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Balanced network flows. III. Strongly polynomial augmentation algorithms

1999
*
Networks
*

The most important part of the

doi:10.1002/(sici)1097-0037(199901)33:1<43::aid-net3>3.3.co;2-y
fatcat:bpf6terg5zeshamckds56xmwpq
*augmentation**algorithm**Balanced**flow**networks*were studied extensively in [4]. is the*balanced**network*search procedure BNS which Solving the maximum*balanced**flow*problem ... We discuss efficient*augmentation**algorithms*for the maximum*balanced**flow*problem which run in O(nm 2 ) time. ... We mention that there are other*polynomial*time*algorithms*for the maximum*balanced**flow*problem: Appar-Especially in the case of 0-1*balanced**flow**networks*, where a version of the Micali/Vazirani*algorithm*...##
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Balanced network flows. III. Strongly polynomial augmentation algorithms

1999
*
Networks
*

The most important part of the

doi:10.1002/(sici)1097-0037(199901)33:1<43::aid-net3>3.0.co;2-6
fatcat:3kuy6jf2zjcn7eehbvfykisdni
*augmentation**algorithm**Balanced**flow**networks*were studied extensively in [4]. is the*balanced**network*search procedure BNS which Solving the maximum*balanced**flow*problem ... We discuss efficient*augmentation**algorithms*for the maximum*balanced**flow*problem which run in O(nm 2 ) time. ... We mention that there are other*polynomial*time*algorithms*for the maximum*balanced**flow*problem: Appar-Especially in the case of 0-1*balanced**flow**networks*, where a version of the Micali/Vazirani*algorithm*...##
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Page 5225 of Mathematical Reviews Vol. , Issue 2000g
[page]

2000
*
Mathematical Reviews
*

*III*.

*Strongly*

*polynomial*

*augmentation*

*algorithms*. (English summary)

*Networks*33 (1999), no. 1, 43-56. ... The authors discuss efficient

*augmentation*

*algorithms*for the max- imum

*balanced*

*flow*problems which run in O(n-m-m) time and a

*balanced*

*network*search procedure which finds valid

*augment*- ing paths of ...

##
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Page 6677 of Mathematical Reviews Vol. , Issue 87k
[page]

1987
*
Mathematical Reviews
*

Nakayama, Akira (J-OTUC) 87k:90101 A

*polynomial**algorithm*for the maximum*balanced**flow*problem with a constant*balancing*rate function. (Japanese summary) J. Oper. Res. Soc. ... In this paper, we propose an*algorithm*for the maximum*balanced**flow*problem which is fast and simple in practice. ...##
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New polynomial-time cycle-canceling algorithms for minimum-cost flows

2000
*
Networks
*

This

doi:10.1002/1097-0037(200008)36:1<53::aid-net6>3.0.co;2-y
fatcat:tvo54whxhvcljinek37wss4tca
*algorithm*maintains a feasible solution x in the*network*G and proceeds by*augmenting**flows*along negative cost directed cycles in the residual*network*G(x) and thereby canceling them. ... We next describe a variant of*algorithm*that solves the minimum cost*flow*problem in*strongly**polynomial*time; the running time of this variant is O(m(m+n log n) min{log (nU), m log n}). ...*Algorithmic*Description Reference Weakly*Polynomial*Bound*Strongly**Polynomial*Bound 1.*Augment**flow*along a negative cycle with a minimum mean cost. ...##
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Some Recent Advances in Network Flows

1991
*
SIAM Review
*

Key words.

doi:10.1137/1033048
fatcat:cmjqcdhw6rhtti4slnnzwb4lyy
*network**flows*,*network**algorithms*,*network*optimization, shortest path problem, maximum*flow*problem, minimum-cost*flow*problem AMS(MOS) subject classifications. 90B I0, 90C35, 9002 * ... This survey illustrates some of these techniques and their usefulness in developing faster*network**flow**algorithms*. ...*strongly**polynomial*time*algorithms*for the shortest path and maximum*flow*problems, we invoke the similarity assumption. ...##
###
Average consensus on general digraphs

2011
*
IEEE Conference on Decision and Control and European Control Conference
*

We propose a linear distributed

doi:10.1109/cdc.2011.6160386
dblp:conf/cdc/CaiI11
fatcat:4ygubqdzefavviwuyu66xewzhq
*algorithm*which guarantees state averaging on arbitrary*strongly*connected digraphs. ... We study the average consensus problem of multiagent systems for general*network*topologies with unidirectional information*flow*. ... The approach enables multi-agent systems to achieve average consensus on arbitrary*strongly*connected*network*topologies with unidirectional information*flow*, where the state sum of agents need not be ...##
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A Simpler and Faster Strongly Polynomial Algorithm for Generalized Flow Maximization
[article]

2020
*
arXiv
*
pre-print

We present a new

arXiv:1611.01778v3
fatcat:fud3udbwjrhivcw7k6m2kskmyu
*strongly**polynomial**algorithm*for generalized*flow*maximization that is significantly simpler and faster than the previous*strongly**polynomial**algorithm*[Végh16]. ... This allows us to work almost exclusively with integral*flows*, in contrast to all previous*algorithms*for the problem. ... Conclusions and future research A next milestone towards a*strongly**polynomial**algorithm*for general linear programming is to find a*strongly**polynomial**algorithm*for the minimum cost generalized*flow*...##
###
A simpler and faster strongly polynomial algorithm for generalized flow maximization

2017
*
Proceedings of the 49th Annual ACM SIGACT Symposium on Theory of Computing - STOC 2017
*

We present a new

doi:10.1145/3055399.3055439
dblp:conf/stoc/OlverV17
fatcat:wd4v2s4m4zeldecieovp6twb6a
*strongly**polynomial**algorithm*for generalized*flow*maximization that is significantly simpler and faster than the previous*strongly**polynomial**algorithm*[34] . ... This allows us to work almost exclusively with integral*flows*, in contrast to all previous*algorithms*for the problem. ... Conclusions and future research A next milestone towards a*strongly**polynomial**algorithm*for general linear programming is to find a*strongly**polynomial**algorithm*for the minimum cost generalized*flow*...##
###
Minimum cost network flows: Problems, algorithms, and software

2013
*
Yugoslav Journal of Operations Research
*

We present a wide range of problems concerning minimum cost

doi:10.2298/yjor121120001s
fatcat:teynps3rx5cmhhkljjuyt5e6v4
*network**flows*, and give an overview of the classic linear single-commodity Minimum Cost*Network**Flow*Problem (MCNFP) and some other closely related ... We also discuss state-of-the-art*algorithmic*approaches and recent advances in the solution methods for the MCNFP. Finally, optimization software packages for the MCNFP are presented. ... If 0 i i N b , then the*network*G will be a*balanced**network*. ...##
###
Combinatorial algorithms for the generalized circulation problem

1988
*
[Proceedings 1988] 29th Annual Symposium on Foundations of Computer Science
*

This problem is a special case of linear programming, and therefore can be solved in

doi:10.1109/sfcs.1988.21959
dblp:conf/focs/GoldbergPT88
fatcat:g5twqyvzwrd4lbhpnzh2zn4qry
*polynomial*time. In this paper we present the first*polynomial*time combinatorial*algorithms*for this problem. ... The*algorithms*are simple and intuitive. ... Acknowledgment We would like to thank Bob Tarjan for allowing us to include his observation that improved the running time of the Fat-Path*algorithm*. ...##
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TWO EFFICIENT ALGORITHMS FOR THE GENERALIZED MAXIMUM BALANCED FLOW PROBLEM

2002
*
Journal of the Operations Research Society of Japan
*

Minoux considered the mavimum

doi:10.15807/jorsj.45.162
fatcat:n7nwcnakfbeinb566eti22lt2m
*balanced**flow*problem, i.e. the problem of finding a maximum*flow*in a two-terminal netwerk YV' = (V; A) with source s and sink t satisfying the constraint that any arc-*flow*... of YV' is bounded by a fixed proportion of the total*flow*value from s to t, where ... in*strongly**polynomial*time, 6. ...##
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Simple Generalized Maximum Flow Algorithms
[chapter]

1998
*
Lecture Notes in Computer Science
*

We present several new efficient

doi:10.1007/3-540-69346-7_24
fatcat:uue5a6wtmbckppk5v6pz4ghk64
*algorithms*for the generalized maximum*flow*problem. ... The generalized maximum*flow*problem is identical to the traditional maximum*flow*problem, except that it can also model*networks*which "leak"*flow*. ... Our new*algorithm*allows a simpler proof the*strongly*-*polynomial*complexity bound. ...##
###
Strongly polynomial algorithm for a class of minimum-cost flow problems with separable convex objectives
[article]

2016
*
arXiv
*
pre-print

, one can give an

arXiv:1110.4882v5
fatcat:n4dylgv42nbw5pazriicmkdglu
*algorithm*using a*strongly**polynomial*number of arithmetic operations and oracle calls only. ... A well-studied nonlinear extension of the minimum-cost*flow*problem is to minimize the objective ∑_ij∈ E C_ij(f_ij) over feasible*flows*f, where on every arc ij of the*network*, C_ij is a convex function ...*strongly**polynomial**algorithm*. ...##
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Strongly polynomial algorithm for a class of minimum-cost flow problems with separable convex objectives

2012
*
Proceedings of the 44th symposium on Theory of Computing - STOC '12
*

We give a

doi:10.1145/2213977.2213981
dblp:conf/stoc/Vegh12
fatcat:imswvzwdvbh4fgbexwuh4rxvx4
*strongly**polynomial**algorithm*for finding an exact optimal solution for a broad class of such problems. ... We thereby give the first*strongly**polynomial**algorithms*for separable quadratic minimum-cost*flows*and for Fisher's market with spending constraint utilities, settling open questions posed e.g. in [15 ... (*iii*) immediately implies (iv), as each*flow**augmentation*decreases Ex(f ) by ∆. Lemma 5.2. F ⊆ F * holds in each step of the*algorithm*. Proof. The proof is by induction. ...
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