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

2022
*
arXiv
*
pre-print

We give an algorithm that computes exact

arXiv:2203.00671v2
fatcat:hwdtmht5mjc4fn73pb3zg5tyte
*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. ...##
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Exact and Heuristic Algorithms for the Weapon-Target Assignment Problem

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. ...

##
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Exact and Heuristic Methods for the Weapon Target Assignment Problem

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. ...

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

2014
*
The Renewable Energies and Power Quality Journal (RE&PQJ)
*

power variations, start-up

doi:10.24084/repqj12.387
fatcat:ltayi6ys5vcghhex4atbwhcnpu
*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. ...##
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Almost optimum placement legalization by minimum cost flow and dynamic programming

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 ...

##
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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. ...##
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Fast approximation algorithms for multicommodity flow problems

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

doi:10.1145/103418.103425
dblp:conf/stoc/LeightonMPSTT91
fatcat:pb2zi5uxeba5bbt4g773hrp4pq
*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. ...##
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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- ...##
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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)). ...##
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Learning-Augmented Maximum Flow
[article]

2022
*
arXiv
*
pre-print

We present an algorithm that, given an m-edge

arXiv:2207.12911v1
fatcat:6ktqqze6erdudh3xjl5sdcyuma
*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. ...##
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A Critical Survey on the Network Optimization Algorithms for Evacuation Planning Problems

2018
*
International Journal of Operations Research
*

We consider the computationally hard

doi:10.6886/ijor.201809_15(3).0002
doaj:fc8f5a7d5fd74095b4d1d0ca4ac04a6b
fatcat:kbtyog7njzhk3h6mg3d4m5bwqa
*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 ...##
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Controlled charging of electric vehicles in residential distribution networks

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

doi:10.1109/isgteurope.2012.6465676
dblp:conf/isgteurope/OConnellFRK12
fatcat:zat4o72vbnd6tl32lorr37emfe
*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 ...##
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A SURVEY OF COMBINATORIAL MAXIMUM FLOW ALGORITHMS ON A NETWORK WITH GAINS(Network Design, Control and Optimization)

2004
*
Journal of the Operations Research Society of Japan
*

This paper surveys combinatorial

doi:10.15807/jorsj.47.244
fatcat:364szjzgufhezhohpfizspqknu
*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. ...##
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A Polynomial Combinatorial Algorithm for Generalized Minimum Cost Flow

2002
*
Mathematics of Operations Research
*

This approach has led to superior algorithms for a variety of optimization problems, including shortest path,

doi:10.1287/moor.27.3.445.313
fatcat:pgiauiin2bcrlky2ej43xvgfri
*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. ...##
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A polynomial combinatorial algorithm for generalized minimum cost flow

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,

doi:10.1145/301250.301261
dblp:conf/stoc/Wayne99
fatcat:lelnvhu6brg77m2mafuenukd2e
*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. ...
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