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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 151 (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.
Approximation Algorithms for Disjoint Paths Problems
, 1996
"... The construction of disjoint paths in a network is a basic issue in combinatorial optimization: given a network, and specified pairs of nodes in it, we are interested in finding disjoint paths between as many of these pairs as possible. This leads to a variety of classical NPcomplete problems for w ..."
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Cited by 139 (0 self)
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The construction of disjoint paths in a network is a basic issue in combinatorial optimization: given a network, and specified pairs of nodes in it, we are interested in finding disjoint paths between as many of these pairs as possible. This leads to a variety of classical NPcomplete problems for which very little is known from the point of view of approximation algorithms. It has recently been brought into focus in work on problems such as VLSI layout and routing in highspeed networks; in these settings, the current lack of understanding of the disjoint paths problem is often an obstacle to the design of practical heuristics.
A FASTER STRONGLY POLYNOMIAL MINIMUM COST FLOW ALGORITHM
, 1991
"... In this paper, we present a new strongly polynomial time algorithm for the minimum cost flow problem, based on a refinement of the EdmondsKarp scaling technique. Our algorithm solves the uncapacitated minimum cost flow problem as a sequence of O(n log n) shortest path problems on networks with n no ..."
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Cited by 116 (10 self)
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In this paper, we present a new strongly polynomial time algorithm for the minimum cost flow problem, based on a refinement of the EdmondsKarp scaling technique. Our algorithm solves the uncapacitated minimum cost flow problem as a sequence of O(n log n) shortest path problems on networks with n nodes and m arcs and runs in O(n log n (m + n log n)) time. Using a standard transformation, thjis approach yields an O(m log n (m + n log n)) algorithm for the capacitated minimum cost flow problem. This algorithm improves the best previous strongly polynomial time algorithm, due to Z. Galil and E. Tardos, by a factor of n 2 /m. Our algorithm for the capacitated minimum cost flow problem is even more efficient if the number of arcs with finite upper bounds, say n', is much less than m. In this case, the running time of the algorithm is O((m ' + n)log n(m + n log n)).
An Efficient Implementation Of A Scaling MinimumCost Flow Algorithm
 Journal of Algorithms
, 1992
"... . The scaling pushrelabel method is an important theoretical development in the area of minimumcost flow algorithms. We study practical implementations of this method. We are especially interested in heuristics which improve reallife performance of the method. Our implementation works very well o ..."
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Cited by 99 (7 self)
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. The scaling pushrelabel method is an important theoretical development in the area of minimumcost flow algorithms. We study practical implementations of this method. We are especially interested in heuristics which improve reallife performance of the method. Our implementation works very well over a wide range of problem classes. In our experiments, it was always competitive with the established codes, and usually outperformed these codes by a wide margin. Some heuristics we develop may apply to other network algorithms. Our experimental work on the minimumcost flow problem motivated theoretical work on related problems. Supported in part by ONR Young Investigator Award N0001491J1855, NSF Presidential Young Investigator Grant CCR8858097 with matching funds from AT&T and DEC, Stanford University Office of Technology Licensing, and a grant form the Powell Foundation. 1 1. Introduction. Significant theoretical progress has been made recently in the area of minimumcost flow ...
Efficient Implementation of Retiming
 In Proc. Intl. Conf. on ComputerAided Design
, 1994
"... Retiming is a technique for optimizing sequential circuits. It repositions the registers in a circuit leaving the combinational cells untouched. The objective of retiming is to find a circuit with the minimum number of registers for a specified clock period. More than ten years have elapsed since Le ..."
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Cited by 46 (0 self)
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Retiming is a technique for optimizing sequential circuits. It repositions the registers in a circuit leaving the combinational cells untouched. The objective of retiming is to find a circuit with the minimum number of registers for a specified clock period. More than ten years have elapsed since Leiserson and Saxe first presented a theoretical formulation to solve this problem for singleclock edgetriggered sequential circuits. Their proposed algorithms have polynomial complexity; however naive implementations of these algorithms exhibit O(n 3 ) time complexity and O(n 2 ) space complexity when applied to digital circuits with n combinational cells. This renders retiming ineffective for circuits with more than 500 combinational cells. This paper addresses the implementation issues required to exploit the sparsity of circuit graphs to allow minperiod retiming and constrained minarea retiming to be applied to circuits with as many as 10,000 combinational cells. We believe this is...
Improved Algorithms For Bipartite Network Flow
, 1994
"... In this paper, we study network flow algorithms for bipartite networks. A network G = (V; E) is called bipartite if its vertex set V can be partitioned into two subsets V 1 and V 2 such that all edges have one endpoint in V 1 and the other in V 2 . Let n = jV j, n 1 = jV 1 j, n 2 = jV 2 j, m = jE ..."
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Cited by 41 (5 self)
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In this paper, we study network flow algorithms for bipartite networks. A network G = (V; E) is called bipartite if its vertex set V can be partitioned into two subsets V 1 and V 2 such that all edges have one endpoint in V 1 and the other in V 2 . Let n = jV j, n 1 = jV 1 j, n 2 = jV 2 j, m = jEj and assume without loss of generality that n 1 n 2 . We call a bipartite network unbalanced if n 1 ΓΈ n 2 and balanced otherwise. (This notion is necessarily imprecise.) We show that several maximum flow algorithms can be substantially sped up when applied to unbalanced networks. The basic idea in these improvements is a twoedge push rule that allows us to "charge" most computation to vertices in V 1 , and hence develop algorithms whose running times depend on n 1 rather than n. For example, we show that the twoedge push version of Goldberg and Tarjan's FIFO preflow push algorithm runs in O(n 1 m + n 3 1 ) time and that the analogous version of Ahuja and Orlin's excess scaling algori...
SublinearTime Parallel Algorithms for Matching and Related Problems
, 1988
"... This paper presents the first sublineartime deterministic parallel algorithms for bipartite matching and several related problems, including maximal nodedisjoint paths, depthfirst search, and flows in zeroone networks. Our results are based on a better understanding of the combinatorial struc ..."
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Cited by 33 (6 self)
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This paper presents the first sublineartime deterministic parallel algorithms for bipartite matching and several related problems, including maximal nodedisjoint paths, depthfirst search, and flows in zeroone networks. Our results are based on a better understanding of the combinatorial structure of the above problems, which leads to new algorithmic techniques. In particular, we show how to use maximal matching to extend, in parallel, a current set of nodedisjoint paths and how to take advantage of the parallelism that arises when a large number of nodes are "active" during an execution of a pushrelabel network flow algorithm. We also show how to apply our techniques to design parallel algorithms for the weighted versions of the above problems. In particular, we present sublineartime deterministic parallel algorithms for finding a minimumweight bipartite matching and for finding a minimumcost flow in a network with zeroone capacities, if the weights are polynomially ...
Efficiently Answering Reachability Queries on Very Large Directed Graphs
"... Efficiently processing queries against very large graphs is an important research topic largely driven by emerging real world applications, as diverse as XML databases, GIS, web mining, social network analysis, ontologies, and bioinformatics. In particular, graph reachability has attracted a lot of ..."
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Cited by 24 (4 self)
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Efficiently processing queries against very large graphs is an important research topic largely driven by emerging real world applications, as diverse as XML databases, GIS, web mining, social network analysis, ontologies, and bioinformatics. In particular, graph reachability has attracted a lot of research attention as reachability queries are not only common on graph databases, but they also serve as fundamental operations for many other graph queries. The main idea behind answering reachability queries in graphs is to build indices based on reachability labels. Essentially, each vertex in the graph is assigned with certain labels such that the reachability between any two vertices can be determined by their labels. Several approaches have been proposed for building these reachability labels; among them are interval labeling (tree cover) and 2hop labeling. However, due to the large number of vertices in many real world graphs (some graphs can easily contain millions of vertices), the computational cost and (index) size of the labels using existing methods would prove too expensive to be practical. In this paper, we introduce a novel graph structure, referred to as pathtree, to help labeling very large graphs. The pathtree cover is a spanning subgraph of G in a tree shape. We demonstrate both analytically and empirically the effectiveness of our new approaches.