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The traveling tournament problem (TTP) is a mathematical optimization problem. The question involves scheduling a series of teams such that: Each team plays every other team twice, once at home and once in the other's stadium. No team plays the same opponent in two consecutive weeks.
There are an additional 2,900 kilometres (1,800 mi) of water routes, which is sectionally navigable by craft drawing less than 0.5 metres (1 ft 8 in). [5] Laos has an ocean-going merchant marine that consisted of one cargo ship of 2,370 gross tonnage (GT) in 2004, [10] and still consisted of one ship in 2023. [5]
Many mathematical problems have been stated but not yet solved. These problems come from many areas of mathematics, such as theoretical physics, computer science, algebra, analysis, combinatorics, algebraic, differential, discrete and Euclidean geometries, graph theory, group theory, model theory, number theory, set theory, Ramsey theory, dynamical systems, and partial differential equations.
Another related problem is the bottleneck travelling salesman problem: Find a Hamiltonian cycle in a weighted graph with the minimal weight of the weightiest edge. A real-world example is avoiding narrow streets with big buses. [15] The problem is of considerable practical importance, apart from evident transportation and logistics areas.
[5] [6] The road shortens the trip by 43 km compared with the existing Route 13. The expressway toll will be 550 kip per kilometre, or about 62,000 kip for a one-way trip between Vientiane and Vang Vieng. [3] The trip from Vientiane to Vang Vieng is shortened from 4 hours to 1.5 hours using the expressway. [7]
Tourism in Laos has become an important part of the economy of Laos, contributing US$700 million to the nation's economy, or 4% of GDP. [1] Tourism is governed by a ministry-level government agency, the Lao National Tourism Administration (LNTA).
A travel itinerary is a schedule of events relating to planned travel, generally including destinations to be visited at specified times and means of transportation to move between those destinations. For example, both the plan of a business trip and the route of a road trip, or the proposed outline of one, are travel itineraries.
A mathematical problem is a problem that can be represented, analyzed, and possibly solved, with the methods of mathematics. This can be a real-world problem, such as computing the orbits of the planets in the solar system, or a problem of a more abstract nature, such as Hilbert's problems .
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