Say in a scheduling scenario you are given a number of jobs, each with a start time and a finish time. Two jobs conflict if they overlap in time, i.e., one of them starts between the start and finish times of the other. Your goal is to select a maximum-size subset of jobs that have no conflicts. Example: Three jobs consuming the intervals [0, 3], [2, 5], and [4, 7]. The optimal solution in this case would consist of the first and third ones. Design and describe a greedy algorithm that computes an optimal solution to this problem. Informally argue why the solution is likely to be optimal and demonstrate on an example. You may assume that there are no ties.

Say in a scheduling scenario you are given a number of jobs, each with a start time and a finish time. Two jobs conflict if they overlap in time, i.e., one of them starts between the start and finish times of the other. Your goal is to select a maximum-size subset of jobs that have no conflicts. Example: Three jobs consuming the intervals [0, 3], [2, 5], and [4, 7]. The optimal solution in this case would consist of the first and third ones. Design and describe a greedy algorithm that computes an optimal solution to this problem. Informally argue why the solution is likely to be optimal and demonstrate on an example. You may assume that there are no ties.

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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8. A school is creating class schedules for its students. The students submit their requested courses and then a program will be designed to find the optimal schedule for all students. The school has determined that finding the absolute best schedule cannot be solved in a reasonablo time. Instead they have decided to use a simpler algorithm that produces a good but non-optimal schedule in a more reasonable amount of time. Which principle does this decision best demonstrate? O A Unreasonable algorithms may sometimes also be undecidable O B. Heuristics can be used to solve some problems for which no reasonable algorithm exsts O C. efficiency Two algorithms that solve the same problem must also have the same O B. Approximate solutions are often identical to optimal solutions
Both the Principle of Optimality (Optimal Substructure) and Insufficient Overlapping Subproblems are valid inputs for dynamic programming. To see how difficult it is to meet these two criteria, consider the case of All-Pairs Shortest Paths.
Simple example in healthcare: Let consider 7 patients with different surgeries times: ST=[4h30, 4h, 3h, 3h, 2h30, 1h30, 1h] We have to decide how to assign patients to the operating rooms. First problem: let consider 3 operating rooms available with their corresponding capacities OR=[7h30, 4h, 4h]. We want to operate the maximum number of patients. Propose a model and solve it using CPLEX
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Given a set of jobs {J1, ... , Jn}, each job Ji = < ti, wi > has a required processing time ti and aweight wi. Design an efficient algorithm (pseudo code) to minimize the weighted sum of overall completion times ∑ni=1wiCi, where Ci is the completion time of job i. What is the time complexityof your algorithm? Note: You first need to briefly explain your ideas to solve the problem, e.g. what data structures are used, how the intermediate results are saved, which sorting strategy is used, and why the final results are correct;
Assume for convenience that demand is constant, the stock keeping unit (SKU) has been stored in k locations of identical size, and all picks are from a single active pick location until that location is exhausted. Then the inventory cycle may be imagined as consisting of k periods, each devoted to a particular pick location. The space utilization in period i is k-(i-1)-12/1 k-i+ k-(i-1) Thus, the average of the space utilization (ASU) of all k periods is asu= (1) The space utilization (SU) of the whole k periods is su = k = k i=1 2 k-i +1 i=1 k-i+ k-i +1 Σk-i+ i=1 k Σ(k-i+1) Use MATLAB® to write the functions to calculate "asu" and "su" of input "K". Employing these functions, program the script to draw the curves that show how both "asu" and "su" increase with additional storage locations, but at a diminishing rate.
pls solve part a
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