On the Complexity of Preflow-Push Algorithms for Maximum-Flow Problems I

Abstract. We study the maximum-flow algorithm of Goldberg and Tarjan and show that the largest-label implementation runs in O(nZxfm) time. We give a new proof of this fact. We compare our proof with the earlier work by Cheriyan and Maheswari who showed that the largest-label implementation of the preflow-push algorithm of Goldberg and Tarjan runs in O(n2x/~) time when implemented with current edges. Our proof that the number of nonsaturating pushes is O(n2x/m), does not rely on implementing pushes with current edges, therefore it is true for a much larger family of largest-label implementation of the preflow-push algorithms

A fast and simple algorithm for the maximum flow problem

Includes bibliographical references (p. 31-33)

Some Recent Advances in Network Flows

The literature on network flow problems is extensive, and over the past 40 years researchers have made continuous improvements to algorithms for solving several classes of problems. However, the surge of activity on the algorithmic aspects of network flow problems over the past few years has been particularly striking. Several techniques have proven to be very successful in permitting researchers to make these recent contributions: (i) scaling of the problem data; (ii) improved analysis of algorithms, especially amortized average case performance and the use of potential functions; and (iii) enhanced data structures. In this survey, we illustrate some of these techniques and their usefulness in developing faster network flow algorithms. Our discussion focuses on the design of faster algorithms from the worst case perspective and we limit our discussion to the following fundamental problems: the shortest path problem, the maximum flow problem, and the minimum cost flow problem. We consider several representative algorithms from each problem class including the radix heap algorithm for the shortest path problem, preflow push algorithms for the maximum flow problem, and the pseudoflow push algorithms for the minimum cost flow problem

Computational investigations of maximum flow algorithms

"April 1995."Includes bibliographical references (p. 55-57).by Ravindra K. Ahuja ... [et al.

Distributed Algorithms for Secure Multipath Routing in Attack-Resistant Networks

To proactively defend against intruders from readily jeopardizing single-path data sessions, we propose a distributed secure multipath solution to route data across multiple paths so that intruders require much more resources to mount successful attacks. Our work exhibits several important properties that include: (1) routing decisions are made locally by network nodes without the centralized information of the entire network topology, (2) routing decisions minimize throughput loss under a single-link attack with respect to different session models, and (3) routing decisions address multiple link attacks via lexicographic optimization. We devise two algorithms termed the Bound-Control algorithm and the Lex-Control algorithm, both of which provide provably optimal solutions. Experiments show that the Bound-Control algorithm is more effective to prevent the worst-case single-link attack when compared to the single-path approach, and that the Lex-Control algorithm further enhances the Bound-Control algorithm by countering severe single-link attacks and various types of multi-link attacks. Moreover, the Lex-Control algorithm offers prominent protection after only a few execution rounds, implying that we can sacrifice minimal routing protection for significantly improved algorithm performance. Finally, we examine the applicability of our proposed algorithms in a specialized defensive network architecture called the attack-resistant network and analyze how the algorithms address resiliency and security in different network settings

Network Flows

Not Availabl

An auction algorithm for the max-flow problem

Caption title.Includes bibliographical references.Supported by the NSF. CCR-9103804by Dimitri P. Bertsekas