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RANDOM

**Published in:** LIPIcs, Volume 245, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2022)

The Chinese restaurant process is a stochastic process closely related to the Dirichlet process that groups sequentially arriving objects into a variable number of classes, such that within each class objects are cyclically ordered. A popular description involves a restaurant, where customers arrive one by one and either sit down next to a randomly chosen customer at one of the existing tables or open a new table. The full state of the process after n steps is given by a permutation of the n objects and cannot be represented in sublinear space. In particular, if we only need specific information about a few objects or classes it would be preferable to obtain the answers without simulating the process completely.
A recent line of research [Oded Goldreich et al., 2010; Moni Naor and Asaf Nussboim, 2007; Amartya Shankha Biswas et al., 2020; Guy Even et al., 2021] attempts to provide access to huge random objects without fully instantiating them. Such local access implementations provide answers to a sequence of queries about the random object, following the same distribution as if the object was fully generated. In this paper, we provide a local access implementation for a generalization of the Chinese restaurant process described above. Our implementation can be used to answer any sequence of adaptive queries about class affiliation of objects, number and sizes of classes at any time, position of elements within a class, or founding time of a class. The running time per query is polylogarithmic in the total size of the object, with high probability. Our approach relies on some ideas from the recent local access implementation for preferential attachment trees by Even et al. [Guy Even et al., 2021]. Such trees are related to the Chinese restaurant process in the sense that both involve a "rich-get-richer" phenomenon. A novel ingredient in our implementation is to embed the process in continuous time, in which the evolution of the different classes becomes stochastically independent [Joyce and Tavaré, 1987]. This independence is used to keep the probabilistic structure manageable even if many queries have already been answered. As similar embeddings are available for a wide range of urn processes [Krishna B. Athreya and Samuel Karlin, 1968], we believe that our approach may be applicable more generally. Moreover, local access implementations for birth and death processes that we encounter along the way may be of independent interest.

Peter Mörters, Christian Sohler, and Stefan Walzer. A Sublinear Local Access Implementation for the Chinese Restaurant Process. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 245, pp. 28:1-28:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{morters_et_al:LIPIcs.APPROX/RANDOM.2022.28, author = {M\"{o}rters, Peter and Sohler, Christian and Walzer, Stefan}, title = {{A Sublinear Local Access Implementation for the Chinese Restaurant Process}}, booktitle = {Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2022)}, pages = {28:1--28:18}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-249-5}, ISSN = {1868-8969}, year = {2022}, volume = {245}, editor = {Chakrabarti, Amit and Swamy, Chaitanya}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2022.28}, URN = {urn:nbn:de:0030-drops-171500}, doi = {10.4230/LIPIcs.APPROX/RANDOM.2022.28}, annote = {Keywords: Chinese restaurant process, Dirichlet process, sublinear time algorithm, random recursive tree, random permutation, random partition, Ewens distribution, simulation, local access implementation, continuous time embedding} }

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RANDOM

**Published in:** LIPIcs, Volume 176, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2020)

We consider the fundamental question of understanding the relative power of two important computational models: property testing and data streaming. We present a novel framework closely linking these areas in the setting of general graphs in the context of constant-query complexity testing and constant-space streaming. Our main result is a generic transformation of a one-sided error property tester in the random-neighbor model with constant query complexity into a one-sided error property tester in the streaming model with constant space complexity. Previously such a generic transformation was only known for bounded-degree graphs.

Artur Czumaj, Hendrik Fichtenberger, Pan Peng, and Christian Sohler. Testable Properties in General Graphs and Random Order Streaming. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 176, pp. 16:1-16:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{czumaj_et_al:LIPIcs.APPROX/RANDOM.2020.16, author = {Czumaj, Artur and Fichtenberger, Hendrik and Peng, Pan and Sohler, Christian}, title = {{Testable Properties in General Graphs and Random Order Streaming}}, booktitle = {Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2020)}, pages = {16:1--16:20}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-164-1}, ISSN = {1868-8969}, year = {2020}, volume = {176}, editor = {Byrka, Jaros{\l}aw and Meka, Raghu}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2020.16}, URN = {urn:nbn:de:0030-drops-126190}, doi = {10.4230/LIPIcs.APPROX/RANDOM.2020.16}, annote = {Keywords: Graph property testing, sublinear algorithms, graph streaming algorithms} }

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Complete Volume

**Published in:** LIPIcs, Volume 87, 25th Annual European Symposium on Algorithms (ESA 2017)

LIPIcs, Volume 87, ESA'17, Complete Volume

25th Annual European Symposium on Algorithms (ESA 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 87, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@Proceedings{pruhs_et_al:LIPIcs.ESA.2017, title = {{LIPIcs, Volume 87, ESA'17, Complete Volume}}, booktitle = {25th Annual European Symposium on Algorithms (ESA 2017)}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-049-1}, ISSN = {1868-8969}, year = {2017}, volume = {87}, editor = {Pruhs, Kirk and Sohler, Christian}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2017}, URN = {urn:nbn:de:0030-drops-79096}, doi = {10.4230/LIPIcs.ESA.2017}, annote = {Keywords: Data Structures, Nonnumerical Algorithms and Problems, Optimization, Discrete Mathematics, Mathematical Software, AlgorithmsProblem Solving, Control Methods, and Search, Computational Geometry and Object Modeling} }

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Front Matter

**Published in:** LIPIcs, Volume 87, 25th Annual European Symposium on Algorithms (ESA 2017)

Front Matter, Table of Contents, Preface, Programm Commitees, External Reviewers

25th Annual European Symposium on Algorithms (ESA 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 87, pp. 0:i-0:xx, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{pruhs_et_al:LIPIcs.ESA.2017.0, author = {Pruhs, Kirk and Sohler, Christian}, title = {{Front Matter, Table of Contents, Preface, Programm Commitees, External Reviewers}}, booktitle = {25th Annual European Symposium on Algorithms (ESA 2017)}, pages = {0:i--0:xx}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-049-1}, ISSN = {1868-8969}, year = {2017}, volume = {87}, editor = {Pruhs, Kirk and Sohler, Christian}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2017.0}, URN = {urn:nbn:de:0030-drops-78147}, doi = {10.4230/LIPIcs.ESA.2017.0}, annote = {Keywords: Front Matter, Table of Contents, Preface, Programm Commitees, External Reviewers} }

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**Published in:** LIPIcs, Volume 80, 44th International Colloquium on Automata, Languages, and Programming (ICALP 2017)

We study which property testing and sublinear time algorithms can be transformed into graph streaming algorithms for random order streams. Our main result is that for bounded degree graphs, any property that is constant-query testable in the adjacency list model can be tested with constant space in a single-pass in random order streams. Our result is obtained by estimating the distribution of local neighborhoods of the vertices on a random order graph stream using constant space.
We then show that our approach can also be applied to constant time approximation algorithms for bounded degree graphs in the adjacency list model: As an example, we obtain a constant-space single-pass random order streaming algorithms for approximating the size of a maximum matching with additive error epsilon n (n is the number of nodes).
Our result establishes for the first time that a large class of sublinear algorithms can be simulated in random order streams, while Omega(n) space is needed for many graph streaming problems for adversarial orders.

Morteza Monemizadeh, S. Muthukrishnan, Pan Peng, and Christian Sohler. Testable Bounded Degree Graph Properties Are Random Order Streamable. In 44th International Colloquium on Automata, Languages, and Programming (ICALP 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 80, pp. 131:1-131:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{monemizadeh_et_al:LIPIcs.ICALP.2017.131, author = {Monemizadeh, Morteza and Muthukrishnan, S. and Peng, Pan and Sohler, Christian}, title = {{Testable Bounded Degree Graph Properties Are Random Order Streamable}}, booktitle = {44th International Colloquium on Automata, Languages, and Programming (ICALP 2017)}, pages = {131:1--131:14}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-041-5}, ISSN = {1868-8969}, year = {2017}, volume = {80}, editor = {Chatzigiannakis, Ioannis and Indyk, Piotr and Kuhn, Fabian and Muscholl, Anca}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2017.131}, URN = {urn:nbn:de:0030-drops-74782}, doi = {10.4230/LIPIcs.ICALP.2017.131}, annote = {Keywords: Graph streaming algorithms, graph property testing, constant-time approximation algorithms} }

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**Published in:** LIPIcs, Volume 80, 44th International Colloquium on Automata, Languages, and Programming (ICALP 2017)

We initiate the study of network monitoring algorithms in a class of hybrid networks in which the nodes are connected by an external network and an internal network (as a short form for externally and internally controlled network). While the external network lies outside of the control of the nodes (or in our case, the monitoring protocol running in them) and might be exposed to continuous changes, the internal network is fully under the control of the nodes. As an example, consider a group of users with mobile devices having access to the cell phone infrastructure. While the network formed by the WiFi connections of the devices is an external network (as its structure is not necessarily under the control of the monitoring protocol), the connections between the devices via the cell phone infrastructure represent an internal network (as it can be controlled by the monitoring protocol). Our goal is to continuously monitor properties of the external network with the help of the internal network. We present scalable distributed algorithms that efficiently monitor the number of edges, the average node degree, the clustering coefficient, the bipartiteness, and the weight of a minimum spanning tree. Their performance bounds demonstrate that monitoring the external network state with the help of an internal network can be done much more efficiently than just using the external network, as is usually done in the literature.

Robert Gmyr, Kristian Hinnenthal, Christian Scheideler, and Christian Sohler. Distributed Monitoring of Network Properties: The Power of Hybrid Networks. In 44th International Colloquium on Automata, Languages, and Programming (ICALP 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 80, pp. 137:1-137:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{gmyr_et_al:LIPIcs.ICALP.2017.137, author = {Gmyr, Robert and Hinnenthal, Kristian and Scheideler, Christian and Sohler, Christian}, title = {{Distributed Monitoring of Network Properties: The Power of Hybrid Networks}}, booktitle = {44th International Colloquium on Automata, Languages, and Programming (ICALP 2017)}, pages = {137:1--137:15}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-041-5}, ISSN = {1868-8969}, year = {2017}, volume = {80}, editor = {Chatzigiannakis, Ioannis and Indyk, Piotr and Kuhn, Fabian and Muscholl, Anca}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2017.137}, URN = {urn:nbn:de:0030-drops-73750}, doi = {10.4230/LIPIcs.ICALP.2017.137}, annote = {Keywords: Network Monitoring, Hybrid Networks, Overlay Networks} }

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**Published in:** LIPIcs, Volume 55, 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)

In this paper we develop streaming algorithms for the diameter problem and the k-center clustering problem in the sliding window model. In this model we are interested in maintaining a solution for the N most recent points of the stream. In the diameter problem we would like to maintain two points whose distance approximates the diameter of the point set in the window. Our algorithm computes a (3 + epsilon)-approximation and uses O(1/epsilon*ln(alpha)) memory cells, where alpha is the ratio of the largest and smallest distance and is assumed to be known in advance. We also prove that under reasonable assumptions obtaining a (3 - epsilon)-approximation requires Omega(N1/3) space.
For the k-center problem, where the goal is to find k centers that minimize the maximum distance of a point to its nearest center, we obtain a (6 + epsilon)-approximation using O(k/epsilon*ln(alpha)) memory cells and a (4 + epsilon)-approximation for the special case k = 2. We also prove that any algorithm for the 2-center problem that achieves an approximation ratio of less than 4 requires Omega(N^{1/3}) space.

Vincent Cohen-Addad, Chris Schwiegelshohn, and Christian Sohler. Diameter and k-Center in Sliding Windows. In 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 55, pp. 19:1-19:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{cohenaddad_et_al:LIPIcs.ICALP.2016.19, author = {Cohen-Addad, Vincent and Schwiegelshohn, Chris and Sohler, Christian}, title = {{Diameter and k-Center in Sliding Windows}}, booktitle = {43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)}, pages = {19:1--19:12}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-013-2}, ISSN = {1868-8969}, year = {2016}, volume = {55}, editor = {Chatzigiannakis, Ioannis and Mitzenmacher, Michael and Rabani, Yuval and Sangiorgi, Davide}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2016.19}, URN = {urn:nbn:de:0030-drops-63401}, doi = {10.4230/LIPIcs.ICALP.2016.19}, annote = {Keywords: Streaming, k-Center, Diameter, Sliding Windows} }

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**Published in:** LIPIcs, Volume 40, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2015)

Let G=(V,E) be an undirected graph with maximum degree d. The k-disc of a vertex v is defined as the rooted subgraph that is induced by all vertices whose distance to v is at most k. The k-disc frequency vector of G, freq(G), is a vector indexed by all isomorphism types of k-discs. For each such isomorphism type Gamma, the k-disc frequency vector counts the fraction of vertices that have k-disc isomorphic to Gamma. Thus, the frequency vector freq(G) of G captures the local structure of G. A natural question is whether one can construct a much smaller graph H such that H has a similar local structure. N. Alon proved that for any epsilon>0 there always exists a graph H whose size is independent of |V| and whose frequency vector satisfies ||freq(G) - freq(G)||_1 <= epsilon. However, his proof is only existential and neither gives an explicit bound on the size of H nor an efficient algorithm. He gave the open problem to find such explicit bounds. In this paper, we solve this problem for the special case of high girth graphs. We show how to efficiently compute a graph H with the above properties when G has girth at least 2k+2 and we give explicit bounds on the size of H.

Hendrik Fichtenberger, Pan Peng, and Christian Sohler. On Constant-Size Graphs That Preserve the Local Structure of High-Girth Graphs. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 40, pp. 786-799, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)

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@InProceedings{fichtenberger_et_al:LIPIcs.APPROX-RANDOM.2015.786, author = {Fichtenberger, Hendrik and Peng, Pan and Sohler, Christian}, title = {{On Constant-Size Graphs That Preserve the Local Structure of High-Girth Graphs}}, booktitle = {Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2015)}, pages = {786--799}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-939897-89-7}, ISSN = {1868-8969}, year = {2015}, volume = {40}, editor = {Garg, Naveen and Jansen, Klaus and Rao, Anup and Rolim, Jos\'{e} D. P.}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX-RANDOM.2015.786}, URN = {urn:nbn:de:0030-drops-53363}, doi = {10.4230/LIPIcs.APPROX-RANDOM.2015.786}, annote = {Keywords: local graph structure, k-disc frequency vector, graph property testing} }

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**Published in:** LIPIcs, Volume 9, 28th International Symposium on Theoretical Aspects of Computer Science (STACS 2011)

The diameter k-clustering problem is the problem of partitioning a finite subset of R^d into k subsets called clusters such that the maximum diameter of the clusters is minimized. One early clustering algorithm that computes a hierarchy of approximate solutions to this problem for all values of k is the agglomerative clustering algorithm with the complete linkage strategy. For decades this algorithm has been widely used by practitioners. However, it is not well studied theoretically. In this paper we analyze the agglomerative complete linkage clustering algorithm. Assuming that the dimension dis a constant, we show that for any k the solution computed by this algorithm is an O(log k)-approximation to the diameter k-clustering problem. Moreover, our analysis does not only hold for the Euclidean distance but for any metric that is based on a norm.

Marcel R. Ackermann, Johannes Bloemer, Daniel Kuntze, and Christian Sohler. Analysis of Agglomerative Clustering. In 28th International Symposium on Theoretical Aspects of Computer Science (STACS 2011). Leibniz International Proceedings in Informatics (LIPIcs), Volume 9, pp. 308-319, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2011)

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@InProceedings{ackermann_et_al:LIPIcs.STACS.2011.308, author = {Ackermann, Marcel R. and Bloemer, Johannes and Kuntze, Daniel and Sohler, Christian}, title = {{Analysis of Agglomerative Clustering}}, booktitle = {28th International Symposium on Theoretical Aspects of Computer Science (STACS 2011)}, pages = {308--319}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-939897-25-5}, ISSN = {1868-8969}, year = {2011}, volume = {9}, editor = {Schwentick, Thomas and D\"{u}rr, Christoph}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2011.308}, URN = {urn:nbn:de:0030-drops-29942}, doi = {10.4230/LIPIcs.STACS.2011.308}, annote = {Keywords: agglomerative clustering, hierarchical clustering, complete linkage, approximation guarantees} }

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**Published in:** Dagstuhl Seminar Proceedings, Volume 8341, Sublinear Algorithms (2008)

From August 17 to August 22, 2008, the Dagstuhl Seminar 08341 ``Sublinear Algorithms'' was held in the International Conference and Research Center (IBFI),
Schloss Dagstuhl.
During the seminar, several participants presented their current
research, and ongoing work and open problems were discussed. Abstracts of
the presentations given during the seminar as well as abstracts of
seminar results and ideas are put together in this paper. The first section
describes the seminar topics and goals in general.
Links to extended abstracts or full papers are provided, if available.

Artur Czumaj, S. Muthu Muthukrishnan, Ronitt Rubinfeld, and Christian Sohler. 08341 Abstracts Collection – Sublinear Algorithms. In Sublinear Algorithms. Dagstuhl Seminar Proceedings, Volume 8341, pp. 1-19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)

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@InProceedings{czumaj_et_al:DagSemProc.08341.1, author = {Czumaj, Artur and Muthukrishnan, S. Muthu and Rubinfeld, Ronitt and Sohler, Christian}, title = {{08341 Abstracts Collection – Sublinear Algorithms}}, booktitle = {Sublinear Algorithms}, pages = {1--19}, series = {Dagstuhl Seminar Proceedings (DagSemProc)}, ISSN = {1862-4405}, year = {2008}, volume = {8341}, editor = {Artur Czumaj and S. Muthu Muthukrishnan and Ronitt Rubinfeld and Christian Sohler}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.08341.1}, URN = {urn:nbn:de:0030-drops-16981}, doi = {10.4230/DagSemProc.08341.1}, annote = {Keywords: Sublinear algorithms, property testing, data streaming, graph algorithms, approximation algorithms} }

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**Published in:** Dagstuhl Seminar Proceedings, Volume 8341, Sublinear Algorithms (2008)

This report summarizes the content and structure of the Dagstuhl seminar `Sublinear Algorithms', which was held from 17.8.2008 to 22.8.2008 in Schloss Dagstuhl, Germany.

Artur Czumaj, S. Muthu Muthukrishnan, Ronitt Rubinfeld, and Christian Sohler. 08341 Executive Summary – Sublinear Algorithms. In Sublinear Algorithms. Dagstuhl Seminar Proceedings, Volume 8341, pp. 1-2, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)

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@InProceedings{czumaj_et_al:DagSemProc.08341.2, author = {Czumaj, Artur and Muthukrishnan, S. Muthu and Rubinfeld, Ronitt and Sohler, Christian}, title = {{08341 Executive Summary – Sublinear Algorithms}}, booktitle = {Sublinear Algorithms}, pages = {1--2}, series = {Dagstuhl Seminar Proceedings (DagSemProc)}, ISSN = {1862-4405}, year = {2008}, volume = {8341}, editor = {Artur Czumaj and S. Muthu Muthukrishnan and Ronitt Rubinfeld and Christian Sohler}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.08341.2}, URN = {urn:nbn:de:0030-drops-16964}, doi = {10.4230/DagSemProc.08341.2}, annote = {Keywords: Sublinear algorithms, property testing, data streaming, graph algorithms, approximation algorithms} }

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**Published in:** Dagstuhl Seminar Proceedings, Volume 5291, Sublinear Algorithms (2006)

From 17.07.05 to 22.07.05, the Dagstuhl Seminar
05291 ``Sublinear Algorithms'' was held
in the International Conference and Research Center (IBFI),
Schloss Dagstuhl.
During the seminar, several participants presented their current
research, and ongoing work and open problems were discussed. Abstracts of
the presentations given during the seminar as well as abstracts of
seminar results and ideas are put together in this paper. The first section
describes the seminar topics and goals in general.
Links to extended abstracts or full papers are provided, if available.

Artur Czumaj, S. Muthu Muthukrishnan, Ronitt Rubinfeld, and Christian Sohler. 05291 Abstracts Collection – Sublinear Algorithms. In Sublinear Algorithms. Dagstuhl Seminar Proceedings, Volume 5291, pp. 1-18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2006)

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@InProceedings{czumaj_et_al:DagSemProc.05291.1, author = {Czumaj, Artur and Muthukrishnan, S. Muthu and Rubinfeld, Ronitt and Sohler, Christian}, title = {{05291 Abstracts Collection – Sublinear Algorithms}}, booktitle = {Sublinear Algorithms}, pages = {1--18}, series = {Dagstuhl Seminar Proceedings (DagSemProc)}, ISSN = {1862-4405}, year = {2006}, volume = {5291}, editor = {Artur Czumaj and S. Muthu Muthukrishnan and Ronitt Rubinfeld and Christian Sohler}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.05291.1}, URN = {urn:nbn:de:0030-drops-6814}, doi = {10.4230/DagSemProc.05291.1}, annote = {Keywords: Property testing, sublinear time approximation algorithms, data streaming algorithms} }

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