PPT-Knapsack Problem

A dynamic approach Knapsack Problem Given a sack able to hold K kg Given a list of objects Each has a weight and a value Try to pack the object in the sack so that the total value is maximized. Networks, 1978. Classic Paper Reading 99.12. Outline. Introduction. NDP is NP-complete. SNDP is NP-complete. Conclusion. 2. Introduction. B96902094 . 傅莉雯. Combinatorial optimization . is a topic in. and. Given positive integers v. i. and w. i. for . i = 1, 2, ..., n.. and positive integers. K . and. W.. Does there exist a subset . S . of. {1, 2, ..., n}. such that:. A special case: S. UBSET. By. Farnoosh Davoodi. 1. Agenda. Min Knapsack Problem. 2 approximation greedy algorithm. Proof . 3/2 approximation greedy algorithm. Proof. Another improved heuristic. Heuristics for the O-1 Min-Knapsack Problem. 1. Tsvi. . Kopelowitz. Knapsack. Given: a set S of n objects with weights and values, and a weight bound:. w. 1. , w. 2. , …, w. n. , B (weights, weight bound).. v. 1. , v. 2. , …, v. n. (values - profit).. 1. Merkle-Hellman Knapsack. Public Key Systems . 2. Merkle-Hellman Knapsack. One of first public key systems. Merkle offered $100 award for breaking singly - iterated knapsack. Singly-iterated Merkle - Hellman KC was broken by Adi Shamir in 1982   . At the CRYPTO ’83 conference, Adleman used an Apple II computer to demonstrate Shamir’s method . and. Given positive integers v. i. and . w. i. for . i = 1, 2, ..., n.. and positive integers. K . and. W.. Does there exist a subset . S . of. {1, 2, ..., n}. such that:. A special case: S. UBSET. Merkle offered $100 award for breaking singly - iterated knapsack. Singly-iterated Merkle - Hellman KC was broken by Adi Shamir in 1982   . At the CRYPTO ’83 conference, Adleman used an Apple II computer to demonstrate Shamir’s method . A dynamic approach. Knapsack Problem. Given a sack, able to hold . W. . kg. Given a list of objects. Each has a weight and a value. Try to pack the object in the sack so that the total value is maximized. 1. Dynamic Programming: . 0/1 Knapsack. Presentation for use with the textbook, . Algorithm Design and Applications. , by M. T. Goodrich and R. Tamassia, Wiley, 2015. Dynamic Programming. 2. The 0/1 Knapsack Problem. Part 5. Summary created by. Kirk Scott. 1. This set of overheads corresponds to . the first . portion of section 12.3 in the book. The overheads for Chapter 12 roughly track the topics in the chapter. 6 of . Dasgupta. . et al.. October 20, 2015. 2. Outline. Intro. Counting combinations. 0-1 Knapsack (section 6.4). Longest common subsequence. Later. Bellman-Ford (single source shortest path). Floyd-. Lecture #23. Limits of Computing. 4.74 degrees of separation?. Researchers at Facebook and the University of Milan found that the avg # of “friends” separating any two people in the world was < 6.. Outline. Knapsack revisited: How to output the optimal solution, and how to prove correctness?. Longest Common Subsequence. Maximum Independent Set on Trees.. Example 2 Knapsack Problem. There is a knapsack that can hold items of total weight at most .