Algorithms and Complexity

COMP36111 Algorithms and Complexity 10 Semester 1 Undergraduate Level 3 Ian Pratt-Hartmann Unit coordinator 1 FHEQ level (Framework for Higher Education Qualifications) ' Last part of a Bachelors ' European Credit Transfer & Accumulation System Rating : 5.0 The Unit constitutes a self-contained introduction to the theory of Computational Complexity. It assumes no pre-requisites other than a knowledge of basic algorithms and mathematical notation. The teaching will be exclusively by means of traditional lectures, supported by the prescribed course text. The Unit is divided into two sections, of roughly equal weight. The first comprises a survey of some classic algorithms in Computer Science and analyses their complexity. The second section looks at the intrinsic complexity of problems (rather than of the algorithms for solving them), and comprises a basic introduction to the theory of computational complexity. The unit aims to explain how to analyse the complexity of a collection of well-known algorithms, and to familiarize students with the basic concepts and techniques of the theory of computational complexity. <wbr style="color: rgb(0, 0, 0); font-family: Times New Roman; font-size: 16px; font-style: normal; font-variant: normal; font-weight: 400; letter-spacing: normal; orphans: 2; text-align: left; text-decoration: none; text-indent: 0px; text-transform: none; -webkit-text-stroke-width: 0px; white-space: normal; word-spacing: 0px;" /><div> <ul> <li> To understand the standard hierarchy of commonly-encountered complexity classes defined in relation to the Turing model of computation.</li> </ul> <ul> <li> To understand the concepts of (problem-) reduction and computational hardness, and to develop familiarity with techniques for establishing lower complexity bounds---especially, NPTime-hardness.</li> </ul> <ul> <li> To be familiar with the most important and central theorems in Complexity Theory (Cook's theorem, Ladner's theorem, Savitch's theorem the Immerman-Szelepcsenyi theorem).</li> </ul> <ul> <li> To be able to access and understand the scientific literature in regard to Complexity Theory.</li> </ul> <ul> <li> To be able to analyse the computational complexity of a range of problems. </li> </ul></div>  Analytical skills Innovation/creativity Problem solving Directed graphs---topological ordering and Kosaraju's algorithm; undirected graphs--- union find; the Grzegorczyk hierarchy; flow networks---optimal flows, min-cost max-flow; 2D matching; string-processing algorithms; Turing Machines and computability; the Entscheidungsproblem; measuring computational complexity; separation theorems; SAT, k-SAT, Horn-SAT and QBF-SAT; hardness and reductions---Cook's theorem; graph-theoretical problems---3-colouring, Hamiltonian and Eulerian circuits; the TSP; integer linear programming; Savitch's theorem and the Immerman-Szelepcsényi theorem. Two 1-hour lectures per week; coursework to provide practice for examination; final lecture on how to pass the examination. 1 Written exam 80% 9 Set exercise 20%  Through coursework in weeks 4, 7 and 10 COMP11120 Mathematical Techniques for Computer Science Pre-Requisite Compulsory COMP11212 Fundamentals of Computation Pre-Requisite Compulsory COMP26120 Algorithms and Data Structures Pre-Requisite Compulsory MATH11121 Mathematical Foundations & Analysis Pre-Requisite Compulsory MATH10111 Foundations of Pure Mathematics B Pre-Requisite Compulsory MATH10101 Foundations of Pure Mathematics A Pre-Requisite Compulsory Pre-requisitesTo enrol students are required to have taken COMP26120 and one of the following:  COMP11120, MATH10101 or MATH10111 or MATH11121. Y Michael Goodrich, Roberto Tamassia: Algorithm design and applications, John Wiley, 2015 Michael Sipser: Introduction to the Theory of Computation, Third ed., Ceenage Learning, 2012 Sanjeev Arora and Boaz Barak: Computational Complexity, a modern approach, Cambridge, 2016 Lectures 22 0 78 Course unit materials<a href="http://studentnet.cs.manchester.ac.uk/ugt/syllabus.php" target="_blank">Links to course unit teaching materials</a> can be found on the School of Computer Science website for current students.