Question: Consider the following Bin-Covering problem: Given n items with sizes a1, . . . , an (0, 1], maximize the number of bins opened so

Consider the following Bin-Covering problem: Given n items with sizes a1, . . . , an (0, 1], maximize the number of bins opened so that each bin has items summing to at least 1. Give an asymptotic PTAS for this problem when restricted to instances in which item sizes are bounded below by c, for a fixed constant c > 0. (Hint: Use similar techniques as the PTAS algorithm for Bin-Packing problem)

I need a specific answerI think this question is related to PTAS algorithm

Step by Step Solution

There are 3 Steps involved in it

1 Expert Approved Answer

Step: 1 Unlock blur-text-image

Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock

Step: 3 Unlock

Students Have Also Explored These Related Databases Questions!

Consider the following Bin-Covering problem: Given n items with sizes a1, . . . , an (0, 1], maximize the number of bins opened so that each bin has items summing to at least 1. Give an asymptotic...

Johns Hopkins University has n courses. In order to graduate, a student must satisfy all requirements of the form "you must take at least 1 course from subset S " . Moreover, courses are allowed to...

This is all given by instructor 1. Partitioning and packing In the Partition problem, you are given a set {a1, a2, An} of nonnegative integers, and you are asked to decide whether there is a subset S...

You have n items with sizes a 1 , . . . , an to be packed into some bins. Each bin has capacity V . Assume that V ai , i = 1 , . . . , n . That is , at most, you need n bins to pack all items. ( i )...

Given a bin size S and n items of sizes a1, . . . , an, the bin packing problem seeks to find the minimum number of bins into which the n items can be stored without exceeding the size of each bin....

(a) You are given a set of n items of sizes a 1 , . . . , a n , and a bin of size B . Your goal is to find a maximum cardinality subset of items that all fit inside the bin. That is, you want to find...

The Bin Packing problem takes as input an infinite supply of bins B_1, B_2, B_3, ..., each bin of size 1 unit. We are also given n items a_1, a_2, ...a_n, ..., and and each item has a size S_j that...

Problem 3 Formulating IP ( 5 0 points ) A . You have n items with sizes A 1 , cdots, A n to be packed into some bins. Each bin has capacity C . Formulate an integer program to find the packing method...

Can you help me with this number? Thanks! Problem 2 ( 10pts) You have n items with sizes a1,,an to be packed into some bins. Each bin has capacity V. (a). Formulate an integer program to find the...

The company regularly buys sweaters from AA company and is allowed trade discounts of 18% and 9% from the list price. the company made a purchase during the year and received an invoice with a list...

Classification by computer of handwritten digits is a standard problem in pattern recognition. The typical application is automatic reading of zip codes on envelopes. In this assignment youll address...

. Which of the following is a completed gift? A ) Greta transfers $ 5 0 , 0 0 0 to a revocable trust benefiting her children Hans and Julio. B ) Juan purchases a ski chalet using his own funds, but...

Compared with half a century ago, adoption has become _ _ _ _ _ _ _ _ _ common, but it is more open and acceptabl e , so we probably discuss it _ _ _ _ _ _ _ . fill in the blanks more or much less or...

Discuss the key ambient conditions and their effects on customers.

Understand the roles of signs, symbols, and artifacts.

Know the theoretical foundation from environ-mental psychology that helps us understand how customers and employees respond to service environments.