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New DistanceDirected Algorithms for Maximum Flow and Parametric Maximum Flow Problems
, 1987
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Distancedirected augmenting path algorithms for maximum flow and parametric maximum flow problems
 Naval Research Logistics
, 1991
"... Until recently, fast algorithms for the maximum flow problem have typically proceeded by constructing layered networks and establishing blocking flows in these networks. However, in recent years, new distancedirected algorithms have been suggested that do not construct layered networks but instead ..."
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Until recently, fast algorithms for the maximum flow problem have typically proceeded by constructing layered networks and establishing blocking flows in these networks. However, in recent years, new distancedirected algorithms have been suggested that do not construct layered networks but instead maintain a distance label with each node. The distance label of a node is a lower bound on the length of the shortest augmenting path from the node to the sink. In this article we develop two distancedirected augmenting path algorithms for the maximum flow problem. Both the algorithms run in O(n 2 m) time on networks with n nodes and m arcs. We also point out the relationship between the distance labels and layered networks. Using a scaling technique, we improve the complexity of our distancedirected algorithms to O(nm log U), where U denotes the largest arc capacity. We also consider applications of these algorithms to unit capacity maximum flow problems and a class of parametric maximum flow problems. t i
Transmissions in a Network with Capacities and Delays
, 1996
"... We examine the problem of transmitting in minimum time a given amount of data between a source and a destination in a network with finite channel capacities and nonzero propagation delays. In the absence of delays, the problem has been shown to be solvable in polynomial time. In this paper, we sho ..."
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We examine the problem of transmitting in minimum time a given amount of data between a source and a destination in a network with finite channel capacities and nonzero propagation delays. In the absence of delays, the problem has been shown to be solvable in polynomial time. In this paper, we show that the general problem is NPcomplete. In addition, we examine transmissions along a single path, called the quickest path, and present algorithms for general and special classes of networks that improve upon previous approaches. The first dynamic algorithm for the quickest path problem is also given. Keywords: Data transmission, sparse network, transmission time, quickest path, dynamic algorithm. 1 Introduction Consider an nnode, medge network N = (V; E; c; l), where G = (V; E) is a directed graph, c : E ! IR + is the capacity function and l : E ! IR is the delay function. The nodes represent transmitters/receivers without data memories and the edges represent communication ...