Optimization Problems: Greedy Algorithms

Description

This lecture covers optimization problems, which aim to minimize or maximize a parameter over all possible inputs, and how greedy algorithms can be used to solve them by making the 'best' choice at each step. The instructor explains the concept through examples like finding the shortest route between cities and encoding messages efficiently. The lecture also delves into the Cashier's Algorithm, demonstrating how to find the least total number of coins for a given amount using a greedy approach. The proof of optimality for the U.S. coin change-making algorithm is discussed, showing that the greedy algorithm indeed produces the fewest coins possible.

Official source

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Optical fiber

An optical fiber, or optical fibre in Commonwealth English, is a flexible, transparent fiber made by drawing glass (silica) or plastic to a diameter slightly thicker than that of a human hair. Optical fibers are used most often as a means to transmit light between the two ends of the fiber and find wide usage in fiber-optic communications, where they permit transmission over longer distances and at higher bandwidths (data transfer rates) than electrical cables.

Fiber-optic communication

Fiber-optic communication is a method of transmitting information from one place to another by sending pulses of infrared or visible light through an optical fiber. The light is a form of carrier wave that is modulated to carry information. Fiber is preferred over electrical cabling when high bandwidth, long distance, or immunity to electromagnetic interference is required. This type of communication can transmit voice, video, and telemetry through local area networks or across long distances.

Multi-mode optical fiber

Multi-mode optical fiber is a type of optical fiber mostly used for communication over short distances, such as within a building or on a campus. Multi-mode links can be used for data rates up to 100 Gbit/s. Multi-mode fiber has a fairly large core diameter that enables multiple light modes to be propagated and limits the maximum length of a transmission link because of modal dispersion. The standard G.651.1 defines the most widely used forms of multi-mode optical fiber.

Constrained optimization

In mathematical optimization, constrained optimization (in some contexts called constraint optimization) is the process of optimizing an objective function with respect to some variables in the presence of constraints on those variables. The objective function is either a cost function or energy function, which is to be minimized, or a reward function or utility function, which is to be maximized.

Duality (optimization)

In mathematical optimization theory, duality or the duality principle is the principle that optimization problems may be viewed from either of two perspectives, the primal problem or the dual problem. If the primal is a minimization problem then the dual is a maximization problem (and vice versa). Any feasible solution to the primal (minimization) problem is at least as large as any feasible solution to the dual (maximization) problem.