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Oblivious Algorithms for the Maximum Directed Cut Problem [article]

Uriel Feige, Shlomo Jozeph
2010 arXiv   pre-print
This paper introduces a special family of randomized algorithms for Max DICUT that we call oblivious algorithms.  ...  The paper also discusses natural extensions of the notion of oblivious algorithms, and extensions to the more general problem of Max 2-AND.  ...  The goal of the maximum directed cut (Max DICUT) problem is finding a set such that the weight of the respective directed cut is as large as possible.  ... 
arXiv:1010.0406v1 fatcat:wfeooenztzh3vfsufs6alizfom

Oblivious routing on node-capacitated and directed graphs

Mohammad Taghi Hajiaghayi, Robert D. Kleinberg, Harald Räcke, Tom Leighton
2007 ACM Transactions on Algorithms  
We present the first non-trivial upper bounds for both these cases, providing algorithms for kcommodity oblivious routing problems with competitive ratio O( √ k log(n)) for undirected node-capacitated  ...  For the directed case, however, we show that the lower bound of Ω( √ n) still holds in low-degree graphs.  ...  The problem for directed graphs seems more challenging, since the best known max-flow min-cut gap is O( √ n) in this case (In all currently known algorithms for oblivious routing this max-flow min-cut  ... 
doi:10.1145/1290672.1290688 fatcat:lj7k2xkv65emdeemyswchzzhou

Routing under Balance [article]

Alina Ene, Gary Miller, Jakub Pachocki, Aaron Sidford
2016 arXiv   pre-print
We also give a fast algorithm for the maximum flow problem in balanced directed graphs.  ...  On the negative side, we present new lower bounds for oblivious routing problems on directed graphs.  ...  Part of this work was done while authors were visiting the Simons Institute for the Theory of Computing, UC Berkeley.  ... 
arXiv:1603.09009v1 fatcat:nwonzg3sgvaavh5ob3rb4nhvdu

An Almost-Linear-Time Algorithm for Approximate Max Flow in Undirected Graphs, and its Multicommodity Generalizations [chapter]

Jonathan A. Kelner, Yin Tat Lee, Lorenzo Orecchia, Aaron Sidford
2013 Proceedings of the Twenty-Fifth Annual ACM-SIAM Symposium on Discrete Algorithms  
In this paper, we introduce a new framework for approximately solving flow problems in capacitated, undirected graphs and apply it to provide asymptotically faster algorithms for the maximum s-t flow and  ...  Using this, we show how to reduce approximate maximum flow and maximum concurrent flow to oblivious routing. • the first almost-linear-time construction of an O(m o(1) )-competitive oblivious routing scheme  ...  Acknowledgements We thank Jonah Sherman for agreeing to coordinate arXiv postings, and we thank Satish Rao, Daniel Spielman, Shang-Hua Teng for many helpful conversations.  ... 
doi:10.1137/1.9781611973402.16 dblp:conf/soda/KelnerLOS14 fatcat:xicukhviyzdk5emjezchnqfd7e

Vertex Sparsification and Oblivious Reductions

Ankur Moitra
2013 SIAM journal on computing (Print)  
These results allow us to derive a more general theory of Steiner cut and flow problems, and allow us to obtain approximation algorithms with guarantees independent of the size of the graph for a number  ...  Given an undirected, capacitated graph G = (V, E) and a set K ⊂ V of terminals of size k, we construct an undirected, capacitated graph G = (K, E ) for which the cut-function approximates the value of  ...  We would like to thank Tom Leighton, Harald Räcke and Satish Rao for many helpful discussions.  ... 
doi:10.1137/100787337 fatcat:6yu5mn6o55frlencngvg7dcjzy

Approximation Algorithms for Multicommodity-Type Problems with Guarantees Independent of the Graph Size

Ankur Moitra
2009 2009 50th Annual IEEE Symposium on Foundations of Computer Science  
ACKNOWLEDGMENTS We would like to thank Yossi Azar, Tom Leighton, Harald Räcke, Satish Rao and Mohit Singh for many helpful discussions.  ...  [17] gives a O(log n log gR) approximation algorithm for this problem, where R is the maximum requirement max i r i .  ...  For a maximum concurrent flow problem, let λ * denote the optimum. We defined the cut function h and the terminal cut function h K in section 1.2.  ... 
doi:10.1109/focs.2009.28 dblp:conf/focs/Moitra09 fatcat:cyr2pizykzeibp6ujitruyy74q

An Almost-Linear-Time Algorithm for Approximate Max Flow in Undirected Graphs, and its Multicommodity Generalizations [article]

Jonathan A. Kelner, Yin Tat Lee, Lorenzo Orecchia, Aaron Sidford
2013 arXiv   pre-print
In this paper, we introduce a new framework for approximately solving flow problems in capacitated, undirected graphs and apply it to provide asymptotically faster algorithms for the maximum s-t flow and  ...  maximum concurrent multicommodity flow problems.  ...  Acknowledgements We thank Jonah Sherman for agreeing to coordinate submissions and we thank Satish Rao, Jonah Sherman, Daniel Spielman, Shang-Hua Teng.  ... 
arXiv:1304.2338v2 fatcat:ia4iuxe35jb4dlkmpy5txfzj4q

Oblivious network design

Anupam Gupta, Mohammad T. Hajiaghayi, Harald Räcke
2006 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm - SODA '06  
Can we get competitive algorithms for this problem?  ...  In this paper, we develop a framework to model oblivious network design problems (of which the above problem is a special case), and give algorithms with poly-logarithmic competitive ratio for problems  ...  Acknowledgments We would like to thank Daniel Golovin, Robert Kleinberg, and Tom Leighton for fruitful discussions.  ... 
doi:10.1145/1109557.1109665 fatcat:xrldnfpgj5bjtii3hyykxfv6cq

Implicit and explicit optimizations for stencil computations

Shoaib Kamil, Kaushik Datta, Samuel Williams, Leonid Oliker, John Shalf, Katherine Yelick
2006 Proceedings of the 2006 workshop on Memory system performance and correctness - MSPC '06  
The optimizations target cache reuse across stencil sweeps, including both an implicit cache oblivious approach and a cache-aware algorithm blocked to match the cache structure.  ...  Overall, results show that a cache-aware approach is significantly faster than a cache oblivious approach and that the explicitly managed memory on Cell is more efficient: Relative to the Power5, it has  ...  We would also like to thank Otto Wohlmouth from IBM Germany for running our code on the new 3.2 GHz Cell machines.  ... 
doi:10.1145/1178597.1178605 dblp:conf/ACMmsp/KamilDWOSY06 fatcat:7kuriq36f5e2rc5iz7vh5vhnma

Reactive local search techniques for the maximum k-conjunctive constraint satisfaction problem (MAX-k-CCSP)

Roberto Battiti, Marco Protasi
1999 Discrete Applied Mathematics  
In this paper the performance of the Hamming-based Reactive Tabu Search algorithm (H-RTS) previously proposed for the Maximum Satisÿability problem is studied for the di erent Maximum k-Conjunctive Constraint  ...  In particular, two relevant special cases of the Maximum k-Conjunctive Constraint Satisfaction problem are considered: Maximum Directed Cut and Maximum Independent Set in cubic graphs.  ...  Leonardi for their useful comments on a preliminary version of this paper.  ... 
doi:10.1016/s0166-218x(99)00030-x fatcat:a4llohtb7vhq3civhukh4itywu

Dynamic Algorithms Against an Adaptive Adversary: Generic Constructions and Lower Bounds [article]

Amos Beimel, Haim Kaplan, Yishay Mansour, Kobbi Nissim, Thatchaphol Saranurak, Uri Stemmer
2021 arXiv   pre-print
We first show a separation result for a search problem and then show a separation result for an estimation problem.  ...  Using this reduction we obtain dynamic algorithms against an adaptive adversary with improved update and query times for global minimum cut, all pairs distances, and all pairs effective resistance.  ...  Let A be an oblivious algorithm for one of our graph problems.  ... 
arXiv:2111.03980v1 fatcat:ovd2fifhjvdurjqtpgosnc3nb4

On the Power of Planned Infections in Networks

Michael Brautbar, Moez Draief, Sanjeev Khanna
2015 Internet Mathematics  
process while maintaining a similar "signature" as the oblivious stochastic infection strategy.  ...  "signature" similar to the oblivious stochastic infection strategy in order not to be discovered.  ...  Throughout our analysis, we will frequently refer to the minimum weighted cut value and maximum weighted cut value in the weighted input graph: the minimum (resp. maximum) weighted cut value, denoted min  ... 
doi:10.1080/15427951.2014.982312 fatcat:ju472izqazhgzl2zuzzpikoica

New lower bounds for oblivious routing in undirected graphs

Mohammad T. Hajiaghayi, Robert D. Kleinberg, Tom Leighton, Harald Räcke
2006 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm - SODA '06  
However, there are directed networks for which the competitive ratio is in Ω( √ n).  ...  Oblivious routing algorithms for general undirected networks were introduced by Räcke, and this work has led to many subsequent improvements and applications.  ...  Open problems The main open problem is that whether we can improve the upper bound O(log 2 n) for oblivious routing with random demands in directed graphs [8] and O(log 2 n log log n) for the adversarial  ... 
doi:10.1145/1109557.1109658 fatcat:43aezo4ibvb7rf3zw3v5lm4svm

On the Relative Merits of Simple Local Search Methods for the MAX-SAT Problem [chapter]

Denis Pankratov, Allan Borodin
2010 Lecture Notes in Computer Science  
Algorithms based on local search are popular for solving many optimization problems including the maximum satisfiability problem (MAXSAT).  ...  The performance results observed for the unweighted MAX-3-SAT problem carry over to the weighted version of the problem, but now the better performance of MWS is more pronounced.  ...  Introduction The maximum satisfiability problem is of great interest in both theoretical [8] and applied computer science [18] . The maximum satisfiability problem is NP-hard.  ... 
doi:10.1007/978-3-642-14186-7_19 fatcat:rcse7yohjfennnpepnx2vbkofe

OSPF routing with optimal oblivious performance ratio under polyhedral demand uncertainty

Ayşegül Altın, Pietro Belotti, Mustafa Ç. Pınar
2009 Optimization and Engineering  
The optimal oblivious routing problem consists in finding a routing for each source-sink pair (s, t) ∈ Q that minimizes the maximum edge utilization, independent of the traffic matrix d.  ...  Notice that the number of SP trees in a network can be huge and hence we develop a branch-and-price algorithm that is strengthened by the inclusion of cutting planes as an exact solution tool for the tree  ... 
doi:10.1007/s11081-009-9098-y fatcat:rwg6rjgrrfchtosmxjrnhyosey
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