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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 195 (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.
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 45 (4 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 ø 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...
Sensitivity Analysis for Shortest Path Problems and Maximum Capacity Path Problems in Undirected Graphs
 MATH. PROGRAM., SER. A
, 2005
"... Let G = (N,A) be an undirected graph with n nodes and m arcs, a designated source node s and a sink node t. This paper addresses sensitivity analysis questions concerning the shortest st path (SP) problem in G and the maximum capacity st path (MCP) problem in G. Suppose that P* is a shortest st p ..."
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Cited by 5 (2 self)
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Let G = (N,A) be an undirected graph with n nodes and m arcs, a designated source node s and a sink node t. This paper addresses sensitivity analysis questions concerning the shortest st path (SP) problem in G and the maximum capacity st path (MCP) problem in G. Suppose that P* is a shortest st path in G with respect to a nonnegative distance vector c. For each arc e A, the lower SP tolerance of an arc e is the minimum nonnegative value that the length of arc e can take (with all other lengths staying fixed) so that P* remains an optimal path. Similarly, the upper SP tolerance of an arc e is the maximum value that the length of arc e can take so that P* remains an optimal path. We show that the problem of finding all upper and lower tolerances of arcs in A can be solved in O(min(n 2 , m log n)) time. Moreover, the problem of finding all tolerances is computationally equivalent to the "Minimum Cost Interval Problem" which we describe as follows. For each i = 1 to m, let [a i , b i ] denote an interval with endpoints in {1, ..., n}, and an associated cost c i . For each k = 1 to n, identify a minimum cost interval [a i , b i ] containing k. Let Q* be the maximum capacity st path in G with respect to capacity vector u. For each arc e A, the lower MCP (resp., upper) tolerance of the arc e is the minimum (resp., maximum) value that the capacity that arc e can take so that Q* remains a maximum capacity path. We show that the problem of finding all upper and lower tolerances of arcs in A can be solved in O(min(n 2 , m log n)) time. Moreover, the problem of finding all tolerances nearly reduces to the "Minimum Cost Interval Problem."
An Implementation of the Binary Blocking Flow Algorithm
, 1998
"... Goldberg and Rao recently devised a new binary blocking flow algorithm for computing maximum flows in networks with integer capacities. We describe an implementation of variants of the binary blocking flow algorithm geared towards practical efficiency and report on preliminary experimental result ..."
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Cited by 2 (1 self)
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Goldberg and Rao recently devised a new binary blocking flow algorithm for computing maximum flows in networks with integer capacities. We describe an implementation of variants of the binary blocking flow algorithm geared towards practical efficiency and report on preliminary experimental results obtained with our implementation.
2.3 Single Path Labeling Methods Beginning With A FeasibleFlowVector......................
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