Telecoms, Architectures and Business Models
Graph theory
Hamiltonian Path, Minimum Spanning Tree
Serafeim (Makis) Gravanis 4413512
1) Is finding Hamiltonian path NP-complete? Why? Also explain in your own words what NP- complete means.
Before we explain why the Hamiltonian path is NP-complete, it will be worth mentioning to refer on the NP-completeness. NP stands for “nondeterministic polynomial time” and its roots are coming form the complexity theory. More specific, this means that although it is possible to verify the correctness of a solution to a problem in polynomial time (quick verification), the use of exponential time is needed in order to compute the exact solution. In other words, the required time to calculate the solution of the problem increases rapidly as the size of the of the
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Indeed in a chess board 3X3 the knight can has 8 possible moves. In Figure 1, can be seen a 3X3 chessboard, which has labeled every square with numbers. The possible moves that the knight can do are: (1,8), (1,6), (2,9), (2,7), (3,4), (3,8), (4,9), (4,3), (6,1), (6,7), (7,2), (7,6), (8,3), (8,1), (9,2), (9,4). We can notice that the square number 5 is not in the aforementioned list of moves. For the same reason the knight’s tour problem cannot be solved in a 4X4 chessboard. More specifically, in the 4X4 chessboard, not even an open tour is possible. In the Figure 2 a knight open tour can be seen. The 4X4 chessboard does not have a knight tour, which would force the four edges 1-2, 2-3, 3-4 and 4-1 to be in any Hamiltonian path of the whole graph. It is clear that after the step to vertex 4 whichever choice we made (left or right) we end up missing several vertices to the way to number 16. Therefore, an open knight tour in a 4X4 chessboard is
When Harriet Tubman was about 28 she had just become a free African American. It was 1849 when her slave owner died, she knew it was the perfect time to go off and become free. When she did, just a year later she started rescuing slaves in 1850. She took big measures to make sure their owners didn’t find them and just bring them back She even took sometimes to Canada. She did this from 1850 to 1860 and rescued 38 slaves and freed them.
Task 1 1.1) Design a networked system to meet the given specification. Your design must satisfy the user requirements and be scalable. [3.1] The design of the network system should include: cost, Bandwidth, system growth, applications, communications, and scalability of the system and selection of components. Introduction - Designing the Network In this design I will be listing and discussing, through the different and necessary designing stages, the various elements involved in designing a network that meets the system requirements given by the client.
It has helped to describe the parameters with an emphasis on lifetime of network, reliability, and the dynamic and static of single and multi-hop networks
He was given a job working in the kitchen until his first great journey. In King Arthur and His Knights of the Round Table by Roger Lancelyn Green, Sir Gareth follows the hero’s cycle as he is called to adventure, faces trials and crises, and returns to a new life at the end of his journey. The first way that Sir Gareth fits the hero’s cycle is that he is called to adventure at the beginning of his journey. He is called when the Lady Linnet comes to King Arthur’s court asking for someone to save her sister, the Lady Lionel.
In 1791, Treasurer Alexander Hamilton proposed the First Bank of the United States, also called the First Bank, which, with the necessary-and-proper clause, allowed the government to act on the four rights stated in the Constitution: “the rights to collect taxes, borrow money, regulate trade among states, and support fleets and armies.” The charter of the First Bank caused a debate that Secretary of State, Thomas Jefferson, a large opponent of a central banking system, later described as “the most bitter and angry contest ever known in Congress before or since the union of the states.” The intensity of it is conveyed in “Cabinet Battle #1” in Hamilton: An American Musical, in which the debate between Hamilton and Jefferson is recreated in
Each network may have a different shape depending on how big it is, how much it expands, and in what direction it is moving in. This is defined as its structure. In order to understand all of this information I will have to look at two areas of knowledge, one of which is mathematics. Mathematics, in comparison to other areas of knowledge, is quite a selective network. It is very limited to what ways of knowing
The debate over the function and definition of the state that would best uphold American liberty began during the Constitutional convention, when the Federalist and Anti-Federalist factions emerged as the bulwarks of their respective ideologies. After the Constitution was ratified, these factions intensified into political parties, justifying their own arguments with varying interpretations of the Constitution. The Federalist party, embodying the Federalist faction, was led by Alexander Hamilton, while the Democratic-Republican party, carrying on many of the ideals of the Anti-Federalist party, was led by Thomas Jefferson. As Madison had noted in Federalist 10, “liberty is to faction what air is to fire…” Both of these men hoisted the preservation
In Hamilton, Mark Steinberg successfully divulges details of the life of Alexander Hamilton from his birth until his death. In as much, Steinberg conveys a wide-ranging journey of cluttered, blog style information on every aspect of Hamilton’s legacy as a revolutionary, statesman, family man, and a lover as an admirer of Hamilton. Therefore, this paper will critique Steinberg’s presentation of personal information about Hamilton as well as his admiration for Hamilton, and will also evaluate Steinberg’s cluttered writing style as he tells the story. This section contains a summary of Hamilton, with Steinberg beginning his book by stating his purpose in writing this book.
4. Discuss the essential differences between Hamiltonians and Jeffersonians during the 1790s. The Hamiltonians, followers of Alexander Hamilton, and the Jeffersonians, followers of Thomas Jefferson created a faction of sorts after the establishment of the Constitution. The Hamiltonians had worked to “establish a national network of influence that embodied all the worst features of a party” (Brinkley, 171).
He is described as a man, “None had seen...with sight in that hall so grand.” (197) Immediately he asks for the leader of the house to which he extends his request for a contest to King Arthur. The unnamed knight then reveals the rules of the game. Carl Martin, in his essay, The Cipher of Violence, elaborates. “ The Green Knight reveals here that while the typical warrior-noble engineers his aggrandizement through public displays of prowess… he is also bound by a strict code of behavior meant to restrain and refine his aggression.”
One of the first paradoxes is seen within the text is with regards to the green giant riding into the dining area of the knights on a horse.
Asia Pratka The first President of the United States, George Washington, and the first Congress set out to create a new banking system for the United States to help its taxing and spending powers become more fluid. Could the federal government create a National Banking system? Twenty-eight years later, McCulloch v. Maryland established the constitutionality of the necessary and proper clause through the Supreme Court. However, was the Supreme Court the right venue to decide if the necessary and proper clause instituted by Congress is constitutionally liberal or expressed, or should "We the People" have the decision?
In the story of Sir Gawain and the Green Knight, we begin in King Arthur’s court at a Christmas feast. A stranger, who calls himself the Green Knight, interrupts the festivities proposing a game. Anyone from King Arthur’s court has the chance to have one swing to chop of the Green Knights head, but in return the brave man who does must find the Green Knight at the Green Chapel in a year’s time, and allow the Green Knight to return the favor. When no knight rushes to take on his challenge, the Green Knight insults the court by calling them cowards. "What, is this Arthur's house...
(Gathering of the Knights pp 23). Thus further proving how humble Arthur is, he created the famous Round Table in order to instill equality for all the knights. Arthur could have easily kept the table the same so he could be the head and receive all the attention and glory, but fame was not as important to
In response to the taunting of the Green Knight, Sir Gawain says, "I shied once: no more. You have my word," (272-273). Gawain, like all natural man, shied away once from the Knight's sword as a defensive reflex, but he quickly shakes off any cowardice and announces to the Green Knight that he was caught in a moment of doubt. From there he goes to say that he ultimately is no coward, but rather a noble and courageous knight of the roundtable who is devoted and loyal to King Arthur. He is more than willing and prepared to take what is coming and preserve the honor of his people, as well as his own.