6417c08 - Elementary Graph Algorithms CONTENTS Complexity...

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1 Elementary Graph Algorithms CONTENTS Complexity Analysis (Section 3.2) Search Algorithms (Section 3.4) Topological Sorting (Section 3.4) Flow Decomposition (Section 3.5)
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2 Complexity Analysis How to judge the goodness of an algorithm? How economically it uses the computing resources: Time efficiency Space efficiency Time is more crucial in practice. How to judge the time requirement of an algorithm?
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3 Two Type of Analysis Empirical Analysis Implementation dependent Often inconclusive Too expensive and time-consuming Worst-Case Analysis Obtain upper bounds on the number of steps Often easy to perform Mostly conclusive Bad examples determine the performance Most popular
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4 Worst-Case Analysis This type of analysis determines an upper bound on the number of steps as a function of the problem size. The size of a problem is the number of bits required to state the problem. The size of a network problem is a function of n, m, log C, and log U, where C denotes largest cost and U denotes the largest capacity. If each piece of data (cost and capacity) fits into a single word, then the size of a network problem is a function of n and m. The worst-case analysis for a network optimization algorithm determines an upper bound on the number of steps as a function of n, m, log C, and log U.
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Big O Notation Estimate the number of steps required to execute the following program: for i : = 1 to n do for j : = 1 to n do c ij : = a ij + b ij ; The precise number of steps is implementation dependent and is very difficult to count. MORALE
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6417c08 - Elementary Graph Algorithms CONTENTS Complexity...

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