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Topic: Bottleneck traveling salesman problem

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Traveling salesman problem

Glossary of graph theory

George Dantzig

Genetic algorithm

	Travelling salesman problem Summary
		A related problem is the bottleneck traveling salesman problem (bottleneck TSP): Find a Hamiltonian cycle in a weighted graph with the minimal length of the longest edge.
		The problem remains NP-hard even for the case when the cities are in the plane with Euclidean distances, as well as in a number of other restrictive cases.
		In March 2005, the traveling salesman problem of visiting all 33,810 points in a circuit board was solved using CONCORDE: a tour of length 66,048,945 units was found and it was proven that no shorter tour exists, the computation took approximately 15.7 CPU years.
	www.bookrags.com /Travelling_salesman_problem (2651 words)

	Traveling salesman problem - Wikipedia, the free encyclopedia
		The traveling salesman problem or travelling salesman problem (TSP), also known as the traveling salesperson problem, is a problem in discrete or combinatorial optimization.
		The problem remains NP-hard even for the case when the cities are in the plane with Euclidean distances, as well as in a number of other restrictive cases.
		In May 2004, the traveling salesman problem of visiting all 24,978 cities in Sweden was solved: a tour of length approximately 72,500 kilometers was found and it was proven that no shorter tour exists.
	en.wikipedia.org /wiki/Traveling_salesman_problem (1785 words)

	Bottleneck traveling salesman problem - Wikipedia, the free encyclopedia
		The decision problem version of this, "for a given length x, is there a Hamiltonian cycle in a graph g with no edge longer than x?", is NP-complete.
		Euclidean bottleneck TSP, or planar bottleneck TSP, is the bottleneck TSP with the distance being the ordinary Euclidean distance.
		An example would be a salesperson traveling by train with a special ticket that is valid for any number of trips between two cities up to a certain distance.
	en.wikipedia.org /wiki/Bottleneck_traveling_salesman_problem (366 words)

	American Mathematical Society :: Feature Column (Site not responding. Last check: 2007-10-26)
		The problem is with the rapid growth of the factorial function (m!) which is involved in the counting of the TSP tours.
		For example, one might have originally wanted to solve a problem for a salesman but realize that the problem of picking up children and taking them to a day camp is a related problem but one with the constraint that one can not exceed the size of the minibus.
		Kruskal, J., On the Shortest Spanning Subtree of a Graph and the Traveling Salesman Problem, Proc.
	0-www.ams.org.library.uor.edu /featurecolumn/archive/tsp.html (5321 words)

	Traveling salesman problem - TheBestLinks.com - Computational complexity, Computational complexity theory, Decision ... (Site not responding. Last check: 2007-10-26)
		The traveling salesman problem (TSP), also known as the traveling salesperson problem, is a problem in discrete or combinatorial optimization.
		The most direct solution would be to try all the combinations and see which one is cheapest, but given that the number of combinations is N! (the factorial of the number of cities), this solution rapidly becomes impractical.
		In most cases, the distance between two nodes in the TSP network is the same in both directions - the special case where the distance from A to B is not equal to the distance from B to A is called Asymmetric TSP and has some practical applications.
	www.thebestlinks.com /Traveling_salesman_problem.html (1360 words)

	Traveling
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	te84.poseidontech.com /traveling.html (1413 words)

	Traveling Salesman Problem: Cities
		The problem is restricted to the Euclidian case where the TSP can be formulated as follows: Given n cities in the plane and their Euclidian distances, the problem is to find the shortest TSP-tour, i.e.
		The traveling salesman problem is a characteristic and well-studied example of combinatorial optimization.
		The prototypical complex optimisation problem is the traveling salesman problem (TSP).
	www.lycos.com /info/traveling-salesman-problem--cities.html (510 words)

	Traveling Salesman Problem: Miscellaneous
		Mathematical problems related to the traveling salesman problem were treated in the 1800s by the Irish mathematician Sir William Rowan Hamilton and by the British mathematician Thomas Penyngton Kirkman.
		The underlying theory of facet generation for the symmetric traveling salesman problem is provided in Grötschel and Padberg (1985) and Jünger, Reinelt and Rinaldi (1994).
		As our understanding of the underlying mathematical structure of the TSP problem improves, and with the continuing advancement in computer technology, it is likely that many difficult and important combinatorial optimization problems will be solved using a combination of cutting plane generation procedures, heuristics, variable fixing through logical implications and reduced costs and tree search.
	www.lycos.com /info/traveling-salesman-problem--miscellaneous.html (495 words)

	Combinatorial Optimization
		Quadratic assignment problem - The quadratic assignment problem (QAP) is one of fundamental combinatorial optimization problems in the branch of optimization or operations research in mathematics, from the category of the facilities location problems.
		Traveling salesman problem The traveling salesman problem (TSP), also known as the traveling salesperson problem, is a problem in discrete or Combinatorial Optimization.
		Traveling salesman problem (TSP), also known as the traveling salesperson problem, is a prominent illustration of a route of the best and most complete texts on Combinatorial Optimization.
	co11.mcechess.com (1361 words)

	American Mathematical Society :: Feature Column
		The salesman, who must travel by car, might want to route himself via his favorite cousin's hometown and perhaps take in an antiques show on the way, while the employer might want to have the salesman follow the cheapest route possible.
		It turns out that the traveling salesman problem is not only an important applied problem with many fascinating variants; it also has important ties to theoretical mathematics and computer science.
		For example, one might have originally wanted to solve a problem for a salesman but realize that the problem of picking up children and taking them to a day camp is a related problem but one with the constraint that one can not exceed the size of the minibus.
	www.ams.org /featurecolumn/archive/tsp.html (5321 words)

	Association of Legal Administrators 35th Annual Educational Conference and Exposition. (Site not responding. Last check: 2007-10-26)
		Ever since the time problem salesman traveling of H. In this case, the distance from node i to node j and the distance problem salesman traveling from node j to node i may be different.
		When problem salesman traveling you are pregnant you must take special precautions to protect both yourself and your unborn child from illness when traveling to underdeveloped countries.
		Unvaccinated dogs must be vaccinated within problem salesman traveling 4 days of arrival at their final U. A female composer would be like having a gun survey female doctor..However, some of our instruments are quite major record label address unique to the Renaissance..
	buytotally.275mb.com /leibniz-englisch.html (2554 words)

	Lesson
		The traveling salesman problem is important because it is the classic problem faced in optimizing the routing of signals in a tele-communications system.
		The basic traveling salesman problem is to compute the shortest route through a given list of cities.
		The traveling salesman problem is a classic example of combinatorial explosion because the number of possible routes increases so rapidly that there are no practical solutions for realistic numbers of cities.
	www.ksi.edu /demo/509/ch01ba.html (2505 words)

	Traveling Salesman
		The Princeton link refers to a "proof" of the TSP problem for a specific configuration of cities in Germany.
		Colin M Davidson ---- :''How fast are the best known deterministic algorithms?'' ---- "Given a number of cities and the costs of travelling from one to the other, what is the cheapest roundtrip route that visits each city and then returns to the starting city?" Shouldn't it be "...
		It is stated as follows: Find the Hamiltonian cycle in a weighted graph with the minimal weight of the most weighty edge.
	www.artistbooking.com /trips/207/traveling-salesman.html (938 words)

	Bottleneck traveling salesman problem - Encyclopedia Glossary Meaning Explanation Bottleneck traveling salesman problem (Site not responding. Last check: 2007-10-26)
		Bottleneck traveling salesman problem - Encyclopedia Glossary Meaning Explanation Bottleneck traveling salesman problem.
		Here you will find more informations about Bottleneck traveling salesman problem.
		It is stated as follows: Find the Hamiltonian cycle in a weighted graph with the minimal length of the longest edge.
	www.encyclopedia-glossary.com /en/Bottleneck-traveling-salesman-problem.html (125 words)

	Traveling salesman - Problem Discrete
		The traveling salesman problem (TSP) is a problem in discrete or combinatorial optimisation.
		The problem is of considerable practical importance, apart from evident transportation and logistics areas.
		In robotic machining or drilling applications, the "cities" are parts to machine or holes (of different sizes) to drill, and the "cost of travel" includes time for retooling the robot (single machine job sequencing problem).
	www.news7res.info /travel/traveling-salesman.htm (288 words)

	Death of an Insurance Salesman
		Traveling death of an insurance salesman problem (bottleneck TSP): Find the Hamiltonian cycle in a weighted graph with the minimal length of the art in theory and algorithms for the problem ("subproblems") for which either exact or better heuristics are recognized.
		In the TSP with triangle inequality A very natural restriction is the Bottleneck traveling traveling salesman problem finally confronts the shattered dreams of the American dream.
		This is not a political gesture but a desperate attempt to capture the American traveling salesman problem from itinerant amateur to trained expert.
	directmail.2vv1.com /deathofaninsurancesalesman.html (984 words)

	Intro to Algorithms: CHAPTER 37: APPROXIMATION ALGORITHMS
		Depending on the problem, an optimal solution may be defined as one with maximum possible cost or one with minimum possible cost; the problem may be a maximization or a minimization problem.
		is an approximation algorithm with a ratio bound of 2 for the traveling-salesman problem with triangle inequality.
		The bottleneck traveling-salesman problem is the problem of finding the hamiltonian cycle such that the length of the longest edge in the cycle is minimized.
	www.personal.kent.edu /~mlu3/CSCourses/AdvAlgorithms/CLR-BOOK/books/book6/chap37.htm (5618 words)

	Traveling Salesman Problem
		Imagine a traveling salesman who has to visit each of a given set of cities by car.
		Implementations: The world-record-setting traveling salesman program is by Applegate, Bixby, Chvatal, and Cook [ABCC95], which has solved instances as large as 7,397 vertices to optimality.
		Algorithm 608 [Wes83] of the Collected Algorithms of the ACM is a Fortran implementation of a heuristic for the quadratic assignment problem, a more general problem that includes the traveling salesman as a special case.
	www2.toki.or.id /book/AlgDesignManual/BOOK/BOOK4/NODE175.HTM (1630 words)

	TSP... to the Maximum Scatter! (Site not responding. Last check: 2007-10-26)
		The MSTSP is, in a sense, the converse of the Bottleneck TSP; its goal is to find the smallest weight between any two points in a Hamiltonian tour.
		Since the optimization problem maximizes the length of the shortest edge in the tour, it is also called the max-min 1-neighbor TSP (MM1NTSP).
		Problem A is at least as hard as problem B if B reduces to A in poly-time.
	www.cs.caltech.edu /~elliottk/intro.html (960 words)

	ipedia.com: Traveling salesman problem Article (Site not responding. Last check: 2007-10-26)
		The traveling salesman problem, also known as the traveling salesperson problem, is a problem in discrete or combinatorial optimization.
		It is a prominent illustration of a class of problems in comput...
		In practice, the running time of this algorithm is too large and heuristics with weaker guarantees are used but they also perform better on instances of Euclidean TSP than on general instances.
	www.ipedia.com /traveling_salesman_problem.html (1315 words)

	Malaria infection poses a special risk for the pregnant traveler and may result in a more severe infection and ... (Site not responding. Last check: 2007-10-26)
		Visa applicants are time traveling expected to provide evidence that they are intending to return to their country of residence.
		If your dog or cat is not single traveling used to traveling by car, make short trips with the pet a week or two in advance of the trip to accustom it to motion and to teach it how t 194 o behave.
		As your traveling buddy visits classrooms, you can do play personal survey many creative activities that will engage both groups of students..Travelling with a cat or dog is now much easier with the astral traveling new EU pet passport..
	buytotally.275mb.com /aye-measels.html (4868 words)

	The Traveling Salesman Problem and its Variation
		The travelling salesman problem (TSP) is perhaps the most well-known combinatorial optimization problem.
		The problem is to find the shortest route for a travelling salesman to set out from home, visit a set number of other cities and return home.
		TSP is a typically hard problem, but recent developments in polyhedral theory and branch-and-cut algebra have significantly increased the number of instances that can be solved to optimality.
	www.booknews.co.uk /Books/Book2532.html (123 words)

	Problem Definitions
		There are two natural formulations of the overlay multicast routing problem: the first seeks to minimize the multicast tree diameter while respecting the degree constraints at individual nodes; and the other optimizes the interface bandwidth usage to reduce the likelihood of bottleneck nodes and constructs the tree satisfying an upper bound on the tree diameter.
		Both the and problems are NP-complete, since they contain the special case in which every node has a degree of two, corresponding to the optimization and the decision version of the Traveling Salesman Problem (TSP) [#!garey-johnson!#], respectively.
		In this case, the problem is polynomially solvable, since a minimum diameter tree can be found by computing a shortest path tree rooted at each vertex and picking the one with the smallest diameter.
	www.arl.wustl.edu /~sherlia/thesis/chap3/node2.html (828 words)

	Perspectives of Monge Properties in Optimization - Burkard, Klinz, Rudolf (ResearchIndex)
		1.3: The Travelling Salesman Problem on Permuted Monge Matrices - Burkard, Deineko, Woeginger (1995)
		5 a problem of Monge (context) - Kantorovich - 1948
		2 antimatroids and the transportation problem with forbidden a..
	citeseer.ist.psu.edu /71816.html (1823 words)

	Life Lyric Salesman
		Heuristics Various approximation algorithms, including the emerging area of domination analysis of a life lyric salesman.' The bottleneck traveling life lyric salesman problem The Bottleneck traveling life lyric salesman problem This article is a brilliant lawyer.
		Related topics Traveling direct marketing association mail preference service problem (bottleneck TSP) is a long-standing (since 1975) open problem to improve 1.5 to a smaller constant.
		History Death of a class of problems in computational complexity of the art in theory and algorithms for finding exact solutions (they will work reasonably fast only for relatively small problem sizes) Devising "suboptimal" or heuristic algorithms, i.e., algorithms that deliver seemingly or provably good solutions, but which could not proved to be optimal.
	directmail.2vv1.com /lifelyricsalesman.html (1891 words)

	Tsp - The Travelling Salesman Problem
		The traveling salesman problem or travelling salesman problem (TSP), also known as the A related problem is the Bottleneck traveling salesman problem
		Fractal Instances of the Traveling Salesman Problem, by Pablo Moscato.
		TSPLIB is a library of sample instances for the TSP (and related This problem is an asymmetric traveling salesman problem with additional constraints.
	yourindexes.com /yrid/tsp.htm (373 words)

	TravellingSalesmanProblem - GenCore - Confluence
		Given a number of cities and the costs of travelling from one to the other, what is the cheapest roundtrip route that visits each city and then returns to the starting city?
		The most direct solution would be to try all the combinations and see which one is cheapest, but given that the number of combinations is N! (the factorial of the number of cities), this solution rapidly becomes impractical.
		The problem has been shown to be NP-hard (more precisely, it is complete for the complexity class FPNP; see the function problem article), and the decision problem version ("given the costs and a number x, decide whether there is a roundtrip route cheaper than x") is NP-complete.
	docs.codehaus.org /display/GENCORE/TravellingSalesmanProblem (261 words)

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