PPT-Approximation Algorithms for Knapsack Problems

Author : mitsue-stanley | Published Date : 2016-05-20

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

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Approximation Algorithms for Knapsack Problems: Transcript

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. . NP-Complete. CSE 680. Prof. Roger Crawfis. Polynomial Time. Most (but not all) of the algorithms we have studied so far are easy, in that they can be solved in polynomial time, be it linear, quadratic, cubic, etc.. Prasad . Raghavendra. . Ning. Chen C. . . Thach. . Nguyen . . . Atri. . Rudra. . . Gyanit. Singh. University of Washington. Roee . Engelberg. Technion. University. . of Edit Distance. Robert Krauthgamer, . Weizmann Institute of Science. SPIRE 2013. TexPoint. fonts used in EMF. . Read the . TexPoint. manual before you delete this box. .: . A. A. A. A. A. A. A. 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. 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 . Algorithms. and Networks 2014/2015. Hans L. . Bodlaender. Johan M. M. van Rooij. C-approximation. Optimization problem: output has a value that we want to . maximize . or . minimize. An algorithm A is an . Peter Andras. School of Computing and Mathematics. Keele University. p.andras@keele.ac.uk. Overview. High-dimensional functions and low-dimensional manifolds. Manifold mapping. Function approximation over low-dimensional projections. Problem. Yan Lu. 2011-04-26. Klaus Jansen SODA 2009. CPSC669 Term Project—Paper Reading. 1. Problem Definition. 2. Approximation Scheme. 2.1 Instances with similar capacities. 2.2 General cases . Outline. 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. How accurate is your estimate?. Differential Notation. The Linear Approximation to . y. = . f. (. x. ) is often written using the “differentials” . dx. and . dy. . In this notation, . dx. is used instead of . 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. Lecture 17. May 27, . 2014. May 27, 2014. 1. CS38 Lecture 17. May 27, 2014. CS38 Lecture 17. 2. Outline. coping with . intractibility. NP-completeness. special cases. fixed parameter complexity. approximation algorithms. 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 .

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