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Unformatted text preview: Algorithms in Systems Engineering IE170 Final Review Dr. Ted Ralphs IE170 Final Review 1 Textbook Sections Covered in Course Introduction to Part I Chapter 1, all sections Chapter 2, all sections Chapter 3, all sections Chapter 4, intro and sections 13 Introduction to Part II Chapter 6, all sections Chapter 7, all sections Introduction to Part III Chapter 10, all sections Chapter 11, intro and sections 14 Chapter 12, all sections Chapter 21, intro and sections 13 Introduction to Part VI Chapter 22, intro and sections 14. Chapter 23, intro and section 3. Chapter 28, intro and sections 1 and 3. Chapter 31, intro and sections 2, 4, 6, 7, 8. Chapter 32, intro and sections 1, 2, and 4. IE170 Review: Algorithms 2 Algorithms IE170 Review: Algorithms 3 Algorithms • The main theme of the course has been the design, implementation, and analysis of algorithms and data structures for solving problems . • A problem specifies the form of the output desired for a given set of inputs. • An algorithm is a specific procedure for converting input to output. • An algorithm is said to be correct for a given problem if it successfully converts each possible input into an output of the desired form, called a solution . • Ultimately, we are interested in algorithms that are fast . • We will judge the speed of an algorithm by the number of fundamental operations required to execute it, generally called the running time . • This provides a measure that is independent of hardware . IE170 Review: Algorithms 4 Analyzing Algorithms • The goal of analyzing an algorithm is to determine its running time. • A problem instance is just a specific set of inputs. • The running time of an algorithm is different for different instances. • This creates difficulties for analysis and leads to two different summary measures of running time. – Worstcase – Averagecase • Worstcase is almost always easier to compute, but averagecase is often a more useful measure. • We can use either theoretical or empirical analysis, or a combination, to determine running time. IE170 Review: Algorithms 5 Models of Computation • In order to analyze the number of steps necessary to execute an algorithm, we have to say what we mean by a “step.” • To define this precisely is tedious and beyond the scope of this course. • A precise definition depends on the exact hardware being used. • Our analysis will assume a very simple model of a computer called a random access machine (RAM). • In a RAM, the following operations take one step. – arithmetic (addition, subtraction, multiplication, division) – data movement (read from memory, store in memory, copy) – comparison – control (function calls, goto commands) • This is a very idealized model, but it works in practice....
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 Spring '07
 Ralphs
 Graph Theory, Data Structures, Systems Engineering

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