Algorithmic adventures: from knowledge to magic by Juraj Hromkovič

By Juraj Hromkovič

The ?rst and superior objective of this lecture sequence used to be to teach the sweetness, intensity and value of the main rules in laptop technology. whereas engaged on the lecture notes, we got here to appreciate that possible realize the genuine spirit of a scienti?c self-discipline merely by way of viewing its contributions within the framework of technology as an entire. We current machine technology the following as a primary technological know-how that, interacting with different scienti?c disciplines, replaced and alterations our view at the global, that contributes to our figuring out of the elemental ideas of technological know-how and that sheds new gentle on and brings new aspiring to a number of of those recommendations. We express that machine technology is a self-discipline that discovers striking, unforeseen proof, that ?nds methods out in likely unsolvable s- uations, and which may do real wonders. The message of this publication is that computing device technological know-how is an engaging study region with a huge effect at the genuine international, choked with fantastic principles and nice ch- lenges. it's a vital part of technological know-how and engineering with an above-average dynamic over the past 30 years and a excessive measure of interdisciplinarity. The target of this ebook isn't average for well known technology writing, whichoftenrestrictsitselftooutliningtheimportanceofaresearch zone. each time attainable we try to deliver complete knowing of the recommendations and effects presented.

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Unfortunately, we can very rarely look ahead and so we have to take decisions without knowing the future. Let us consider the management of a medical emergency center with mobile doctors. The aim of the center is to deploy doctors efficiently, although nobody knows when and from where the next emergency call will arrive. For instance, the control desk can try to minimize the average (or the maximum) waiting time of patients or to minimize the overall length of all driven routes. One can develop various strategies for determining what a doctor has to do after handling a case: wait for the next case at the present location, or go back to the medical center, or take up another, strategically selected, waiting position.

This way, one sacrifices absolute reliability in the sense of the guarantee to always compute a correct solution, because one allows some sequences of random events (coin tosses) to execute unsuccessful computations. An unsuccessful computation may be a computation without any result or even a computation with a false result. But if one can reduce the probability of executing an unsuccessful computation to one in a billion, then the algorithm may be very useful. We call attention to the fact that in practice randomized algorithms with very small error probabilities can even be more reliable than their best deterministic counterparts.

2. This computer model consists of the following parts: • A memory that consists of a large number of memory cells. These memory cells are called registers. The registers are numbered by positive integers and we call them addresses of the registers. For instance 112 is the address of Register(112). This corresponds to the image in which the registers are houses on one side of a long street. Each register can save an arbitrarily large number2 . • A special memory in which the whole program is saved.

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