Filters








10 Hits in 5.7 sec

Regularized Box-Simplex Games and Dynamic Decremental Bipartite Matching [article]

Arun Jambulapati, Yujia Jin, Aaron Sidford, Kevin Tian
2022 arXiv   pre-print
Through our reduction framework, our regularized box-simplex game solver implies a new algorithm for dynamic decremental bipartite matching in total time Õ(m ·ϵ^-3), from an initial graph with m edges  ...  Box-simplex games are a family of bilinear minimax objectives which encapsulate graph-structured problems such as maximum flow [She17], optimal transport [JST19], and bipartite matching [AJJ+22].  ...  of Sinkhorn's algorithm (in the original submission, we claimed no such rate had been stated previously), and Monika Henzinger and Thatchaphol Saranurak for helpful information regarding prior work.  ... 
arXiv:2204.12721v3 fatcat:qe65bhaeordnjhrsl77v5fywoi

Regularized Box-Simplex Games and Dynamic Decremental Bipartite Matching

Arun Jambulapati, Yujia Jin, Aaron Sidford, Kevin Tian, Mikołaj Bojańczyk, Emanuela Merelli, David P. Woodruff
2022
Through our reduction framework, our regularized box-simplex game solver implies a new algorithm for dynamic decremental bipartite matching in total time Õ(m ⋅ ε^{-3}), from an initial graph with m edges  ...  Box-simplex games are a family of bilinear minimax objectives which encapsulate graph-structured problems such as maximum flow [Sherman, 2017], optimal transport [Arun Jambulapati et al., 2019], and bipartite  ...  of Sinkhorn's algorithm (in the original submission, we claimed no such rate had been stated previously), and Monika Henzinger and Thatchaphol Saranurak for helpful information regarding prior work.  ... 
doi:10.4230/lipics.icalp.2022.77 fatcat:766ilb2n2nhsvfgrnbuqhtl3ry

Simplicial and cellular trees [chapter]

Art M. Duval, Caroline J. Klivans, Jeremy L. Martin
2016 IMA Volumes in Mathematics and its Applications  
Cellular trees are the starting point for further high-dimensional extensions of concepts from algebraic graph theory including the critical group, cut and flow spaces, and discrete dynamical systems such  ...  As observed first by Bolker, Kalai and Adin, and more recently by numerous authors, the fundamental topological properties of a tree -namely acyclicity and connectedness -can be generalized to arbitrary  ...  Acknowledgements We thank our colleagues Amy Wagler and Jennifer Wagner for valuable suggestions regarding exposition and clarity.  ... 
doi:10.1007/978-3-319-24298-9_28 fatcat:oh5q37h55jcmvady7lukhisolq

Simplicial and Cellular Trees [article]

Art M. Duval, Caroline J. Klivans, Jeremy L. Martin
2015 arXiv   pre-print
Cellular trees are the starting point for further high-dimensional extensions of concepts from algebraic graph theory including the critical group, cut and flow spaces, and discrete dynamical systems such  ...  As observed first by Bolker, Kalai and Adin, and more recently by numerous authors, the fundamental topological properties of a tree --- namely acyclicity and connectedness --- can be generalized to arbitrary  ...  Acknowledgements We thank our colleagues Amy Wagler and Jennifer Wagner for valuable suggestions regarding exposition and clarity.  ... 
arXiv:1506.06819v1 fatcat:hjorlrfwljemnawlytoz57ppp4

Linear Programming: Foundations and Extensions

R J Vanderbei
1998 Journal of the Operational Research Society  
Exercises 11.1 Players A and B each hide a nickel or a dime. If the hidden coins match, player A gets both; if they don't match, then B gets both. Find the optimal strategies.  ...  Now let's look at the dynamics of the simplex method. Each iteration focuses on exactly one of the negative values.  ...  For example, we saw in Chapter 13 that for network flow problems with integer data, the simplex method automatically produces integer solutions. But that was just luck.  ... 
doi:10.1038/sj.jors.2600987 fatcat:d4xmw4dy7rflnextmoz2bytkqa

Nearly-Linear Time Positive LP Solver with Faster Convergence Rate

Zeyuan Allen-Zhu, Lorenzo Orecchia
2015 Proceedings of the Forty-Seventh Annual ACM on Symposium on Theory of Computing - STOC '15  
Positive linear programs (LP), also known as packing and covering linear programs, are an important class of problems that bridges computer science, operation research, and optimization.  ...  Our work also introduces a sequence of new techniques, including the stochastic and the nonsymmetric execution of gradient truncation operations, which may be of independent interest.  ...  Therefore, our algorithm yields an O(mε −1 ) approximate algorithm and an O(m √ n) exact algorithm 4 that arise purely from optimization for bipartite matching, without the use of any dynamic trees.  ... 
doi:10.1145/2746539.2746573 dblp:conf/stoc/ZhuO15 fatcat:vveqgjdginc5lom6hu4ngjjqye

Training and Understanding Deep Neural Networks for Robotics, Design, and Visual Perception

Jason Yosinski
2018
He attended Caltech and studied Mechanical Engineering and Control and Dynamical systems.  ...  This more common approach is known as bipartite matching. 6 A matching that maximizes the sum of the chosen correlation values may be found efficiently via the Hopcroft-Karp algorithm (Hopcroft and Karp  ...  This type of assignment is known as a bipartite semi-matching in graph theory (Lawler, 1976) , and we adopt the same nomenclature here.  ... 
doi:10.7298/x4513wgb fatcat:22phuhdq45eihpwevmtosb5lem

Dagstuhl Reports, Volume 7, Issue 1, January 2017, Complete Issue [article]

2017
We use this viewpoint to explore and compare the power of paradigms such as branching and dynamic programming, and to shed light on the true complexity of various problems.  ...  Behavioural types describe dynamic aspects of a program, in contrast to data types, which describe the fixed structure of data.  ...  to cope with the problem (e.g. polynomial identity testing, or deciding whether there exists a perfect matching with exactly b red edges in an edge-colored bipartite graph).  ... 
doi:10.4230/dagrep.7.1 fatcat:eb5yydhkhnb4xpbvalztqllpt4

Privacy Preserving in Online Social Network Data Sharing and Publication

Tianchong Gao
2019
To conclude, this dissertation studies the online data privacy problem from both defenders' and attackers' point of view and introduces privacy and utility enhancement mechanisms in different novel angles  ...  It draws on the design of the privacy criterion, the graph abstraction model, the utility method, and the anonymization method to further address the balance between utility and privacy.  ...  After getting the similarity score for top-k users, we assign a bipartite matching process to obtain the maximum sum of scores.  ... 
doi:10.25394/pgs.9901862.v1 fatcat:wmh7djcsqvb2rdkwc7s2zva65y

Preferences in Case-Based Reasoning

Amira Abdel-Aziz, Hüllermeier, Eyke (Prof. Dr.)
2016
and methods for knowledge representation and reasoning with preferences.  ...  Despite its great practical success, work on the theoretical foundations of CBR is still under way, and a coherent and universally applicable methodological framework is yet missing.  ...  It follows then to say that if a correct classification occurs then the weights of the matching features are incremented, while those of mismatching features are decremented of the new query, by a fixed  ... 
doi:10.17192/z2016.0800 fatcat:ziiiitbfq5drvnmrbt4kjr24um