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Topic: Maximal flow problem

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	Maximum flow problem - Wikipedia, the free encyclopedia
		The maximum flow problem can be seen as special case of more complex network flow problems.
		For example, it is the multi-commodity flow problem with only one commodity, and it is the minimum-cost flow problem with all costs set to zero except for an additional arc from the sink to the source, which has a cost of negative one and no capacity.
		The maximum s-t flow in a network is equal to the minimum cardinality s-t cut in the network, as stated in the Max-flow min-cut theorem.
	en.wikipedia.org /wiki/Maximum_flow_problem (293 words)

	Max-flow min-cut theorem - Wikipedia, the free encyclopedia
		The max-flow min-cut theorem is a statement in optimization theory about maximal flows in flow networks.
		The maximal amount of a flow is equal to the capacity of a minimal cut.
		Determining maximum flows is a special kind of linear programming problem, and the max flow min cut theorem can be seen as a special case of the duality theorem for linear programming.
	en.wikipedia.org /wiki/Max_flow_min_cut_theorem (480 words)

	Graph theory - Wikipedia, the free encyclopedia
		In 1852 Francis Guthrie posed the four color problem which asks if it is possible to color, using only four colors, any map of countries in such a way as to prevent two bordering countries from having the same color.
		This problem, which was only solved a century later in 1976 by Kenneth Appel and Wolfgang Haken, can be considered the birth of graph theory.
		Covering problems are specific instances of subgraph-finding problems, and they tend to be closely related to the clique problem or the independent set problem.
	en.wikipedia.org /wiki/Graph_theory (1803 words)

	Network Flow Problems
		There are a few "generic" network flow problems and a large number of problem types with variations that are made necessary by the practical applications.
		This network flow problem is one that we all use in our daily lives: what is the fastest route to take between two locations in the city during the rush hour, what is the "most" scenic route to drive, or the cheapest route to fly, between two cities in our vacation.
		The fundamental basis of maximal flow problems is that there exists a capacitated network and costs are constant regardless of how much flow is flowing in the arcs.
	www.csulb.edu /~obenli/Research/IE-encyc/networks.html (2337 words)

	[No title]
		Formalization of this problem use capacity graph, which is a connected non-oriented weighted graph with a positive weight function representing capacities of the edges.
		The graph P has the same set of vertices, and each couple of distinct vertices in P is connected by an edge with a weight equal to the maximal flow between these vertices in G. Suppose a complete weighted graph P with positive weights of all edges is given.
		The subject of the talk is the solution of this inverse maximal flow problem.
	www.math.technion.ac.il /~techm/20011030151520011030roz (257 words)

	New Page 1 (Site not responding. Last check: 2007-10-30)
		The mathematical formulation of the problem was solved two decades ago (Lerchs and Grossman 1965) and several algorithms on the topic have been published since the event of computer applications in the mineral industry.
		He wrote: "...the problem of finding a maximal closure of a graph is equivalent to solving the maximal flow problem in a network formed by the graph G with infinite capacities on its arcs, a source linked to each node v
		The network flow algorithm for pit optimization is thus resolved much faster by computer than the L and G, especially when an efficient maximum flow algorithm is used.
	activesolid.ncf.ca /flowPit.htm (858 words)

	Ch5. Lecture Notes
		Three problems (a transshipment problem with capacity limits, a maximal flow problem, and an equipment replacement problem) are descibed in the attached handout and formulated for Solver solution on the attached spreadsheet.
		The problem can be used to determine the optimal scale of a production (or generating) facility or to identify bottlenecks in a transmission grid for determining optimal investments of funds to increase capacities.
		The problem is described in the attached spreadsheet.
	www.ndsu.nodak.edu /instruct/swandal/AGEC339f/ch2211.htm (821 words)

	0540515 (Site not responding. Last check: 2007-10-30)
		To show how network flow problems arise in real life; to show how network flow problems may be solved; and to see the significance of solutions for the original real-life problems.
		To ensure that the students are able (i) to construct network flow models which represent problems in real life, (ii) to solve certain problems posed within these models, and (iii) to appreciate the possible impact of the solution on the real-life problem.
		Flows on networks which arise in real life; and how these may be modelled.
	www.york.ac.uk /depts/maths/ugrad/courses/nextyear/0540515.htm (302 words)

	MATHEMATICS: Outline of all the courses
		Prime and maximal ideals; consequences of Zorn's Lemma; nilradical and Jacobson radical; the spectrum of a ring; Zariski's topology.
		Maximal Flow Problem - min cut-max flow theorem; incremental chains algorithm; computational complexity and practical efficiency.
		Minimal Cost Flow Problem - Simplex algorithm; particular cases (transportation and assignment problems); shortest path and maximal flow problems as a particular problem.
	www.mat.uc.pt /licenciaturas/outlines.html (2136 words)

	Programas de la USC
		• The knowledge of the mathematical models and the techniques which are necessary to solve decision problems and the display of its applications.
		The shortest path problem and the maximal flow problem.
		It is possible that we offer a virtual course within the virtual platform of the University of Santiago de Compostela, to support and to complete the theoretical and practical class.
	www.usc.es /estaticos/conectate/conectate_programas/850/12215_7.htm (464 words)

	Maximal Biflow in an Undirected Network (Site not responding. Last check: 2007-10-30)
		In this network flow problem we deal with two distinct commodities, each commodity being identified by a pair of source and sink nodes.
		It is solved by an inductive algorithm which starts with a maximal multiterminal flow from the set of sources to the set of sinks in the network, yields the value of the maximal biflow and terminates with the construction of the maximal biflow itself.
		Computational experience shows that this algorithm can also be used in the three-commodity flow problem to obtain a good lower bound for the value of a maximal three-commodity flow.
	domino.research.ibm.com /tchjr/journalindex.nsf/0/966e70c82f1647ff85256bfa0068403a?OpenDocument (119 words)

	PROC NETFLOW Statement (Site not responding. Last check: 2007-10-30)
		This arc is directed from the SOURCE to the SINK and will eventually convey flow equal to INFINITY minus the maximal flow through the network.
		You can possibly introduce new nonarc variables to the problem, that is, nonarc variables that were not in the problem when the warm start was generated.
		PROC NETFLOW automatically assigns a supply of one flow unit to the SOURCE= node, and the SINK= node is assigned to have a one flow unit demand.
	www.asu.edu /sas/sasdoc/sashtml/ormp/chap4/sect15.htm (5573 words)

	Annotated Bibliography on Linear Programming Models
		Johnson (1957) showed that this problem could be solved directly, without resort to an iterative algorithm.
		Chemical equilibrium problem expressed in the form of minimizing the free energy using a piece-wise linear approximation to the free energy function.
		Thorndike, R.L., "The problem of classification of personnel," Psychometrika, vol.
	catt.okstate.edu /itorms/volumes/vol1/papers/murphy/index.html (10162 words)

	Handbook for Graduate Students Temple University Department of Mathematics
		Incomplete grades frequently create problems, since no student is allowed to graduate with an incomplete on his or her transcript.
		Part II tests the ability to attack a problem in the subject; it contains three questions, of which two are to be answered.
		However, the instructor should detect a problem if there is one, and take a remedial action before the students start to complain.
	www.math.temple.edu /grad/handbook_for_grad_students_2005.html (7623 words)

	Heart Info - Heart FAQ (Site not responding. Last check: 2007-10-30)
		The treatment has been shown to produce improvement in blood flow to the heart that may last for up to 2 to 3 years in some patients, presumably due to the growth of new blood vessels in the heart muscle.
		Side effects seem to be minimal; however, EECP should not be performed on people with uncontrolled heart failure, uncontrolled irregular heart rhythms, severe heart valve problems, bleeding or blood-clotting problems, severe peripheral vascular disease (very poor circulation to the limbs), or blood clots in the legs.
		While primary problems to your heart, such as an abnormality in the heart’s electrical circuitry, always need to be considered, these conditions are usually most likely to occur in the presence of other symptoms such as light-headedness, flout episodes, and shortness of breath.
	www.heartinfo.com /ms/nav/faq/main.html (6001 words)

	Anderson, Sweeney, Williams IMS Learning Objectives
		Understand that managerial problem situations have both quantitative and qualitative considerations that are important in the decision making process.
		Be able to use network-based algorithms to solve shortest route, maximal flow, and minimal spanning tree problems.
		Be able to analyze a simple decision analysis problem from both a payoff table and decision tree point of view.
	www.swlearning.com /quant/asw/ims_11e/learning_objectives.html (1853 words)

	[No title]
		The system throughput is the objective function to be maximized and the speed of the devices are the decision variables.
		We present some solutions to this multi-access broadcast problem, giving the throughput-delay profile both for long-range communication systems (such as satellite packet switching) and for local access in a ground radio packet switching environment.
		There are two components to the problem of sharing a single resource: (1) how to specify the usage pattern of the resource; and (2) how to restrict access to the resource so that the specified usage pattern can be realized.
	www.cs.columbia.edu /~hgs/bib/net79.bib (6017 words)

	[No title]
		(a) The problem can be formulated as a maximal flow problem as follows.
		For the network above the maximal flow equals five (check it!) and the flow on red arks is 1, the flow on the other arcs equals 0.
		To solve this problem as an assignment problem we need to write the cost matrix.
	rutcor.rutgers.edu /~boliac/SolutionsReviewFinal2.doc (828 words)

	EVEGA - Homepage
		A flow is a function f:E->Nat such that for every edge e the amount of flow units f(e) is positive and less than or equal to the edge's capacity c(e).
		For a given function f and a pair of vertices (source s and target t), the flow can be calculated as the sum of the flow units on all outgoing edges of s (resp.
		The idea behind the algorithm is to send as many flow units as possible from the source and distribute all units within the graph (1st phase), finally all unused flow units are drawn back to the source.
	wwwmayr.informatik.tu-muenchen.de /EVEGA/algorithms.html (787 words)

	Computational Maximum Flow Bibliography
		Implementing the Push-Relabel Method for the Maximum Flow Problem on the Connection Machine, F. Alizadeh and A. Goldberg, in Network Flows and Matching: First DIMACS Implementation Challenge, refereed proceedings, D. Johnson and C. McGeoch (editors), 65-96, AMS, 1993.
		Determining the Maximal Flow in a Network by the Method of Preflows, A. Karzanov, Soviet Math.
		A New Approach to the Maximum Flow Problem, A. Goldberg and R. Tarjan, JACM (35), 921-940, 1988.
	www.avglab.com /andrew/CATS/maxflow_bib.htm (502 words)

	Ken Brakke's Papers (Site not responding. Last check: 2007-10-30)
		The proof uses the maximal flow problem that is dual to the minimal surface problem.
		This model applies to unoriented films, films with singularities, films touching only part of a knotted curve, films that deformation retract to their boundaries, and other examples that have proved troublesome for previous soap film models.
		Abstract: The soap film problem is to minimize area, and its dual is to maximize the flux of a divergenceless bounded vectorfield.
	www.susqu.edu /facstaff/b/brakke/papers/default.htm (992 words)

	[No title]
		A selection of the following topics are covered: matrix games, the transportation problem, the assignment problem, the maximal flow problem, the shortest route problem, the critical path method.
		In problem 4b) for both tests there are ten integer pairs in the region of feasible solutions.
		The objective row of the first tableau should be "2 -1 0 1 0 -3" and the objective row of the second tableau should be "4 0 1 1 0 -2".
	www.math.toronto.edu /mpugh/Teaching/APM236_03/apm236.html (1725 words)

	Systems Engineering (Site not responding. Last check: 2007-10-30)
		Steepest descent, Introduction to unconstrained and constrained nonlinear problem.
		Structuring decision problems: single criterion versus multiple criteria, certainty versus risk and uncertainty versus conflict, criteria and attributes, payoffs and losses.
		Variety of sequencing and scheduling problems in O.R., job shop and flow shop scheduling, discussion of performance measures, dynamic programming, integer programming, computational complexity and NP-completeness results, discussion of well solved problems, branch and bound methods, variety of heuristic approaches for intractable practical problems, guaranteed accuracy heuristics.
	www.ccse.kfupm.edu.sa /se/prog.jsp?contentID=gcrdesc (2904 words)

	_E 3XX - Course Title
		This course focuses on the deterministic models, especially linear, integer and network flow models as well as the solution techniques such as simplex method and branch and bound.
		Example problems will be drawn from real world applications in diverse fields such as manufacturing, transportation, and logistics, to name a few.
		You will be asked to identify a problem, build the mathematical model, code it in Xpress, interpret the result, implement it if possible and finally give a 15 minute presentation in class.
	www.wright.edu /~xinhui.zhang/DORMODELS/Syllabus.htm (843 words)

	Efficient Continuous-Time Dynamic Network Flow Algorithms - Fleischer, Tardos (ResearchIndex) (Site not responding. Last check: 2007-10-30)
		Abstract: We extend the discrete-time dynamic flow algorithms presented in [5, 19, 13, 9, 10, 8] to solve the analogous continuous-time dynamic flow problems.
		These problems include finding maximum dynamic flows, quickest flows, universally maximum dynamic flows, lexicographically maximum dynamic flows, dynamic transshipments, and quickest transshipments in networks with capacities and transit times on the edges.
		22 The quickest transshipment problem - Hoppe, Tardos - 1995
	citeseer.ist.psu.edu /22910.html (617 words)

	bp_render_qam_8\|Chapter 12: Network Models\|Essay Questions
		List three different network models that can be used to optimize the solution to a variety of problems.
		To create paragraphs in your essay response, type at the beginning of the paragraph, and at the end.
		Describe, briefly, why the solution to a maximal-flow problem is unique.
	wps.prenhall.com /bp_render_qam_8/0,,400086-,00.utf8.html (494 words)

	Optimal Decisions
		Dangalchev Ch., The direct support method for solving partially- linear problems obtained when absolute value functions are twice applied, Mathematics and education in mathematics, Sofia, 1989, pp.
		Dangalchev Ch., Transportation problem with fixed supplies, Mathematics and education in mathematics, Sofia, 1991, pp.
		Dangalchev Ch., Quadratic transportation problem with fixed supplies, Mathematics and education in mathematics, Sofia, 1992, pp.
	members.surfbest.net /decisions@surfbest.net/about_us.html (777 words)

	Linear Optimization
		The Simplex Method for Problems in Standard Form (section 2.1, everything up to "Forming a New Tableau" part on p.
		Homework assigned: problems 2,4,14, 34 in section 1.3 (due Thursday, Febryary5) Solutions
		problems 2,4,8,11 in section 1.1 (due Thursday, January 29)
	rutcor.rutgers.edu /~boliac/LPS2004/LP354.htm (214 words)

	Healthy Sports Nutrition - Bradventures Coaching & Supplements
		PS is vital to the production of numerous brain chemicals (70% of brain cell membranes are phosphatidylserine - the highest concentration in your body) and the regulation of all aspects of brain activity.
		Absorption efficiency and vitamin C utilization may be greatly enhanced during conditions of physiological stress, such as trauma or infection.
		Maximal absorption is attained by the ingestion of several doses spaced throughout the day rather than in one, larger dose.
	www.bradventures.com /athlete-stress-formula.shtml (5547 words)

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