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New DistanceDirected Algorithms for Maximum Flow and Parametric Maximum Flow Problems
, 1987
"... ..."
Maximum flows by incremental breadthfirst search
 In ESA, LNCS 6942
, 2011
"... Abstract. Maximum flow and minimum st cut algorithms are used to solve several fundamental problems in computer vision. These problems have special structure, and standard techniques perform worse than the specialpurpose BoykovKolmogorov (BK) algorithm. We introduce the incremental breadthfirst ..."
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Abstract. Maximum flow and minimum st cut algorithms are used to solve several fundamental problems in computer vision. These problems have special structure, and standard techniques perform worse than the specialpurpose BoykovKolmogorov (BK) algorithm. We introduce the incremental breadthfirst search (IBFS) method, which uses ideas from BK but augments on shortest paths. IBFS is theoretically justified (runs in polynomial time) and usually outperforms BK on vision problems. 1
Approximation Scheme for Lowest Outdegree Orientation and Graph Density Measures
"... Abstract. We deal with the problem of finding such an orientation of a given graph that the largest number of edges leaving a vertex (called the outdegree of the orientation) is small. For any ε ∈ (0, 1) we show an Õ(E(G)/ε) time algorithm3 which finds an orientation of an input graph G with outde ..."
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Cited by 2 (0 self)
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Abstract. We deal with the problem of finding such an orientation of a given graph that the largest number of edges leaving a vertex (called the outdegree of the orientation) is small. For any ε ∈ (0, 1) we show an Õ(E(G)/ε) time algorithm3 which finds an orientation of an input graph G with outdegree at most ⌈(1 + ε)d ∗ ⌉, where d ∗ is the maximum density of a subgraph of G. It is known that the optimal value of orientation outdegree is ⌈d ∗ ⌉. Our algorithm has applications in constructing labeling schemes, introduced by Kannan et al. in [18] and in approximating such graph density measures as arboricity, pseudoarboricity and maximum density. Our results improve over the previous, 2approximation algorithms by Aichholzer et al. [1] (for orientation / pseudoarboricity), by Arikati et al. [3] (for arboricity) and by Charikar [5] (for maximum density). 1
A Faster Primal Network Simplex Algorithm
, 1996
"... A faster primal network simplex algorithm ..."
Max flows in O(nm) time, or better
, 2012
"... In this paper, we present improved polynomial time algorithms for the max flow problem defined on a network with n nodes and m arcs. We show how to solve the max flow problem in O(nm) time, improving upon the best previous algorithm due to King, Rao, and Tarjan, who solved the max flow problem in O( ..."
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In this paper, we present improved polynomial time algorithms for the max flow problem defined on a network with n nodes and m arcs. We show how to solve the max flow problem in O(nm) time, improving upon the best previous algorithm due to King, Rao, and Tarjan, who solved the max flow problem in O(nm log m/(n log n) n) time. In the case that m = O(n), we improve the running time to O(n 2 / log n). We further improve the running time in the case that U ∗ = Umax/Umin is not too large, where Umax denotes the largest finite capacity and Umin denotes the smallest nonzero capacity. If log(U ∗ ) = O(n 1/3 log −3 n), we show how to solve the max flow problem in O(nm / log n) steps. In the case that log(U ∗ ) = O(log k n) for some fixed positive integer k, we show how to solve the max flow problem in Õ(n8/3) time. This latter algorithm relies on a subroutine for fast matrix multiplication. 1