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Balanced network flows. III. Strongly polynomial augmentation algorithms

Christian Fremuth‐Paeger, Dieter Jungnickel
1999 Networks  
The most important part of the 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  ... 
doi:10.1002/(sici)1097-0037(199901)33:1<43::aid-net3>3.3.co;2-y fatcat:bpf6terg5zeshamckds56xmwpq

Balanced network flows. III. Strongly polynomial augmentation algorithms

Christian Fremuth-Paeger, Dieter Jungnickel
1999 Networks  
The most important part of the 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  ... 
doi:10.1002/(sici)1097-0037(199901)33:1<43::aid-net3>3.0.co;2-6 fatcat:3kuy6jf2zjcn7eehbvfykisdni

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  ... 

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.  ... 

New polynomial-time cycle-canceling algorithms for minimum-cost flows

P. T. Sokkalingam, Ravindra K. Ahuja, James B. Orlin
2000 Networks  
This 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.  ... 
doi:10.1002/1097-0037(200008)36:1<53::aid-net6>3.0.co;2-y fatcat:tvo54whxhvcljinek37wss4tca

Some Recent Advances in Network Flows

Ravindra K. Ahuja, Thomas L. Magnanti, James B. Orlin
1991 SIAM Review  
Key words. 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.  ... 
doi:10.1137/1033048 fatcat:cmjqcdhw6rhtti4slnnzwb4lyy

Average consensus on general digraphs

Kai Cai, Hideaki Ishii
2011 IEEE Conference on Decision and Control and European Control Conference  
We propose a linear distributed 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  ... 
doi:10.1109/cdc.2011.6160386 dblp:conf/cdc/CaiI11 fatcat:4ygubqdzefavviwuyu66xewzhq

A Simpler and Faster Strongly Polynomial Algorithm for Generalized Flow Maximization [article]

Neil Olver, László A. Végh
2020 arXiv   pre-print
We present a new 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  ... 
arXiv:1611.01778v3 fatcat:fud3udbwjrhivcw7k6m2kskmyu

A simpler and faster strongly polynomial algorithm for generalized flow maximization

Neil Olver, László A. Végh
2017 Proceedings of the 49th Annual ACM SIGACT Symposium on Theory of Computing - STOC 2017  
We present a new 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  ... 
doi:10.1145/3055399.3055439 dblp:conf/stoc/OlverV17 fatcat:wd4v2s4m4zeldecieovp6twb6a

Minimum cost network flows: Problems, algorithms, and software

Angelo Sifaleras
2013 Yugoslav Journal of Operations Research  
We present a wide range of problems concerning minimum cost 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.  ... 
doi:10.2298/yjor121120001s fatcat:teynps3rx5cmhhkljjuyt5e6v4

Combinatorial algorithms for the generalized circulation problem

A.V. Goldberg, S.A. Plotkin, E. Tardos
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 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.  ... 
doi:10.1109/sfcs.1988.21959 dblp:conf/focs/GoldbergPT88 fatcat:g5twqyvzwrd4lbhpnzh2zn4qry

TWO EFFICIENT ALGORITHMS FOR THE GENERALIZED MAXIMUM BALANCED FLOW PROBLEM

Akira Nakayama, Chien Fei Su
2002 Journal of the Operations Research Society of Japan  
Minoux considered the mavimum 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.  ... 
doi:10.15807/jorsj.45.162 fatcat:n7nwcnakfbeinb566eti22lt2m

Simple Generalized Maximum Flow Algorithms [chapter]

Éva Tardos, Kevin D. Wayne
1998 Lecture Notes in Computer Science  
We present several new efficient 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.  ... 
doi:10.1007/3-540-69346-7_24 fatcat:uue5a6wtmbckppk5v6pz4ghk64

Strongly polynomial algorithm for a class of minimum-cost flow problems with separable convex objectives [article]

Laszlo A. Vegh
2016 arXiv   pre-print
, one can give an 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.  ... 
arXiv:1110.4882v5 fatcat:n4dylgv42nbw5pazriicmkdglu

Strongly polynomial algorithm for a class of minimum-cost flow problems with separable convex objectives

László A. Végh
2012 Proceedings of the 44th symposium on Theory of Computing - STOC '12  
We give a 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.  ... 
doi:10.1145/2213977.2213981 dblp:conf/stoc/Vegh12 fatcat:imswvzwdvbh4fgbexwuh4rxvx4
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