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Massively Parallel Computation and Sublinear-Time Algorithms for Embedded Planar Graphs [article]

Jacob Holm, Jakub Tětek
2022 arXiv   pre-print
Specifically, we focus on sublinear-time computation and massively parallel computation (MPC).  ...  Our main technical contribution is a sublinear-time algorithm for computing a relaxed version of an r-division. We then show how this can be used to estimate Lipschitz additive graph parameters.  ...  The authors are also grateful to Mikkel Thorup and Tomáš Gavenčiak for helpful discussions.  ... 
arXiv:2204.09035v1 fatcat:txs5s74vjrcxjell5nghepnfu4

Graph Drawing in the Cloud: Privately Visualizing Relational Data Using Small Working Storage [chapter]

Michael T. Goodrich, Olga Ohrimenko, Roberto Tamassia
2013 Lecture Notes in Computer Science  
We study graph drawing in a cloud-computing context where data is stored externally and processed using a small local working storage.  ...  We show that a number of classic graph drawing algorithms can be efficiently implemented in such a framework where the client can maintain privacy while constructing a drawing of her graph.  ...  drawings of trees, dominance drawings of planar acyclic digraphs [8] , and Δ-drawings of series-parallel graphs [3] .  ... 
doi:10.1007/978-3-642-36763-2_5 fatcat:p73ob6exzrbr3mzttzatowggie

Data-Oblivious Graph Drawing Model and Algorithms [article]

Michael T. Goodrich and Olga Ohrimenko and Roberto Tamassia
2012 arXiv   pre-print
We study graph drawing in a cloud-computing context where data is stored externally and processed using a small local working storage.  ...  We show that a number of classic graph drawing algorithms can be efficiently implemented in such a framework where the client can maintain privacy while constructing a drawing of her graph.  ...  We would like to thank Giuseppe Di Battista for useful discussions.  ... 
arXiv:1209.0756v1 fatcat:hqabf3xb2rczdp6od62wtwufna

Scalable Algorithms for Data and Network Analysis

Shang-Hua Teng
2016 Foundations and Trends® in Theoretical Computer Science  
Acknowledgements The writing of this article is supported in part by a Simons Investigator Award from the Simons Foundation and the NSF grant CCF-1111270. Shang-Hua Teng Los Angeles  ...  After my talk, "The Laplacian Paradigm: Emerging Algorithms for Massive Graphs," [329] at 7th Annual Conference on Theory and Applications of Models of Computation, Jaroslav Nešetřil (my former officemate  ...  This scalable Laplacian solver has initiated and enabled many new scalable algorithms for spectral approximation [319] , geometric and statistical approximation [98] , graph embedding [335] , machine  ... 
doi:10.1561/0400000051 fatcat:jkfytl34ifh4ldfdsiugrrgv7m

INHERENTLY PARALLEL GEOMETRIC COMPUTATIONS

SELIM G. AKL
2006 Parallel Processing Letters  
A new computational paradigm is described which o ers the possibility of superlinear and sometimes unbounded speedup, when parallel computation is used.  ...  We show that in transforming one triangulation of a polygon into another, a parallel algorithm achieves a superlinear speedup.  ...  Both approaches were used to obtain parallel algorithms for real-time computation. They include algorithms for data accumulation 22,27 and data correction 25 .  ... 
doi:10.1142/s0129626406002447 fatcat:eqwshbqwczgwrocwd4zzqave5i

An Optimal Time-Power Tradeoff for Sorting on a Mesh-Connected Computer with On-Chip Optics

Patrick Poon, Quentin F. Stout
2014 International Journal of Networking and Computing  
Energy consumption has become a critical factor constraining the design of massively parallel computers, necessitating the development of new models and energy-efficient algorithms.  ...  For sorting, standard mesh algorithms minimize time and total data movement, and hence constraining the mesh to use only half its processors at any instant must double the time.  ...  Acknowledgements Research partially supported by NSF grant CDI-1027192, DOE grant DE-FC52-08NA28616 and King Abdulaziz University.  ... 
doi:10.15803/ijnc.4.1_70 fatcat:qcddni7fynhlrmscaturoxrapq

A (Centralized) Local Guide

Reut Levi, Moti Medina
2017 Bulletin of the European Association for Theoretical Computer Science  
In this survey we focus on CentLocal algorithms for computational graph problems.  ...  Massive graphs, which contain millions and even billions of nodes, modeling the Internet, the World Wide Web, semantic networks and social networks, are being analyzed and processed constantly.  ...  For the family of graphs with an excluded fixed minor (which in particular includes planar graphs), [39] provide an algorithm whose probe and time complexities are polynomial in 1/ and in d.  ... 
dblp:journals/eatcs/LeviM17 fatcat:623xklmovnczhhulwjhyvbjemq

Narrowing the LOCAL-CONGEST Gaps in Sparse Networks via Expander Decompositions

Yi-Jun Chang, Hsin-Hao Su
2022 Proceedings of the 2022 ACM Symposium on Principles of Distributed Computing  
network decompositions [Ghaffari, Kuhn, and Maus, STOC 2018].  ...  Many combinatorial optimization problems, including maximum weighted matching and maximum independent set, can be approximated within (1±𝜖) factors in poly(log 𝑛, 1/𝜖) rounds in the LOCAL model via  ...  For learning the graph topology of 𝐺 [𝑉 𝑖 ] and routing, we apply the routing algorithms of Lemmas 2.4 and 2.5 to 𝐺 [𝑉 𝑖 ], in parallel for all 1 ≤ 𝑖 ≤ 𝑘.  ... 
doi:10.1145/3519270.3538423 fatcat:jv7pwb6wmrhjfirawnl2v4qdra

Recent Advances in Graph Partitioning [chapter]

Aydın Buluç, Henning Meyerhenke, Ilya Safro, Peter Sanders, Christian Schulz
2016 Lecture Notes in Computer Science  
We survey recent trends in practical algorithms for balanced graph partitioning together with applications and future research directions.  ...  Acknowledgements We express our gratitude to Bruce Hendrickson, Dominique LaSalle, and George Karypis for many valuable comments on a preliminary draft of the manuscript.  ...  Since all of this is very time consuming and since the partitions are often used for parallel computing, parallel aspects of GP are very important.  ... 
doi:10.1007/978-3-319-49487-6_4 fatcat:4zamxcmgvfbaxndjgxv6jog6km

Recent Advances in Graph Partitioning [article]

Aydin Buluc, Henning Meyerhenke, Ilya Safro, Peter Sanders, Christian Schulz
2015 arXiv   pre-print
We survey recent trends in practical algorithms for balanced graph partitioning together with applications and future research directions.  ...  Acknowledgements We express our gratitude to Bruce Hendrickson, Dominique LaSalle, and George Karypis for many valuable comments on a preliminary draft of the manuscript.  ...  Since all of this is very time consuming and since the partitions are often used for parallel computing, parallel aspects of GP are very important.  ... 
arXiv:1311.3144v3 fatcat:zmvhlkh7ynbzvm353fv22f2gnq

Repetitive Hidden Surface Removal for Polyhedra

Marco Pellegrini
1996 Journal of Algorithms  
We also improve worst-case time/storage bounds for the repetitive hidden surface removal problem when the polyhedral scene is composed of unrestricted polyhedra.  ...  Let n be the number total of edges, vertices and faces of the polyhedral objects and let k be the number of vertices and edges of the image.  ...  For perspective views a method in 36] computes the aspect graph in time O(n 5 + n 2 jGj) and O(n 2 jGj) working storage.  ... 
doi:10.1006/jagm.1996.0038 fatcat:gxu7rvkqdjdqhihmw4tvie4fjm

Limits to parallel computation: P-completeness theory

1996 ChoiceReviews  
PREFACE ix the best known parallel algorithms for the problem.  ...  That is, algorithm designers have failed to find NC algorithms, feasible highly parallel solutions that take time polynomial in the logarithm of the problem size while using only a polynomial number of  ...  Computing a depth-first vertex numbering for planar graphs is in NC (He and Yesha [152], Smith [334] ).  ... 
doi:10.5860/choice.33-3959 fatcat:qjoueeu225gr7jvwdf6gkoxfbq

Narrowing the LOCALx2013CONGEST Gaps in Sparse Networks via Expander Decompositions [article]

Yi-Jun Chang, Hsin-Hao Su
2022 arXiv   pre-print
, significantly generalizing the previous distributed property testing algorithm for planarity in [Levi, Medina, and Ron, PODC 2018 Distributed Computing 2021].  ...  This class of graphs covers many sparse network classes that have been studied in the literature, including planar graphs, bounded-genus graphs, and bounded-treewidth graphs.  ...  For learning the graph topology of G[V i ] and routing, we apply the routing algorithms of Lemmas 2.2 and 2.3 to G[V i ], in parallel for all 1 ≤ i ≤ k.  ... 
arXiv:2205.08093v1 fatcat:h2wxmhc3lnhtdcghxhogjqbgre

Beyond Worst-Case Analysis [article]

Tim Roughgarden
2018 arXiv   pre-print
This article covers a number of modeling methods for going beyond worst-case analysis and articulating which inputs are the most relevant.  ...  This approach has countless success stories, but there are also important computational problems --- like linear programming, clustering, online caching, and neural network training --- where the worst-case  ...  Acknowledgments I thank Sanjeev Arora, Ankur Moitra, Aravindan Vijayaraghavan, and four anonymous reviewers for several helpful suggestions.  ... 
arXiv:1806.09817v1 fatcat:s4idpks5ozghrflwqfkcjigeve

Reuse of algorithms

Karsten Weihe
1997 SIGPLAN notices  
This paper is about reusable, efficient implementations of complex algorithms and their integration into software packages.  ...  It seems that this problem is not yetwell understood, and that it is not at all clear how object-oriented and other approaches may contribute to a solution.  ...  Special thanks to Dietmar Kiihl and Marco Nissen for their strong engagement in the project and to Dorothea Wagner for her overall support and encouragement.  ... 
doi:10.1145/263700.263704 fatcat:uhlivdcefrd4tbdmpfda5jts24
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