Data structures and algorithms Create the table filled with sum total $ for each square, determine which items to select. Show all your “how-I-did-it” work. Knapsack w=15kg Item1 w= 2kg v=$2 Item2 w= 1kg v=$1 Item3 w= 4kg v=$10 Item4 w= 1kg v=$2 Item5 w= 12g v=$4
Give a nondeterministic polynomial time algorithm for the sum of subset problem. Define the transformation from the partition problem to the sum of subsets problem.
ASSIGNMENT Total: 100 points) Let X(1..n) and Y(1..n) contain two lists of n integers, each sorted in nondecreasing order. Give the best (worst-case complexity) algorithm that you can think for finding (a) the largest integer of all 2n combined elements. (b) the second largest integer of all 2n combined elements. (c) the median (or the […]
Does the greedy allocation rule maximize social welfare? Prove the claim or construct an explicit counterexample.
You can earn extra credit by typing up your solutions in LaTeX. Use Overleaf asa LaTeX editor. Exercise adapted from Problem 4.3:Consider a set M of distinct items. There are n bidders, and each bidder i has a publicly known subset Ti ⊆ M of items that it wants, and a private valuation vi for […]
Explain how to implement a welfare-maximizing DSIC mechanism by invoking this subroutine n + 1 times, where n is the number of participants.
08.0-pp-39-54 Lecture 4 Algorithmic Mechanism Design ExercisesExercise 4.1 Consider an arbitrary single-parameter environment, with feasible set X. Prove that the welfare-maximizing allocation rulex(b) = argmax(x1,…,xn)∈Xn∑i=1bixi (4.2)is monotone in the sense of Definition 3.6.[Assume that ties are broken in a deterministic and consistent way,such as lexicographically.] Exercise 4.2 Continuing the previous exercise, restrict now to fea-sible […]