Scheduling Algorithms Programs In C

Fd74%2Fd7487411-c97b-4c0c-a728-0631cc855d22%2Fphpp0hAbr.png' alt='Scheduling Algorithms Programs In C' title='Scheduling Algorithms Programs In C' />Feature Column from the AMSSome of the fascinating mathematics of sports scheduling. Joseph Malkevitch. York College CUNYmalkevitch at york. Introduction. Sports in America is both big business and democracy in action. Baseball, football, and basketball have become writ large, with games on television and cable television generating huge sums of money that goes into the American economy. But sports are also a mechanism whereby American children learn the values of fair play, hard effort, and the meaning of friendship. Mathematics Awareness Month was created to help focus the publics attention on the nature of mathematics and the way it affects our daily lives and fosters the development of new tools to solve problems for individuals, businesses, and governments. This year the theme for Mathematics Awareness Month is Mathematics and Sports. The first areas where people think about mathematics being applied are in the sciences and engineering. Pes 2008 For Pc Compressed. Yet mathematics plays a large role in the efficiency of sports. Coaches constantly try to find ways to get the most out of their athletes, and sometimes they turn to mathematics for help. This help may include the best batting order for a team to maximize the number of runs it can score or the putting together of a program for an Olympic skater so that the jumps the skater makes take advantage of the scoring bonus when these jumps are performed later in a program when tiredness starts to set in. There are also mathematical issues involved in scoring systems for some of the complex and subjective aspects of scoring sports events. However, the sheer magnitude of the number of games that must be played in league sports creates a large domain for mathematics to assist in the efficient operation of sports. Scheduling Algorithms Programs In C' title='Scheduling Algorithms Programs In C' />This runs the gamut from intellectual sports such as bridge, whist, and chess, to sports such as baseball, football, basketball, soccer, and cricket. Here I will limit myself to some of the fascinating mathematics of sports scheduling and some related fairness and optimization questions that use relatively elementary or quick starting methods. One way of getting insight into a complex environment is to classify what one sees and study the objects in each of the categories separately as a way of simplifying things. In fact there are many types of tournaments round robin tournament each team plays exactly k games against every other team playerNote Very often the value of k 1 is so each team or player gets to play exactly one game match against every other team or player. Note there are variants of this, especially double elimination tournaments. In this idea losers in the various rounds of elimination play against each other and, thus, a later series of victories can lead to a final victory. Perhaps the very first question that arises in scheduling is to design the matches that must occur for a round robin tournament. In a single round robin tournament SRRT each team must play exactly one game against every other team. We will devote what follows mostly to single round robin tournaments. Many questions arise where mathematics provides insight. Disk scheduling is is done by operating systems to schedule IO requests arriving for disk. Disk scheduling is also known as IO scheduling. Disk scheduling is. First, there is the issue of scheduling. If there are 8 teams, what is an efficient way to schedule the matches that must take place Another question, about which there is a huge literature but which will not be treated here, is how to decide on the winner based on the results or scores that the players attain. For example, if one has 8 teams, could the number of wins of the eight teams in decreasing order be 6, 5, 5, 4, 4, 2, 2, 0 Questions about rankings for teams in tournaments are closely related to the issues of ranking candidates in an election or ranking choices for economic policy. Graph theory helps schedule tournaments. Graph theory, a branch of combinatorics which draws heavily on geometrical ideas, uses diagrams consisting of dots and lines to help get insight into a variety of mathematical problems. In computing, scheduling is the method by which work specified by some means is assigned to resources that complete the work. The work may be virtual computation. This set of Operating System Multiple Choice Questions Answers MCQs focuses on Virtual Memory Page Replacement Algorithms 1. Tukel, O. I. 1996. Scheduling resourceconstrained projects when nonconformities exist. Project Management Journal, 273, 4755. Start exploring endless computing possibilities with your own Raspberry Pi computer and accessories. Perfect for beginners and students. TABLE 101 Critical Path Scheduling Algorithms ActivityonBranch Representation Event Numbering Algorithm Step 1 Give the starting event number 0. This set of 1000 Operating System Questions and Answers focuses on Process Scheduling Queues 1 Which of the following do not belong to queues for processes Download the free trial version below to get started. Doubleclick the downloaded file to install the software. The complete graph on n vertices has exactly one edge between every pair of vertices. These graphs are denoted Kn Figure 1 shows K4 and Figure 2 shows K5. Figure 1. Figure 2. In each case the vertices of the graph are labeled with the names of the people or teams involved in the tournament or competition. Think of the vertices dots of a complete graph as representing the teams in a tournament and think of an edge joining two teams as being a match played by those two teams. The number of edges of the complete graph with n vertices is nn 12, which is the number of matches that must be carried out in order to have each team play every other team exactly once. Scheduling Algorithms Programs In C' title='Scheduling Algorithms Programs In C' />Note that in the graph Kn each vertex has n 1 edges at each vertex. The number of edges at a vertex of a graph is known as its degree or valence. Consider first the case where there are 4 teams that must play each other. This means a total of 432 6 matches must be played. These matches could be played in 6 time slots, say one a week for 6 weeks. However, it might be desirable if venues rooms playing fields for the matches are available to have several matches per time slot and the games be completed over a shorter period of time. Thus, since there are 4 players, and 42 is 2, we could consider having two matches per time slot, and complete the tournament in three weeks rather than 6 weeks. When I use the phase time slot, there are various possibilities as to how the matches are actually played. Note that two matches per time slot might mean that there would be two games at exactly the same time or that the games be played in the morning and afternoon on the same court of a single day. There are a variety of terms used other than time slots, and a common one is rounds, which I will use interchangeably with time slots and Event Window. Figure 3 shows the details of how the scheduling could work. Figure 3. Edges in the graph that have the same color would occur during one time slot. Thus, for Event Window 1 shown in blue there would be matches between team 0 and team 3 and team 1 and team 2 for Event Window 2 shown in black we would pair team 0 and team 1 and team 2 and team 3 and for Event Window 3 shown in red we would pair team 0 and team 2 and team 1 and team 3. In attempting to use the ideas above we come to a complication when we try to extend what we have done from 4 teams to 5 teams. Since 5 is an odd number we can not merely have all the teams play in pairs during an Event Window. There is a natural way to handle this problem. The concept of a bye in sports scheduling refers to a teams not having to play a match game during a particular Event Window. If one has 5 teams, there are 1. Since 52 is not an integer, we can not play 3 games per Event Window but we can play 2 games per Event Window 4 teams play and assign a bye to one team. Thus, in five Event Windows we can schedule the whole tournament. You can see the way a schedule for the five Event Windows can be constructed and see the team which has a bye in each Event Window by consulting Figure 4. Figure 4. The edges in different colors signify which teams play in an Event Window.