You are given a set W of n widgets and a set G of n gadgets. Each widget w has a weight W(v) and each gadget g has a weight W(g). You would like to match each widget w in W to a unique gadget g in G so as to minimize the sum of the absolute values of the weight differences of the matched pairs. That is, you would like to find a perfect matching M between W and G that minimizes |W(w) – W (g)|. (w,g)ƐM Design an efficient greedy algorithm to solve the given problem. Prove that your algorithm is correct. Analyze the worst-case running time of your algorithm
You are given a set W of n widgets and a set G of n gadgets. Each widget w has a weight W(v) and each gadget g has a weight W(g). You would like to match each widget w in W to a unique gadget g in G so as to minimize the sum of the absolute values of the weight differences of the matched pairs. That is, you would like to find a perfect matching M between W and G that minimizes |W(w) – W (g)|. (w,g)ƐM Design an efficient greedy algorithm to solve the given problem. Prove that your algorithm is correct. Analyze the worst-case running time of your algorithm
Database System Concepts
7th Edition
ISBN:9780078022159
Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan
Chapter1: Introduction
Section: Chapter Questions
Problem 1PE
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![You are given a set W of n widgets and a set Gof n gadgets. Each
widget w has a weight W(v) and each gadget g has a weight W(g). You would like to match
each widget w in W to a unique gadget g in G so as to minimize the sum of the absolute
values of the weight differences of the matched pairs. That is, you would like to find a perfect
matching M between W and G that minimizes
E
Σ
|W(w) – W (g)|.
-
(w,g)EM
Design an efficient greedy algorithm to solve the given problem. Prove that your algorithm
is correct. Analyze the worst-case running time of your algorithm](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F5e4bd05f-4aef-4fd9-8644-85e7420659f6%2F045e0e09-abd6-4ccb-99f6-1ba759b242cd%2F38c0rcd_processed.png&w=3840&q=75)
Transcribed Image Text:You are given a set W of n widgets and a set Gof n gadgets. Each
widget w has a weight W(v) and each gadget g has a weight W(g). You would like to match
each widget w in W to a unique gadget g in G so as to minimize the sum of the absolute
values of the weight differences of the matched pairs. That is, you would like to find a perfect
matching M between W and G that minimizes
E
Σ
|W(w) – W (g)|.
-
(w,g)EM
Design an efficient greedy algorithm to solve the given problem. Prove that your algorithm
is correct. Analyze the worst-case running time of your algorithm
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