Ebook Algorithms unplugged: Part 2
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Ebook Algorithms unplugged: Part 2
Part IIIPlanning, Coordination and SimulationOverviewHelmut Alt and Riidiger ReischukFreie Universităt Berlin. Berlin. GermanyVnivcrsitat ZU Liibeck, Ebook Algorithms unplugged: Part 2 Lubeck, GermanyStrategic thinking and planning are commonly regarded as typically human capabilities. Ever since computer programs demonstrated that they can beat chess grand masters, however, one can see that some of these skills can be successfully managed by machines. On the other hand, some gam Ebook Algorithms unplugged: Part 2es can be won with very simple strategies, one must have the right knowledge. In a chapter in this part of the book we see this demonstrated impressivEbook Algorithms unplugged: Part 2
ely by the match game Nim.In many games, it is important that we don’t allow the enemy to anticipate our movesj A simple strategy - referred to in comPart IIIPlanning, Coordination and SimulationOverviewHelmut Alt and Riidiger ReischukFreie Universităt Berlin. Berlin. GermanyVnivcrsitat ZU Liibeck, Ebook Algorithms unplugged: Part 2rock paper scissors would be quite boring. Many algorithms can be improved or be speeded up in this way these are called probabilistic or randomized algorithms. Now we need to ask ourselves how a computer could toss a coin, given that we would expect only full precision? The chapter here on random n Ebook Algorithms unplugged: Part 2umbers provides an answer.A strategic and algorithmic approach makes sense even with everyday problems, and not just during games. For example, if weEbook Algorithms unplugged: Part 2
wish to disseminate a message to a broad group of people through phone calls or to many computers via an electronic network, then we need a good plan Part IIIPlanning, Coordination and SimulationOverviewHelmut Alt and Riidiger ReischukFreie Universităt Berlin. Berlin. GermanyVnivcrsitat ZU Liibeck, Ebook Algorithms unplugged: Part 2determining the winner of an election.Some tasks require careful long-term planning. An example is the game schedule for the Bundesliga, the German soccer league, which requires US to consider various constraints.Two chapters in this section deal with simulations, i.e., simulating natural processes Ebook Algorithms unplugged: Part 2using computers. First we consider a problem from physics. We see how to calculate the heat distribution in a metal rod or plate using so-called GaussEbook Algorithms unplugged: Part 2
-Seidel iteration. In the other chapter we consider a theme from biology. We see how one can determine how closely two organisms are related toB. VockPart IIIPlanning, Coordination and SimulationOverviewHelmut Alt and Riidiger ReischukFreie Universităt Berlin. Berlin. GermanyVnivcrsitat ZU Liibeck, Ebook Algorithms unplugged: Part 2 minimal changes in the genetic heritage, how far apart they are from each other or from a common ancestor.The famous mathematician Leonhard Euler posed the Kònigsberg Bridges Problem: Can you cross all seven bridges exactly once on a walk and then return to the starting point? Tills playful questio Ebook Algorithms unplugged: Part 2n by the way. the answer is “No”! - has important applications, such as in route planning, covered in the chapter on Eulerian circuits. In vehicle navEbook Algorithms unplugged: Part 2
igation we are now accustomed to a friendly voice that offers directions or tells US the distance to travel before the next turn. For a long time natuPart IIIPlanning, Coordination and SimulationOverviewHelmut Alt and Riidiger ReischukFreie Universităt Berlin. Berlin. GermanyVnivcrsitat ZU Liibeck, Ebook Algorithms unplugged: Part 2al effort.Finally, we consider a problem in computer graphics. Draw a circle as round as possible on a screen, realized using a grid of individual pixels. Strictly speaking we cannot draw a slanted or curved line, as we could with paper and pencil. However, a detailed analysis of the problem leads t Ebook Algorithms unplugged: Part 2o surprisingly easy and fast solution algorithms.22Broadcasting - How Can I Quickly Disseminate Information?Christian ScheidelerUniversilat Paderborn.Ebook Algorithms unplugged: Part 2
Paderborn, Germanyill the Middle Ages, there was no mass media like TV or radio. As most people were not able to write or read, information was mostlPart IIIPlanning, Coordination and SimulationOverviewHelmut Alt and Riidiger ReischukFreie Universităt Berlin. Berlin. GermanyVnivcrsitat ZU Liibeck, Ebook Algorithms unplugged: Part 2ostly bounded by the speed of horses (though other means like pigeons and smoke or light signals were also used occasionally). Nowadays, the telephone and other media like rhe Internet allow anyone to spread information very quickly around rhe world. Let US consider a specific example here.Steffi li Ebook Algorithms unplugged: Part 2as just been given the task to organize a party for her class, and this at a time when the school holidays have just started! Now. she has to try to rEbook Algorithms unplugged: Part 2
each all fellow students by phone or email. Unfortunately, Steffi does not know their email addresses, but she has a list of all 121 students with thePart IIIPlanning, Coordination and SimulationOverviewHelmut Alt and Riidiger ReischukFreie Universităt Berlin. Berlin. GermanyVnivcrsitat ZU Liibeck, Ebook Algorithms unplugged: Part 2ls, which would consume a lot of time. Hence, she thinks about an alternative approach to reach all students as quickly and cheaply as possible.Strategy 1: Call everybody directlyB. Vòcking et al. (eds.), Algorithms Unplugged,224 Christian ScheidelerThe first strategy that conies to her mind is the Ebook Algorithms unplugged: Part 2silent post game: she just calls the first person on the list and asks him or her to call the next one on the list, who will then call the next one. aEbook Algorithms unplugged: Part 2
nd so on, until everybody on the list has been reached.0 0 0-0Strategy 2: Silent postThe advantage of this strategy is that every student only has to Part IIIPlanning, Coordination and SimulationOverviewHelmut Alt and Riidiger ReischukFreie Universităt Berlin. Berlin. GermanyVnivcrsitat ZU Liibeck, Ebook Algorithms unplugged: Part 2fact, if just 10% of the students do not reach the next one on the list within the same day they were called, it takes at least 12 days until everybody has been informed. Even worse: if someone does not bother to call the next one on the list, the whole system will break down! Thus. Steffi thinks ab Ebook Algorithms unplugged: Part 2out an alternative approach.Since she is interested in computer science, she recalls a sorting method that has also been presented in Chap. 3. There,Ebook Algorithms unplugged: Part 2
a master uses two helpers to cut a sorting problem into two smaller sorting problems, who themselves use two helpers each to cut their sorting problemPart IIIPlanning, Coordination and SimulationOverviewHelmut Alt and Riidiger ReischukFreie Universităt Berlin. Berlin. GermanyVnivcrsitat ZU Liibeck, Ebook Algorithms unplugged: Part 2 example, Steffi could divide the phone list into two halves and call the first person on each of the two halves. Each of them will then be asked to cut their list into two further halves and call the first person on these halves. This is continued until everybody has been called, i.e., we reach a l Ebook Algorithms unplugged: Part 2evel in which people are called who just have to take care of an empty list. Ill this way, the students can be reached much quicker.Strategy 3: PartitEbook Algorithms unplugged: Part 2
ioning the phone list into sublists22 Broadcasting225Part IIIPlanning, Coordination and SimulationOverviewHelmut Alt and Riidiger ReischukFreie Universităt Berlin. Berlin. GermanyVnivcrsitat ZU Liibeck, Part IIIPlanning, Coordination and SimulationOverviewHelmut Alt and Riidiger ReischukFreie Universităt Berlin. Berlin. GermanyVnivcrsitat ZU Liibeck,Gọi ngay
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