Interval Selection Problem (ISP). In the ISP, we are given n intervals (81, f1), (82, f2), ..., (Sn; fn), and are asked to find a largest subset of intervals that are mutually disjoint. For simplicity, let's assume that all s, f values are distinct. We refer to s; and fi as interval i's start and finish times, respectively. Also assume that intervals are ordered in increasing order of their finish time, i.e., fi < f2 < ... < fn· Prove that the greedy algorithm, EE (Earliest Ending), is optimal.

Interval Selection Problem (ISP). In the ISP, we are given n intervals (81, f1), (82, f2), ..., (Sn; fn), and are asked to find a largest subset of intervals that are mutually disjoint. For simplicity, let's assume that all s, f values are distinct. We refer to s; and fi as interval i's start and finish times, respectively. Also assume that intervals are ordered in increasing order of their finish time, i.e., fi < f2 < ... < fn· Prove that the greedy algorithm, EE (Earliest Ending), is optimal.

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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For this question, you will be required to use the binary search to find the root of some function f(x)f(x) on the domain x∈[a,b]x∈[a,b] by continuously bisecting the domain. In our case, the root of the function can be defined as the x-values where the function will return 0, i.e. f(x)=0f(x)=0 For example, for the function: f(x)=sin2(x)x2−2f(x)=sin2(x)x2−2 on the domain [0,2][0,2], the root can be found at x≈1.43x≈1.43 Constraints Stopping criteria: ∣∣f(root)∣∣<0.0001|f(root)|<0.0001 or you reach a maximum of 1000 iterations. Round your answer to two decimal places. Function specifications Argument(s): f (function) →→ mathematical expression in the form of a lambda function. domain (tuple) →→ the domain of the function given a set of two integers. MAX (int) →→ the maximum number of iterations that will be performed by the function. Return: root (float) →→ return the root (rounded to two decimals) of the given function. START FUNCTION def binary_search(f,domain, MAX =…
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