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Polynomial-Time Highest-Gain Augmenting Path Algorithms for the Generalized Circulation Problem
1997
Mathematics of Operations Research
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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
1988
[Proceedings 1988] 29th Annual Symposium on Foundations of Computer Science
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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
1991
Mathematics of Operations Research
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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)
2004
Journal of the Operations Research Society of Japan
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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
1998
Mathematics of Operations Research
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-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]
2020
arXiv
pre-print
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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
2017
Proceedings of the 49th Annual ACM SIGACT Symposium on Theory of Computing - STOC 2017
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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
2014
Mathematics of Operations Research
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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]
2012
arXiv
pre-print
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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
2012
2012 IEEE 53rd Annual Symposium on Foundations of Computer Science
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[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
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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
2006
Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm - SODA '06
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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
2007
Mathematical programming
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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]
2016
arXiv
pre-print
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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
2014
Proceedings of the 46th Annual ACM Symposium on Theory of Computing - STOC '14
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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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