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Complexity handouts). Show that First Fit has an approximation ratio of at most 2. In particular, for any input instance, you should find a value B so that every solution uses at least B bins and then show that First Fit uses at most 2B bins. (Hint: It may be helpful to show that, in the solution produced by First Fit, there is at most one bin that is less than half full.) • A simple greedy algorithm is the First Fit algorithm • Process items one by one in an arbitrary order. Place each item in the first bin which was enough space for the item. Open a new bin of such a bin does not exist e.g. < 0.9,0.3, 0.8, 0.5, 0.1, 0.1, 0.3, 0.2, 0.4, 0.2, 0.4, 0.5, 0.5, 0.8,0.6,0.4,0.5>

Complexity handouts). Show that First Fit has an approximation ratio of at most 2. In particular, for any input instance, you should find a value B so that every solution uses at least B bins and then show that First Fit uses at most 2B bins. (Hint: It may be helpful to show that, in the solution produced by First Fit, there is at most one bin that is less than half full.) • A simple greedy algorithm is the First Fit algorithm • Process items one by one in an arbitrary order. Place each item in the first bin which was enough space for the item. Open a new bin of such a bin does not exist e.g. < 0.9,0.3, 0.8, 0.5, 0.1, 0.1, 0.3, 0.2, 0.4, 0.2, 0.4, 0.5, 0.5, 0.8,0.6,0.4,0.5>

Computer Networking: A Top-Down Approach (7th Edition)
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
Section: Chapter Questions
Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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Problem 1 Recall the First Fit algorithm for bin packing (see slide 58 of the Complexity handouts). Show that First Fit has an approximation ratio of at most 2. In particular, for any input instance, you should find a value B so that every solution uses at least B bins and then show that First Fit uses at most 2B bins. (Hint: It may be helpful to show that, in the solution produced by First Fit, there is at most one bin that is less than half full.) • A simple greedy algorithm is the First Fit algorithm Process items one by one in an arbitrary order. Place each item in the first bin which was enough space for the item. Open a new bin of such a bin does not exist • e.g. < 0.9,0.3, 0.8, 0.5, 0.1, 0.1, 0.3, 0.2,0.4, 0.2, 0.4, 0.5, 0.5, 0.8, 0.6,0.4,0.5> ●
Transcribed Image Text:Problem 1 Recall the First Fit algorithm for bin packing (see slide 58 of the Complexity handouts). Show that First Fit has an approximation ratio of at most 2. In particular, for any input instance, you should find a value B so that every solution uses at least B bins and then show that First Fit uses at most 2B bins. (Hint: It may be helpful to show that, in the solution produced by First Fit, there is at most one bin that is less than half full.) • A simple greedy algorithm is the First Fit algorithm Process items one by one in an arbitrary order. Place each item in the first bin which was enough space for the item. Open a new bin of such a bin does not exist • e.g. < 0.9,0.3, 0.8, 0.5, 0.1, 0.1, 0.3, 0.2,0.4, 0.2, 0.4, 0.5, 0.5, 0.8, 0.6,0.4,0.5> ●
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