for NAIKEE(Good Works).
Contact for More Information : MERITEHREER786@gmail.com
WinJS, Apache Cordova & NFC - HTML5 apps for Android and Windows PhoneAndreas Jakl
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How to create cross-platform mobile apps with HTML5 that integrate directly into the platform.
By combining several enterprise-class frameworks and tools, you can create apps that run on all mobile devices, developed in a central repository and tool.
In this presentation, you will learn how to create HTML5 apps with the Visual Studio Multi-Device Hybrid Apps plug-in. Apache Cordova is directly integrated and resposible for creating native apps for the mobile platforms.
WinJS can be used as a major UI framework that is now open source and works accross all platforms and browsers.
To check how you can integrate apps deeper with the native platforms, you will also see how to install and use a custom plug-in that enables Near Field Communication (NFC) on both Android and Windows Phone.
This document describes the structure and function of the female genitalia and internal genital organs. It provides details on the external genitalia including the labia majora, labia minora, clitoris, urethral meatus and vestibular glands. It then describes the internal genitalia such as the vagina, cervix, uterus and fallopian tubes. The document outlines the process for physical examination including inspection and palpation of the external and internal genitalia. It lists some common health problems of the genitourinary system and abnormalities that may be observed during examination.
Chess pieces made through cnc lathe programming . It includes all the chess pieces except knight with their cad drawing and their programes based on cnc codding .
The Document will help you up to create a HACCP plan for cooked meat " not shelf stable" that includes all related documents with instructions to assist food safety specialist to create and establish and implement HACCP plan food catering and food products in general.
Have a look, when ever you need any assistance please contact me via:
Skype: Karam2013
Email: Eng.karam@outlook.com OR VIA
Mobile: +962780777241
This document provides citations for 30 sources that discuss various aspects of economic development in South Korea and East Asia from the 1970s to present day. The sources include newspaper and magazine articles, books, academic journal articles, and government reports that cover topics like South Korea's economic miracle and growth, the role of the developmental state, rural development programs, comparisons with Latin America, and the transition to neoliberal reforms.
The document summarizes a tiger team project for an exercise management application. The team includes four members and their project manager. The project overview introduces the Android-based app that uses GPS, Google Maps and SQLite to help users plan exercises by providing consumed calories and time. Technical issues addressed working with GPS and using SQLite for the database. Design considerations covered using Agile and Waterfall methods, the development schedule, and plans to improve the app by adding distance tracking, more maintainable code, a network database, and saving map images.