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59
On implementing the pushrelabel method for the maximum flow problem
, 1994
"... We study efficient implementations of the pushrelabel method for the maximum flow problem. The resulting codes are faster than the previous codes, and much faster on some problem families. The speedup is due to the combination of heuristics used in our implementation. We also exhibit a family of p ..."
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Cited by 208 (10 self)
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We study efficient implementations of the pushrelabel method for the maximum flow problem. The resulting codes are faster than the previous codes, and much faster on some problem families. The speedup is due to the combination of heuristics used in our implementation. We also exhibit a family of problems for which all known methods seem to have almost quadratic time growth rate.
A new approach to the minimum cut problem
 Journal of the ACM
, 1996
"... Abstract. This paper presents a new approach to finding minimum cuts in undirected graphs. The fundamental principle is simple: the edges in a graph’s minimum cut form an extremely small fraction of the graph’s edges. Using this idea, we give a randomized, strongly polynomial algorithm that finds th ..."
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Cited by 126 (9 self)
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Abstract. This paper presents a new approach to finding minimum cuts in undirected graphs. The fundamental principle is simple: the edges in a graph’s minimum cut form an extremely small fraction of the graph’s edges. Using this idea, we give a randomized, strongly polynomial algorithm that finds the minimum cut in an arbitrarily weighted undirected graph with high probability. The algorithm runs in O(n 2 log 3 n) time, a significant improvement over the previous Õ(mn) time bounds based on maximum flows. It is simple and intuitive and uses no complex data structures. Our algorithm can be parallelized to run in �� � with n 2 processors; this gives the first proof that the minimum cut problem can be solved in ���. The algorithm does more than find a single minimum cut; it finds all of them. With minor modifications, our algorithm solves two other problems of interest. Our algorithm finds all cuts with value within a multiplicative factor of � of the minimum cut’s in expected Õ(n 2 � ) time, or in �� � with n 2 � processors. The problem of finding a minimum multiway cut of a graph into r pieces is solved in expected Õ(n 2(r�1) ) time, or in �� � with n 2(r�1) processors. The “trace ” of the algorithm’s execution on these two problems forms a new compact data structure for representing all small cuts and all multiway cuts in a graph. This data structure can be efficiently transformed into the
Authentication Metric Analysis and Design
 ACM Transactions on Information and System Security
, 1999
"... Authentication using a path of trusted intermediaries, each able to authenticate the next in the path, is a wellknown technique for authenticating entities in a largescale system. Recent work has extended this technique to include multiple paths in an effort to bolster authentication, but the succ ..."
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Cited by 87 (1 self)
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Authentication using a path of trusted intermediaries, each able to authenticate the next in the path, is a wellknown technique for authenticating entities in a largescale system. Recent work has extended this technique to include multiple paths in an effort to bolster authentication, but the success of this approach may be unclear in the face of intersecting paths, ambiguities in the meaning of certificates, and interdependencies in the use of different keys. Thus, several authors have proposed metrics to evaluate the confidence afforded by a set of paths. In this paper we develop a set of guiding principles for the design of such metrics. We motivate our principles by showing how previous approaches failed with respect to these priniciples and what the consequences to authentication might be. We then propose a new metric that appears to meet our principles, and so to be a satisfactory metric of authentication.
Graph Sandwich Problems
, 1994
"... The graph sandwich problem for property \Pi is defined as follows: Given two graphs G ) such that E ` E , is there a graph G = (V; E) such that E which satisfies property \Pi? Such problems generalize recognition problems and arise in various applications. Concentrating mainly o ..."
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Cited by 68 (8 self)
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The graph sandwich problem for property \Pi is defined as follows: Given two graphs G ) such that E ` E , is there a graph G = (V; E) such that E which satisfies property \Pi? Such problems generalize recognition problems and arise in various applications. Concentrating mainly on properties characterizing subfamilies of perfect graphs, we give polynomial algorithms for several properties and prove the NPcompleteness of others. We describe
Toward acceptable metrics of authentication
 in Proceedings of IEEE Symposium on Security and Privacy
, 1997
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Finding kcuts within Twice the Optimal
, 1995
"... Two simple approximation algorithms for the minimum kcut problem are presented. Each algorithm finds a kcut having weight within a factor of (2 \Gamma 2=k) of the optimal. One of our algorithms is particularly efficient  it requires a total of only n \Gamma 1 maximum flow computations for find ..."
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Cited by 48 (2 self)
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Two simple approximation algorithms for the minimum kcut problem are presented. Each algorithm finds a kcut having weight within a factor of (2 \Gamma 2=k) of the optimal. One of our algorithms is particularly efficient  it requires a total of only n \Gamma 1 maximum flow computations for finding a set of nearoptimal kcuts, one for each value of k between 2 and n. i 1 Introduction The minimum kcut problem is as follows: given an undirected graph G = (V; E) with nonnegative edge weights and a positive integer k, find a set S ` E of minimum weight whose removal leaves k connected components. This problem is of considerable practical significance, especially in the area of VLSI design. Solving this problem exactly is NPhard [GH], but no efficient approximation algorithms were known for it. In this paper we give two simple algorithms for finding kcuts. We prove a performance guarantee of (2 \Gamma 2=k) for each algorithm; however, neither algorithm dominates the other on a...
Improved approximation algorithms for unsplittable flow problems (Extended Abstract)
 In Proceedings of the 38th Annual Symposium on Foundations of Computer Science
, 1997
"... ) Stavros G. Kolliopoulos 1 Clifford Stein 1 Abstract In the singlesource unsplittable flow problem we are given a graph G; a source vertex s and a set of sinks t 1 ; : : : ; t k with associated demands. We seek a single st i flow path for each commodity i so that the demands are satisfied and ..."
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Cited by 45 (2 self)
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) Stavros G. Kolliopoulos 1 Clifford Stein 1 Abstract In the singlesource unsplittable flow problem we are given a graph G; a source vertex s and a set of sinks t 1 ; : : : ; t k with associated demands. We seek a single st i flow path for each commodity i so that the demands are satisfied and the total flow routed across any edge e is bounded by its capacity c e : The problem is an NPhard variant of max flow and a generalization of singlesource edgedisjoint paths with applications to scheduling, load balancing and virtualcircuit routing problems. In a significant development, Kleinberg gave recently constantfactor approximation algorithms for several natural optimization versions of the problem [18]. In this paper we give a generic framework that yields simpler algorithms and significant improvements upon the constant factors. Our framework, with appropriate subroutines, applies to all optimization versions previously considered and treats in a unified manner directed and u...
A Faster Algorithm for Finding the Minimum Cut in a Directed Graph
 JOURNAL OF ALGORITHMS
, 1994
"... We consider the problem of finding the minimum capacity cut in a directed network G with n nodes. This problem has applications to network reliability and survivability and is useful in subroutines for other network optimization problems. One can use a maximum flow problem to find a minimum cut sepa ..."
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Cited by 45 (0 self)
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We consider the problem of finding the minimum capacity cut in a directed network G with n nodes. This problem has applications to network reliability and survivability and is useful in subroutines for other network optimization problems. One can use a maximum flow problem to find a minimum cut separating a designated source node s from a designated sink node t, and by varying the sink node one can find a minimum cut in G as a sequence of at most 2n 2 maximum flow problems. We then show how to reduce the running time of these 2n 2 maximum flow algorithms to the running time for solving a single maximum flow problem. The resulting running time is O(nm log(n 2 /m)) for finding the minimum cut in either a directed or an undirected network. © 1994 Academic Press, Inc. 1.
Experimental Study of Minimum Cut Algorithms
 PROCEEDINGS OF THE EIGHTH ANNUAL ACMSIAM SYMPOSIUM ON DISCRETE ALGORITHMS (SODA)
, 1997
"... Recently, several new algorithms have been developed for the minimum cut problem. These algorithms are very different from the earlier ones and from each other and substantially improve worstcase time bounds for the problem. We conduct experimental evaluation the relative performance of these algor ..."
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Cited by 42 (3 self)
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Recently, several new algorithms have been developed for the minimum cut problem. These algorithms are very different from the earlier ones and from each other and substantially improve worstcase time bounds for the problem. We conduct experimental evaluation the relative performance of these algorithms. In the process, we develop heuristics and data structures that substantially improve practical performance of the algorithms. We also develop problem families for testing minimum cut algorithms. Our work leads to a better understanding of practical performance of the minimum cut algorithms and produces very efficient codes for the problem.