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Maximum Flow and Minimum-Cost Flow in Almost-Linear Time [article]

Li Chen, Rasmus Kyng, Yang P. Liu, Richard Peng, Maximilian Probst Gutenberg, Sushant Sachdeva
2022 arXiv   pre-print
We give an algorithm that computes exact maximum flows and minimum-cost flows on directed graphs with m edges and polynomially bounded integral demands, costs, and capacities in m^1+o(1) time.  ...  This gives almost-linear time algorithms for several problems including entropy-regularized optimal transport, matrix scaling, p-norm flows, and p-norm isotonic regression on arbitrary directed acyclic  ...  We give the first almost-linear time algorithm for min-cost flow, achieving the optimal running time up to subpolynomial factors. Theorem 1.1.  ... 
arXiv:2203.00671v2 fatcat:hwdtmht5mjc4fn73pb3zg5tyte

Exact and Heuristic Algorithms for the Weapon-Target Assignment Problem

Ravindra K. Ahuja, Arvind Kumar, Krishna C. Jha, James B. Orlin
2007 Operations Research  
In this paper, we suggest linear programming, integer programming, and network flow based lower bounding methods using which we obtain several branch and bound algorithms for the WTA problem.  ...  We also propose a network flow based construction heuristic and a very large-scale neighborhood (VLSN) search algorithm.  ...  Robert Murphey at the Air Force Research Laboratory, Eglin Air Force Base to bring this problem to our notice and for helpful discussions.  ... 
doi:10.1287/opre.1070.0440 fatcat:ls7x7ljk7nafldk27ifdpfdqwi

Exact and Heuristic Methods for the Weapon Target Assignment Problem

Ravindra K. Ahuja, Arvind Kumar, Krishna Jha, James B. Orlin
2003 Social Science Research Network  
In this paper, we suggest linear programming, integer programming, and network flow based lower bounding methods using which we obtain several branch and bound algorithms for the WTA problem.  ...  We also propose a network flow based construction heuristic and a very large-scale neighborhood (VLSN) search algorithm.  ...  Robert Murphey at the Air Force Research Laboratory, Eglin Air Force Base to bring this problem to our notice and for helpful discussions.  ... 
doi:10.2139/ssrn.489802 fatcat:u6eqi6yn4jdbfbhtdnnlaku75i

Effects of the maximum flow ramping rates on the long-term operation decisions of a hydropower plant

I. Guisández, J.I. Pérez-Díaz, J.R. Wilhelmi
2014 The Renewable Energies and Power Quality Journal (RE&PQJ)  
power variations, start-up and shut-down costs of hydro units, and minimum environmental flows and maximum ramping rates.  ...  in shorter time horizons.  ...  power variations, start-up and shut-down costs of hydro units, and minimum environmental flows and maximum ramping rates.  ... 
doi:10.24084/repqj12.387 fatcat:ltayi6ys5vcghhex4atbwhcnpu

Almost optimum placement legalization by minimum cost flow and dynamic programming

Ulrich Brenner, Anna Pauli, Jens Vygen
2004 Proceedings of the 2004 international symposium on Physical design - ISPD '04  
In particular, we analyze a generic legalization algorithm based on minimum cost flows and dynamic programming.  ...  Our experiments demonstrate that minimizing total (weighted, squared) movement has almost no negative effect on the timing properties, routability and netlength.  ...  The SB-minimum cost flow instance has the following properties (see [2] for proofs): Flow Realization In this section we realize a maximum ×-Ø-flow of minimum cost, in the model described in the previous  ... 
doi:10.1145/981066.981069 dblp:conf/ispd/BrennerPV04 fatcat:l23y5bo5knfbzkzxeis7q6vfv4

Page 5241 of Mathematical Reviews Vol. , Issue 85k [page]

1985 Mathematical Reviews  
Our algo- rithm is almost dual to the lexico-shortest route algorithm for the minimum cost flow problem with an additional linear constraint. For example, a loop is replaced by a cutset.  ...  Kobayashi, Takashi (J-SAI) 85k:90069 The lexico-bounded flow algorithm for solving the minimum cost project scheduling problem with an additional linear constraint. (Japanese summary) J. Oper. Res.  ... 

Fast approximation algorithms for multicommodity flow problems

Tom Leighton, Clifford Stein, Fillia Makedon, Éva Tardos, Serge Plotkin, Spyros Tragoudas
1991 Proceedings of the twenty-third annual ACM symposium on Theory of computing - STOC '91  
Acknowledgments We are grateful to Andrew Goldberg, Tishya Leong, Jim Orlin, Rina Rotshild, David Shimoys and Peter Shor for helpful discussions.  ...  Proof: The Goldberg-Tarjan minimum-cost flow algorithm runs in O(1m log(11 2 /h ) g( O()) time, where C is the maximum value of the cost of an edge assuming that the costs are integral.  ...  , minimum cut linear arrangement, and minimum area layout.  ... 
doi:10.1145/103418.103425 dblp:conf/stoc/LeightonMPSTT91 fatcat:pb2zi5uxeba5bbt4g773hrp4pq

Page 5177 of Mathematical Reviews Vol. , Issue 2001G [page]

2001 Mathematical Reviews  
We also show that the cycle-canceling algorithm (i) can solve the uncapacitated minimum-cost flow problem in O(n(m+nlogn)log(nU)) time; (ii) can obtain an integer optimal solution of the convex cost-flow  ...  For the minimum-cost flow problem with integral data, the generic version of the cycle-canceling algorithm runs in pseudopolynomial time, but several polynomial-time specific implementations can be ob-  ... 

Page 1650 of Mathematical Reviews Vol. , Issue 84d [page]

1984 Mathematical Reviews  
Itai and Y. Shiloach, same journal 8 (1979), 135-150; MR 80i:90052] has time O(n? log(n)); the s-r cut is a byproduct of the maximum flow computed by their algorithm.  ...  This paper presents an algorithm for computing a minimum (cost) s-¢ cut of N. For general L, this algorithm runs in time O(nlog?(n)).  ... 

Learning-Augmented Maximum Flow [article]

Adam Polak, Maksym Zub
2022 arXiv   pre-print
We present an algorithm that, given an m-edge flow network and a predicted flow, computes a maximum flow in O(mη) time, where η is the ℓ_1 error of the prediction, i.e., the sum over the edges of the absolute  ...  difference between the predicted and optimal flow values.  ...  Acknowledgments We would like to thank Alexandra Lassota, Sai Ganesh Nagarajan, and Moritz Venzin for helpful discussion.  ... 
arXiv:2207.12911v1 fatcat:6ktqqze6erdudh3xjl5sdcyuma

A Critical Survey on the Network Optimization Algorithms for Evacuation Planning Problems

Tanka Nath Dhamala, Urmila Pyakurel, Stephan Dempe
2018 International Journal of Operations Research  
We consider the computationally hard flows over time problems from wider perspective including flow/time dependent attributes (dynamic flows), a possibility of flows loss on paths while travelling (lossy  ...  The topics also include the networks for relief distribution, location-allocation of facilities, multicriterion characteristics and transit based flow models in brief.  ...  ACKNOWLEDGEMENTS This research has been carried out during the research stays of the first author under the AvH Research Group Linkage Program and the second author as a research fellow with George Foster  ... 
doi:10.6886/ijor.201809_15(3).0002 doaj:fc8f5a7d5fd74095b4d1d0ca4ac04a6b fatcat:kbtyog7njzhk3h6mg3d4m5bwqa

Controlled charging of electric vehicles in residential distribution networks

Alison O'Connell, Damian Flynn, Peter Richardson, Andrew Keane
2012 2012 3rd IEEE PES Innovative Smart Grid Technologies Europe (ISGT Europe)  
This work presents an optimisation method which focuses on controlling the rate at which EVs charge over a 24-hour time horizon, subject to certain constraints.  ...  A sample distribution network is used and the optimisation tool is tested for multiple objective functions.  ...  The uncontrolled case, as well as causing unacceptably voltages, costs C34.61, which is almost double that of the minimum cost scenario, while both the maximum power and maximum wind objectives show results  ... 
doi:10.1109/isgteurope.2012.6465676 dblp:conf/isgteurope/OConnellFRK12 fatcat:zat4o72vbnd6tl32lorr37emfe

A SURVEY OF COMBINATORIAL MAXIMUM FLOW ALGORITHMS ON A NETWORK WITH GAINS(Network Design, Control and Optimization)

Maiko Shigeno
2004 Journal of the Operations Research Society of Japan  
This paper surveys combinatorial maximum Ilow algorithms on the gene:alizecl network and compares algorithms for traditional network flows,  ...  While a traditional network assumes that each flow is conserved on every arc, a flow along an arc may increa$e or clecrease by a fixed factor during it$ traversal of that arc in a generalized network.  ...  This is especially in respect to'polynomial time algorithms for shortest paths, maximum flows, and minimum cost flows that underwent intensive development in 80s to 90s.  ... 
doi:10.15807/jorsj.47.244 fatcat:364szjzgufhezhohpfizspqknu

A Polynomial Combinatorial Algorithm for Generalized Minimum Cost Flow

Kevin D. Wayne
2002 Mathematics of Operations Research  
This approach has led to superior algorithms for a variety of optimization problems, including shortest path, maximum flow, minimum spanning tree, matching, and minimum cost flow.  ...  We propose the first combinatorial solution to one of the most classic problems in combinatorial optimization: the generalized minimum cost flow problem (flow with losses and gains).  ...  The author is thankful toÉva Tardos and Tom McCormick for helpful discussions and comments on an earlier version of this paper.  ... 
doi:10.1287/moor.27.3.445.313 fatcat:pgiauiin2bcrlky2ej43xvgfri

A polynomial combinatorial algorithm for generalized minimum cost flow

Kevin D. Wayne
1999 Proceedings of the thirty-first annual ACM symposium on Theory of computing - STOC '99  
This approach has led to superior algorithms for a variety of optimization problems, including shortest path, maximum flow, minimum spanning tree, matching, and minimum cost flow.  ...  We propose the first combinatorial solution to one of the most classic problems in combinatorial optimization: the generalized minimum cost flow problem (flow with losses and gains).  ...  The author is thankful toÉva Tardos and Tom McCormick for helpful discussions and comments on an earlier version of this paper.  ... 
doi:10.1145/301250.301261 dblp:conf/stoc/Wayne99 fatcat:lelnvhu6brg77m2mafuenukd2e
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