Concepts inA new approach to the maximum-flow problem
Maximum flow problem
In optimization theory, the maximum flow problem is to find a feasible flow through a single-source, single-sink flow network that is maximum. The maximum flow problem can be seen as a special case of more complex network flow problems, such as the circulation problem. The maximum value of an s-t flow is equal to the minimum capacity of an s-t cut in the network, as stated in the max-flow min-cut theorem.
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Daniel Sleator
Daniel Dominic Kaplan Sleator is a professor of computer science at Carnegie Mellon University. He discovered amortized analysis and he invented many data structures with Robert Tarjan, such as splay trees, link/cut trees, and skew heaps. He also pioneered the theory of link grammars and developed the technique of competitive analysis for online algorithms. Because of his contribution in computer science, he won the Paris Kanellakis Award in 1999.
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Robert Tarjan
Robert Endre Tarjan (born April 30, 1948) is an American computer scientist. He is the discoverer of several graph algorithms, including Tarjan's off-line least common ancestors algorithm, and co-inventor of both splay trees and Fibonacci heaps. Tarjan is currently the James S. McDonnell Distinguished University Professor of Computer Science at Princeton University, and is also a Senior Fellow at Hewlett-Packard.
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Dense graph
In mathematics, a dense graph is a graph in which the number of edges is close to the maximal number of edges. The opposite, a graph with only a few edges, is a sparse graph. The distinction between sparse and dense graphs is rather vague, and depends on the context. For undirected simple graphs, the graph density is defined as: The maximum number of edges is ½ |V| (|V|¿1), so the maximal density is 1 and the minimal density is 0.
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Flow network
In graph theory, a flow network (also known as a transportation network) is a directed graph where each edge has a capacity and each edge receives a flow. The amount of flow on an edge cannot exceed the capacity of the edge. Often in Operations Research, a directed graph is called a network, the vertices are called nodes and the edges are called arcs.
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Path (graph theory)
In graph theory, a path in a graph is a sequence of vertices such that from each of its vertices there is an edge to the next vertex in the sequence. A path may be infinite, but a finite path always has a first vertex, called its start vertex, and a last vertex, called its end vertex. Both of them are called terminal vertices of the path. The other vertices in the path are internal vertices. A cycle is a path such that the start vertex and end vertex are the same.
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Shortest path problem
In graph theory, the shortest path problem is the problem of finding a path between two vertices (or nodes) in a graph such that the sum of the weights of its constituent edges is minimized. An example is finding the quickest way to get from one location to another on a road map; in this case, the vertices represent locations and the edges represent segments of road and are weighted by the time needed to travel that segment.
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Analysis of algorithms
In computer science, the analysis of algorithms is the determination of the amount of resources (such as time and storage) necessary to execute them. Most algorithms are designed to work with inputs of arbitrary length. Usually the efficiency or running time of an algorithm is stated as a function relating the input length to the number of steps or storage locations (space complexity).
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