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Polynomial-Time Highest-Gain Augmenting Path Algorithms for the Generalized Circulation Problem

Donald Goldfarb, Zhiying Jin, James B. Orlin
1997 Mathematics of Operations Research  
After an initial step in which all flow-generating cycles are canceled and excesses are created, both algorithms bring these excesses to the sink via highest-gain augmenting paths.  ...  This paper presents two new combinatorial algorithms for the generalized circulation problem.  ...  A Highest-Gain Augmenting Path Algorithm In this section we present the first of two new algorithms for the generalized circulation problem.  ... 
doi:10.1287/moor.22.4.793 fatcat:u23ssd34xnfmlbjdpvenubfr3u

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  
In this paper we present the first polynomial time combinatorial algorithms for this problem. The algorithms are simple and intuitive.  ...  The goal is to maximize the amount of flow excess at the source. This problem is a special case of linear programming, and therefore can be solved in polynomial time.  ...  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

Combinatorial Algorithms for the Generalized Circulation Problem

Andrew V. Goldberg, Serge A. Plotkin, Éva Tardos
1991 Mathematics of Operations Research  
In this paper we present the rst polynomial time combinatorial algorithms for this problem. The algorithms are simple and intuitive.  ...  The goal is to maximize the amount of ow excess at the source. This problem is a special case of linear programming, and therefore can be solved in polynomial time.  ...  Acknowledgment We would like to thank Bob Tarjan and Bruce Maggs for allowing us to include theirs observations that improved the running time of the Fat-Path algorithm.  ... 
doi:10.1287/moor.16.2.351 fatcat:qby6x5z26zdv3pk4babncfbktq

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,  ...  Network optimization experienced a fast development, during the last few decades.  ...  Acknowledgments The author gratefu1 to anonymous referees for their helpfu1 comments that improved the presentation of this paper,  ... 
doi:10.15807/jorsj.47.244 fatcat:364szjzgufhezhohpfizspqknu

Faster Algorithms for the Generalized Network Flow Problem

Tomasz Radzik
1998 Mathematics of Operations Research  
-We give an algorithm which solves this problem in O(m2 ( m + n log log B ) log B ) time, where B is the largest integer used to represent the gain factors, the capacities, and the initial supplies at  ...  Abst 1: act We consider the generalized network flow problem. Each arc e in the network has a gain factor y ( e ) .  ...  Acknowledgements I would like to thank Eva Tardos and Edith Cohen for helpful discussions.  ... 
doi:10.1287/moor.23.1.69 fatcat:qsbpbwhfdjgi5k5ldv2smmineu

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].  ...  Even for small numerical parameter values, our running time bound is comparable to the best weakly polynomial algorithms. The key new technical idea is relaxing the primal feasibility conditions.  ...  We thank the anonymous referees for their detailed and constructive comments that helped improve the exposition.  ... 
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] .  ...  Even for small numerical parameter values, our running time bound is comparable to the best weakly polynomial algorithms. The key new technical idea is relaxing the primal feasibility conditions.  ...  We thank the anonymous referees for their detailed and constructive comments that helped improve the exposition.  ... 
doi:10.1145/3055399.3055439 dblp:conf/stoc/OlverV17 fatcat:wd4v2s4m4zeldecieovp6twb6a

Concave Generalized Flows with Applications to Market Equilibria

László A. Végh
2014 Mathematics of Operations Research  
We give a polynomial time combinatorial algorithm for solving corresponding flow maximization problems, finding an ε-approximate solution in O(m(m + log n) log(M U m/ε)) arithmetic operations and value  ...  This also gives a new algorithm for linear generalized flows, an efficient, purely scaling variant of the Fat-Path algorithm by Goldberg, Plotkin and Tardos [13], not using any cycle cancellations.  ...  Acknowledgments The author is grateful to Vijay Vazirani for several fruitful discussions on market equilibrium problems.  ... 
doi:10.1287/moor.2013.0623 fatcat:hyuzhn6u4vetfpn4rx7xelljfe

Concave Generalized Flows with Applications to Market Equilibria [article]

Laszlo A. Vegh
2012 arXiv   pre-print
We give a polynomial time combinatorial algorithm for solving corresponding flow maximization problems, finding an epsilon-approximate solution in O(m(m+log n)log(MUm/epsilon)) arithmetic operations and  ...  This also gives a new algorithm for linear generalized flows, an efficient, purely scaling variant of the Fat-Path algorithm by Goldberg, Plotkin and Tardos, not using any cycle cancellations.  ...  Acknowledgments The author is grateful to Vijay Vazirani for several fruitful discussions on market equilibrium problems.  ... 
arXiv:1109.3893v3 fatcat:qbfocax22ffy7osh4gvyi6km7q

Concave Generalized Flows with Applications to Market Equilibria

Laszlo A. Vegh
2012 2012 IEEE 53rd Annual Symposium on Foundations of Computer Science  
[Goldberg AV, Plotkin SA, Tardos É (1991) Combinatorial algorithms for the generalized circulation problem. Math. Oper. Res. 16(2):351-381], not using any cycle cancellations.  ...  This also gives a new algorithm for linear generalized flows, an efficient, purely scaling variant of the Fat-Path algorithm by Goldberg et al.  ...  The author is grateful to Vijay Vazirani for several fruitful discussions on market equilibrium problems.  ... 
doi:10.1109/focs.2012.33 dblp:conf/focs/Vegh12 fatcat:mbq5oa6yyfdknkj6ljpcfoa7x4

Page 6685 of Mathematical Reviews Vol. , Issue 98J [page]

1998 Mathematical Reviews  
York, NY); Jin, Zhi Ying (1-GTE; Waltham, MA); Orlin, James B. (1-MIT-MG; Cambridge, MA Polynomial-time highest-gain augmenting path algorithms for the generalized circulation problem.  ...  After an initial step in which all flow-generating cycles are canceled and excesses are cre- ated, both algorithms bring these excesses to the sink via highest- gain augmenting paths.  ... 

A simple GAP-canceling algorithm for the generalized maximum flow problem

Mateo Restrepo, David P. Williamson
2006 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm - SODA '06  
We give a simple primal algorithm for the generalized maximum flow problem that repeatedly finds and cancels generalized augmenting paths (GAPs).  ...  for the generalized minimum-cost circulation problem [30] .  ...  Acknowledgements The second author wishes to thank Michel Goemans andÉva Tardos for useful conversations, and Sergei Vassilvitskii for some early discussions on this research.  ... 
doi:10.1145/1109557.1109616 fatcat:67z4o5rer5ecjc7asjmkfqzqgy

A simple GAP-canceling algorithm for the generalized maximum flow problem

Mateo Restrepo, David P. Williamson
2007 Mathematical programming  
We give a simple primal algorithm for the generalized maximum flow problem that repeatedly finds and cancels generalized augmenting paths (GAPs).  ...  for the generalized minimum-cost circulation problem [30] .  ...  Acknowledgements The second author wishes to thank Michel Goemans andÉva Tardos for useful conversations, and Sergei Vassilvitskii for some early discussions on this research.  ... 
doi:10.1007/s10107-007-0183-8 fatcat:tk4xlm36zzhslkuuompqdru4z4

A strongly polynomial algorithm for generalized flow maximization [article]

László A. Végh
2016 arXiv   pre-print
A strongly polynomial algorithm is given for the generalized flow maximization problem. It uses a new variant of the scaling technique, called continuous scaling.  ...  As a consequence of the result, we also obtain a strongly polynomial algorithm for the linear feasibility problem with at most two nonzero entries per column in the constraint matrix.  ...  Acknowledgment The author is grateful to Joseph Cheriyan, Ian Post, and the anonymous referees for several suggestions that helped to improve the presentation.  ... 
arXiv:1307.6809v4 fatcat:pznqxcyqwrcpdf2mtrd6ny6xki

A strongly polynomial algorithm for generalized flow maximization

László A. Végh
2014 Proceedings of the 46th Annual ACM Symposium on Theory of Computing - STOC '14  
A strongly polynomial algorithm is given for the generalized flow maximization problem. It uses a new variant of the scaling technique, called continuous scaling.  ...  As a consequence of the result, we also obtain a strongly polynomial algorithm for the linear feasibility problem with at most two nonzero entries per column in the constraint matrix.  ...  Acknowledgment The author is grateful to Joseph Cheriyan, Ian Post, and the anonymous referees for several suggestions that helped to improve the presentation.  ... 
doi:10.1145/2591796.2591806 dblp:conf/stoc/Vegh14 fatcat:n3m2kmyclvd73eofu3j5aopqy4
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