23 Search Results for "Paul, Wolfgang"

Document
DOI: 10.4230/LIPIcs.SoCG.2022.49
Dynamic Connectivity in Disk Graphs

Authors: Haim Kaplan, Alexander Kauer, Katharina Klost, Kristin Knorr, Wolfgang Mulzer, Liam Roditty, and Paul Seiferth

Published in: LIPIcs, Volume 224, 38th International Symposium on Computational Geometry (SoCG 2022)

Abstract
Let S ⊆ ℝ² be a set of n planar sites, such that each s ∈ S has an associated radius r_s > 0. Let 𝒟(S) be the disk intersection graph for S. It has vertex set S and an edge between two distinct sites s, t ∈ S if and only if the disks with centers s, t and radii r_s, r_t intersect. Our goal is to design data structures that maintain the connectivity structure of 𝒟(S) as sites are inserted and/or deleted. First, we consider unit disk graphs, i.e., r_s = 1, for all s ∈ S. We describe a data structure that has O(log² n) amortized update and O(log n/log log n) amortized query time. Second, we look at disk graphs with bounded radius ratio Ψ, i.e., for all s ∈ S, we have 1 ≤ r_s ≤ Ψ, for a Ψ ≥ 1 known in advance. In the fully dynamic case, we achieve amortized update time O(Ψ λ₆(log n) log⁷ n) and query time O(log n/log log n), where λ_s(n) is the maximum length of a Davenport-Schinzel sequence of order s on n symbols. In the incremental case, where only insertions are allowed, we get logarithmic dependency on Ψ, with O(α(n)) query time and O(logΨ λ₆(log n) log⁷ n) update time. For the decremental setting, where only deletions are allowed, we first develop an efficient disk revealing structure: given two sets R and B of disks, we can delete disks from R, and upon each deletion, we receive a list of all disks in B that no longer intersect the union of R. Using this, we get decremental data structures with amortized query time O(log n/log log n) that support m deletions in O((nlog⁵ n + m log⁷ n) λ₆(log n) + nlog Ψ log⁴n) overall time for bounded radius ratio Ψ and O((nlog⁶ n + m log⁸n) λ₆(log n)) for arbitrary radii.
Cite as

Haim Kaplan, Alexander Kauer, Katharina Klost, Kristin Knorr, Wolfgang Mulzer, Liam Roditty, and Paul Seiferth. Dynamic Connectivity in Disk Graphs. In 38th International Symposium on Computational Geometry (SoCG 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 224, pp. 49:1-49:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{kaplan_et_al:LIPIcs.SoCG.2022.49,
  author =	{Kaplan, Haim and Kauer, Alexander and Klost, Katharina and Knorr, Kristin and Mulzer, Wolfgang and Roditty, Liam and Seiferth, Paul},
  title =	{{Dynamic Connectivity in Disk Graphs}},
  booktitle =	{38th International Symposium on Computational Geometry (SoCG 2022)},
  pages =	{49:1--49:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-227-3},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{224},
  editor =	{Goaoc, Xavier and Kerber, Michael},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.SoCG.2022.49},
  URN =		{urn:nbn:de:0030-drops-160572},
  doi =		{10.4230/LIPIcs.SoCG.2022.49},
  annote =	{Keywords: Disk Graphs, Connectivity, Lower Envelopes}
}
Document
DOI: 10.4230/LIPIcs.STACS.2020.31
Maximum Matchings in Geometric Intersection Graphs

Authors: Édouard Bonnet, Sergio Cabello, and Wolfgang Mulzer

Published in: LIPIcs, Volume 154, 37th International Symposium on Theoretical Aspects of Computer Science (STACS 2020)

Abstract
Let G be an intersection graph of n geometric objects in the plane. We show that a maximum matching in G can be found in O(ρ^{3ω/2}n^{ω/2}) time with high probability, where ρ is the density of the geometric objects and ω>2 is a constant such that n × n matrices can be multiplied in O(n^ω) time. The same result holds for any subgraph of G, as long as a geometric representation is at hand. For this, we combine algebraic methods, namely computing the rank of a matrix via Gaussian elimination, with the fact that geometric intersection graphs have small separators. We also show that in many interesting cases, the maximum matching problem in a general geometric intersection graph can be reduced to the case of bounded density. In particular, a maximum matching in the intersection graph of any family of translates of a convex object in the plane can be found in O(n^{ω/2}) time with high probability, and a maximum matching in the intersection graph of a family of planar disks with radii in [1, Ψ] can be found in O(Ψ⁶log^11 n + Ψ^{12 ω} n^{ω/2}) time with high probability.
Cite as

Édouard Bonnet, Sergio Cabello, and Wolfgang Mulzer. Maximum Matchings in Geometric Intersection Graphs. In 37th International Symposium on Theoretical Aspects of Computer Science (STACS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 154, pp. 31:1-31:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{bonnet_et_al:LIPIcs.STACS.2020.31,
  author =	{Bonnet, \'{E}douard and Cabello, Sergio and Mulzer, Wolfgang},
  title =	{{Maximum Matchings in Geometric Intersection Graphs}},
  booktitle =	{37th International Symposium on Theoretical Aspects of Computer Science (STACS 2020)},
  pages =	{31:1--31:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-140-5},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{154},
  editor =	{Paul, Christophe and Bl\"{a}ser, Markus},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2020.31},
  URN =		{urn:nbn:de:0030-drops-118926},
  doi =		{10.4230/LIPIcs.STACS.2020.31},
  annote =	{Keywords: computational geometry, geometric intersection graph, maximum matching, disk graph, unit-disk graph}
}
Document
DOI: 10.4230/LIPIcs.ESA.2019.64
Triangles and Girth in Disk Graphs and Transmission Graphs

Authors: Haim Kaplan, Katharina Klost, Wolfgang Mulzer, Liam Roditty, Paul Seiferth, and Micha Sharir

Published in: LIPIcs, Volume 144, 27th Annual European Symposium on Algorithms (ESA 2019)

Abstract
Let S subset R^2 be a set of n sites, where each s in S has an associated radius r_s > 0. The disk graph D(S) is the undirected graph with vertex set S and an undirected edge between two sites s, t in S if and only if |st| <= r_s + r_t, i.e., if the disks with centers s and t and respective radii r_s and r_t intersect. Disk graphs are used to model sensor networks. Similarly, the transmission graph T(S) is the directed graph with vertex set S and a directed edge from a site s to a site t if and only if |st| <= r_s, i.e., if t lies in the disk with center s and radius r_s. We provide algorithms for detecting (directed) triangles and, more generally, computing the length of a shortest cycle (the girth) in D(S) and in T(S). These problems are notoriously hard in general, but better solutions exist for special graph classes such as planar graphs. We obtain similarly efficient results for disk graphs and for transmission graphs. More precisely, we show that a shortest (Euclidean) triangle in D(S) and in T(S) can be found in O(n log n) expected time, and that the (weighted) girth of D(S) can be found in O(n log n) expected time. For this, we develop new tools for batched range searching that may be of independent interest.
Cite as

Haim Kaplan, Katharina Klost, Wolfgang Mulzer, Liam Roditty, Paul Seiferth, and Micha Sharir. Triangles and Girth in Disk Graphs and Transmission Graphs. In 27th Annual European Symposium on Algorithms (ESA 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 144, pp. 64:1-64:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{kaplan_et_al:LIPIcs.ESA.2019.64,
  author =	{Kaplan, Haim and Klost, Katharina and Mulzer, Wolfgang and Roditty, Liam and Seiferth, Paul and Sharir, Micha},
  title =	{{Triangles and Girth in Disk Graphs and Transmission Graphs}},
  booktitle =	{27th Annual European Symposium on Algorithms (ESA 2019)},
  pages =	{64:1--64:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-124-5},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{144},
  editor =	{Bender, Michael A. and Svensson, Ola and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2019.64},
  URN =		{urn:nbn:de:0030-drops-111859},
  doi =		{10.4230/LIPIcs.ESA.2019.64},
  annote =	{Keywords: disk graph, transmission graph, triangle, girth}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2018.50
Stabbing Pairwise Intersecting Disks by Five Points

Authors: Sariel Har-Peled, Haim Kaplan, Wolfgang Mulzer, Liam Roditty, Paul Seiferth, Micha Sharir, and Max Willert

Published in: LIPIcs, Volume 123, 29th International Symposium on Algorithms and Computation (ISAAC 2018)

Abstract
Suppose we are given a set D of n pairwise intersecting disks in the plane. A planar point set P stabs D if and only if each disk in D contains at least one point from P. We present a deterministic algorithm that takes O(n) time to find five points that stab D. Furthermore, we give a simple example of 13 pairwise intersecting disks that cannot be stabbed by three points. This provides a simple - albeit slightly weaker - algorithmic version of a classical result by Danzer that such a set D can always be stabbed by four points.
Cite as

Sariel Har-Peled, Haim Kaplan, Wolfgang Mulzer, Liam Roditty, Paul Seiferth, Micha Sharir, and Max Willert. Stabbing Pairwise Intersecting Disks by Five Points. In 29th International Symposium on Algorithms and Computation (ISAAC 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 123, pp. 50:1-50:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{harpeled_et_al:LIPIcs.ISAAC.2018.50,
  author =	{Har-Peled, Sariel and Kaplan, Haim and Mulzer, Wolfgang and Roditty, Liam and Seiferth, Paul and Sharir, Micha and Willert, Max},
  title =	{{Stabbing Pairwise Intersecting Disks by Five Points}},
  booktitle =	{29th International Symposium on Algorithms and Computation (ISAAC 2018)},
  pages =	{50:1--50:12},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-094-1},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{123},
  editor =	{Hsu, Wen-Lian and Lee, Der-Tsai and Liao, Chung-Shou},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2018.50},
  URN =		{urn:nbn:de:0030-drops-99989},
  doi =		{10.4230/LIPIcs.ISAAC.2018.50},
  annote =	{Keywords: Disk graph, piercing set, LP-type problem}
}
Document
DOI: 10.4230/LIPIcs.ISAAC.2017.10
Routing in Polygonal Domains

Authors: Bahareh Banyassady, Man-Kwun Chiu, Matias Korman, Wolfgang Mulzer, André van Renssen, Marcel Roeloffzen, Paul Seiferth, Yannik Stein, Birgit Vogtenhuber, and Max Willert

Published in: LIPIcs, Volume 92, 28th International Symposium on Algorithms and Computation (ISAAC 2017)

Abstract
We consider the problem of routing a data packet through the visibility graph of a polygonal domain P with n vertices and h holes. We may preprocess P to obtain a label and a routing table for each vertex. Then, we must be able to route a data packet between any two vertices p and q of P , where each step must use only the label of the target node q and the routing table of the current node. For any fixed eps > 0, we pre ent a routing scheme that always achieves a routing path that exceeds the shortest path by a factor of at most 1 + eps. The labels have O(log n) bits, and the routing tables are of size O((eps^{-1} + h) log n). The preprocessing time is O(n^2 log n + hn^2 + eps^{-1}hn). It can be improved to O(n 2 + eps^{-1}n) for simple polygons.
Cite as

Bahareh Banyassady, Man-Kwun Chiu, Matias Korman, Wolfgang Mulzer, André van Renssen, Marcel Roeloffzen, Paul Seiferth, Yannik Stein, Birgit Vogtenhuber, and Max Willert. Routing in Polygonal Domains. In 28th International Symposium on Algorithms and Computation (ISAAC 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 92, pp. 10:1-10:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{banyassady_et_al:LIPIcs.ISAAC.2017.10,
  author =	{Banyassady, Bahareh and Chiu, Man-Kwun and Korman, Matias and Mulzer, Wolfgang and van Renssen, Andr\'{e} and Roeloffzen, Marcel and Seiferth, Paul and Stein, Yannik and Vogtenhuber, Birgit and Willert, Max},
  title =	{{Routing in Polygonal Domains}},
  booktitle =	{28th International Symposium on Algorithms and Computation (ISAAC 2017)},
  pages =	{10:1--10:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-054-5},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{92},
  editor =	{Okamoto, Yoshio and Tokuyama, Takeshi},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ISAAC.2017.10},
  URN =		{urn:nbn:de:0030-drops-82379},
  doi =		{10.4230/LIPIcs.ISAAC.2017.10},
  annote =	{Keywords: polygonal domains, routing scheme, small stretch,Yao graph}
}
Document
DOI: 10.4230/LIPIcs.STACS.2017.9
Improved Time-Space Trade-Offs for Computing Voronoi Diagrams

Authors: Bahareh Banyassady, Matias Korman, Wolfgang Mulzer, André van Renssen, Marcel Roeloffzen, Paul Seiferth, and Yannik Stein

Published in: LIPIcs, Volume 66, 34th Symposium on Theoretical Aspects of Computer Science (STACS 2017)

Abstract
Let P be a planar n-point set in general position. For k between 1 and n-1, the Voronoi diagram of order k is obtained by subdividing the plane into regions such that points in the same cell have the same set of nearest k neighbors in P. The (nearest point) Voronoi diagram (NVD) and the farthest point Voronoi diagram (FVD) are the particular cases of k=1 and k=n-1, respectively. It is known that the family of all higher-order Voronoi diagrams of order 1 to K for P can be computed in total time O(n K^2 + n log n) using O(K^2(n-K)) space. Also NVD and FVD can be computed in O(n log n) time using O(n) space. For s in {1, ..., n}, an s-workspace algorithm has random access to a read-only array with the sites of P in arbitrary order. Additionally, the algorithm may use O(s) words of Theta(log n) bits each for reading and writing intermediate data. The output can be written only once and cannot be accessed afterwards. We describe a deterministic s-workspace algorithm for computing an NVD and also an FVD for P that runs in O((n^2/s) log s) time. Moreover, we generalize our s-workspace algorithm for computing the family of all higher-order Voronoi diagrams of P up to order K in O(sqrt(s)) in total time O( (n^2 K^6 / s) log^(1+epsilon)(K) (log s / log K)^(O(1)) ) for any fixed epsilon > 0. Previously, for Voronoi diagrams, the only known s-workspace algorithm was to find an NVD for P in expected time O((n^2/s) log s + n log s log^*s). Unlike the previous algorithm, our new method is very simple and does not rely on advanced data structures or random sampling techniques.
Cite as

Bahareh Banyassady, Matias Korman, Wolfgang Mulzer, André van Renssen, Marcel Roeloffzen, Paul Seiferth, and Yannik Stein. Improved Time-Space Trade-Offs for Computing Voronoi Diagrams. In 34th Symposium on Theoretical Aspects of Computer Science (STACS 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 66, pp. 9:1-9:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{banyassady_et_al:LIPIcs.STACS.2017.9,
  author =	{Banyassady, Bahareh and Korman, Matias and Mulzer, Wolfgang and van Renssen, Andr\'{e} and Roeloffzen, Marcel and Seiferth, Paul and Stein, Yannik},
  title =	{{Improved Time-Space Trade-Offs for Computing Voronoi Diagrams}},
  booktitle =	{34th Symposium on Theoretical Aspects of Computer Science (STACS 2017)},
  pages =	{9:1--9:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-028-6},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{66},
  editor =	{Vollmer, Heribert and Vall\'{e}e, Brigitte},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2017.9},
  URN =		{urn:nbn:de:0030-drops-70249},
  doi =		{10.4230/LIPIcs.STACS.2017.9},
  annote =	{Keywords: memory-constrained model, Voronoi diagram, time-space trade-off}
}
Document
DOI: 10.4230/LIPIcs.SOCG.2015.156
Spanners and Reachability Oracles for Directed Transmission Graphs

Authors: Haim Kaplan, Wolfgang Mulzer, Liam Roditty, and Paul Seiferth

Published in: LIPIcs, Volume 34, 31st International Symposium on Computational Geometry (SoCG 2015)

Abstract
Let P be a set of n points in d dimensions, each with an associated radius r_p > 0. The transmission graph G for P has vertex set P and an edge from p to q if and only if q lies in the ball with radius r_p around p. Let t > 1. A t-spanner H for G is a sparse subgraph of G such that for any two vertices p, q connected by a path of length l in G, there is a p-q-path of length at most tl in H. We show how to compute a t-spanner for G if d=2. The running time is O(n (log n + log Psi)), where Psi is the ratio of the largest and smallest radius of two points in P. We extend this construction to be independent of Psi at the expense of a polylogarithmic overhead in the running time. As a first application, we prove a property of the t-spanner that allows us to find a BFS tree in G for any given start vertex s of P in the same time. After that, we deal with reachability oracles for G. These are data structures that answer reachability queries: given two vertices, is there a directed path between them? The quality of a reachability oracle is measured by the space S(n), the query time Q(n), and the preproccesing time. For d=1, we show how to compute an oracle with Q(n) = O(1) and S(n) = O(n) in time O(n log n). For d=2, the radius ratio Psi again turns out to be an important measure for the complexity of the problem. We present three different data structures whose quality depends on Psi: (i) if Psi < sqrt(3), we achieve Q(n) = O(1) with S(n) = O(n) and preproccesing time O(n log n); (ii) if Psi >= sqrt(3), we get Q(n) = O(Psi^3 sqrt(n)) and S(n) = O(Psi^5 n^(3/2)); and (iii) if Psi is polynomially bounded in n, we use probabilistic methods to obtain an oracle with Q(n) = O(n^(2/3)log n) and S(n) = O(n^(5/3) log n) that answers queries correctly with high probability. We employ our t-spanner to achieve a fast preproccesing time of O(Psi^5 n^(3/2)) and O(n^(5/3) log^2 n) in case (ii) and (iii), respectively.
Cite as

Haim Kaplan, Wolfgang Mulzer, Liam Roditty, and Paul Seiferth. Spanners and Reachability Oracles for Directed Transmission Graphs. In 31st International Symposium on Computational Geometry (SoCG 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 34, pp. 156-170, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)

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@InProceedings{kaplan_et_al:LIPIcs.SOCG.2015.156,
  author =	{Kaplan, Haim and Mulzer, Wolfgang and Roditty, Liam and Seiferth, Paul},
  title =	{{Spanners and Reachability Oracles for Directed Transmission Graphs}},
  booktitle =	{31st International Symposium on Computational Geometry (SoCG 2015)},
  pages =	{156--170},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-83-5},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{34},
  editor =	{Arge, Lars and Pach, J\'{a}nos},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.SOCG.2015.156},
  URN =		{urn:nbn:de:0030-drops-51062},
  doi =		{10.4230/LIPIcs.SOCG.2015.156},
  annote =	{Keywords: Transmission Graphs, Reachability Oracles, Spanner, Intersection Graph}
}
Document
DOI: 10.4230/DagSemProc.07462.5
Ambient Assisted Living Systems - The Conflicts between Technology, Acceptance, Ethics and Privacy

Authors: Wolfgang L. Zagler, Paul Panek, and Marjo Rauhala

Published in: Dagstuhl Seminar Proceedings, Volume 7462, Assisted Living Systems - Models, Architectures and Engineering Approaches (2008)

Abstract
Installing and using AAL Smart Home-systems in the homes of older people not only offers a tremendous potential for increasing safety and quality of life but may also evoke reluctance and anxiety. Will such a system become a "Big Brother" watching the steps and the behaviour of the inhabitants and betray them to their outside world? In several field-trials of an AAL Smart Home-system with inhabitants of senior residences we were able to learn about the issues concerning acceptance, ethics and privacy when senior citizens and their care persons are confronted with this kind of technology for the first time.
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Wolfgang L. Zagler, Paul Panek, and Marjo Rauhala. Ambient Assisted Living Systems - The Conflicts between Technology, Acceptance, Ethics and Privacy. In Assisted Living Systems - Models, Architectures and Engineering Approaches. Dagstuhl Seminar Proceedings, Volume 7462, pp. 1-4, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)

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@InProceedings{zagler_et_al:DagSemProc.07462.5,
  author =	{Zagler, Wolfgang L. and Panek, Paul and Rauhala, Marjo},
  title =	{{Ambient Assisted Living Systems - The Conflicts between Technology, Acceptance, Ethics and Privacy}},
  booktitle =	{Assisted Living Systems - Models, Architectures and Engineering Approaches},
  pages =	{1--4},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2008},
  volume =	{7462},
  editor =	{Arthur I. Karshmer and J\"{u}rgen Nehmer and Hartmut Raffler and Gerhard Tr\"{o}ster},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DagSemProc.07462.5},
  URN =		{urn:nbn:de:0030-drops-14549},
  doi =		{10.4230/DagSemProc.07462.5},
  annote =	{Keywords: AAL, Ambient Assisted Living, Smart Homes, field trials, acceptance, ethics, privacy protection, data protection}
}
Document
DOI: 10.4230/DagSemProc.06051.1
06051 Abstracts Collection – Kolmogorov Complexity and Applications

Authors: Marcus Hutter, Wolfgang Merkle, and Paul M.B. Vitanyi

Published in: Dagstuhl Seminar Proceedings, Volume 6051, Kolmogorov Complexity and Applications (2006)

Abstract
From 29.01.06 to 03.02.06, the Dagstuhl Seminar 06051 ``Kolmogorov Complexity and Applications'' 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.
Cite as

Marcus Hutter, Wolfgang Merkle, and Paul M.B. Vitanyi. 06051 Abstracts Collection – Kolmogorov Complexity and Applications. In Kolmogorov Complexity and Applications. Dagstuhl Seminar Proceedings, Volume 6051, pp. 1-17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2006)

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@InProceedings{hutter_et_al:DagSemProc.06051.1,
  author =	{Hutter, Marcus and Merkle, Wolfgang and Vitanyi, Paul M.B.},
  title =	{{06051 Abstracts Collection – Kolmogorov Complexity and Applications}},
  booktitle =	{Kolmogorov Complexity and Applications},
  pages =	{1--17},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2006},
  volume =	{6051},
  editor =	{Marcus Hutter and Wolfgang Merkle and Paul M.B. Vitanyi},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DagSemProc.06051.1},
  URN =		{urn:nbn:de:0030-drops-6632},
  doi =		{10.4230/DagSemProc.06051.1},
  annote =	{Keywords: Information theory, Kolmogorov Complexity, effective randomnes, algorithmic probability, recursion theory, computational complexity, machine learning knowledge discovery}
}
Document
DOI: 10.4230/DagSemProc.06051.2
Application of Kolmogorov complexity and universal codes to identity testing and nonparametric testing of serial independence for time series.

Authors: Boris Ryabko, Jaakko Astola, and Alex Gammerman

Published in: Dagstuhl Seminar Proceedings, Volume 6051, Kolmogorov Complexity and Applications (2006)

Abstract
We show that Kolmogorov complexity and such its estimators as universal codes (or data compression methods) can be applied for hypothesis testing in a framework of classical mathematical statistics. The methods for identity testing and nonparametric testing of serial independence for time series are described.
Cite as

Boris Ryabko, Jaakko Astola, and Alex Gammerman. Application of Kolmogorov complexity and universal codes to identity testing and nonparametric testing of serial independence for time series.. In Kolmogorov Complexity and Applications. Dagstuhl Seminar Proceedings, Volume 6051, pp. 1-13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2006)

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@InProceedings{ryabko_et_al:DagSemProc.06051.2,
  author =	{Ryabko, Boris and Astola, Jaakko and Gammerman, Alex},
  title =	{{Application of Kolmogorov complexity and universal codes to identity testing and nonparametric testing of serial independence for time series.}},
  booktitle =	{Kolmogorov Complexity and Applications},
  pages =	{1--13},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2006},
  volume =	{6051},
  editor =	{Marcus Hutter and Wolfgang Merkle and Paul M.B. Vitanyi},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DagSemProc.06051.2},
  URN =		{urn:nbn:de:0030-drops-6363},
  doi =		{10.4230/DagSemProc.06051.2},
  annote =	{Keywords: Algorithmic complexity, algorithmic information theory, Kolmogorov complexity, universal coding, hypothesis testing}
}
Document
DOI: 10.4230/DagSemProc.06051.3
Automatic Meaning Discovery Using Google

Authors: Rudi Cilibrasi and Paul M.B. Vitanyi

Published in: Dagstuhl Seminar Proceedings, Volume 6051, Kolmogorov Complexity and Applications (2006)

Abstract
We survey a new area of parameter-free similarity distance measures useful in data-mining, pattern recognition, learning and automatic semantics extraction. Given a family of distances on a set of objects, a distance is universal up to a certain precision for that family if it minorizes every distance in the family between every two objects in the set, up to the stated precision (we do not require the universal distance to be an element of the family). We consider similarity distances for two types of objects: literal objects that as such contain all of their meaning, like genomes or books, and names for objects. The latter may have literal embodyments like the first type, but may also be abstract like ``red'' or ``christianity.'' For the first type we consider a family of computable distance measures corresponding to parameters expressing similarity according to particular features between pairs of literal objects. For the second type we consider similarity distances generated by web users corresponding to particular semantic relations between the (names for) the designated objects. For both families we give universal similarity distance measures, incorporating all particular distance measures in the family. In the first case the universal distance is based on compression and in the second case it is based on Google page counts related to search terms. In both cases experiments on a massive scale give evidence of the viability of the approaches.
Cite as

Rudi Cilibrasi and Paul M.B. Vitanyi. Automatic Meaning Discovery Using Google. In Kolmogorov Complexity and Applications. Dagstuhl Seminar Proceedings, Volume 6051, pp. 1-23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2006)

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@InProceedings{cilibrasi_et_al:DagSemProc.06051.3,
  author =	{Cilibrasi, Rudi and Vitanyi, Paul M.B.},
  title =	{{Automatic Meaning Discovery Using Google}},
  booktitle =	{Kolmogorov Complexity and Applications},
  pages =	{1--23},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2006},
  volume =	{6051},
  editor =	{Marcus Hutter and Wolfgang Merkle and Paul M.B. Vitanyi},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DagSemProc.06051.3},
  URN =		{urn:nbn:de:0030-drops-6296},
  doi =		{10.4230/DagSemProc.06051.3},
  annote =	{Keywords: Normalized Compression Distance, Clustering, Clasification, Relative Semantics of Terms, Google, World-Wide-Web, Kolmogorov complexity}
}
Document
DOI: 10.4230/DagSemProc.06051.4
Binary Lambda Calculus and Combinatory Logic

Authors: John Tromp

Published in: Dagstuhl Seminar Proceedings, Volume 6051, Kolmogorov Complexity and Applications (2006)

Abstract
We introduce binary representations of both lambda calculus and combinatory logic terms, and demonstrate their simplicity by providing very compact parser-interpreters for these binary languages. We demonstrate their application to Algorithmic Information Theory with several concrete upper bounds on program-size complexity, including an elegant self-delimiting code for binary strings.
Cite as

John Tromp. Binary Lambda Calculus and Combinatory Logic. In Kolmogorov Complexity and Applications. Dagstuhl Seminar Proceedings, Volume 6051, pp. 1-20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2006)

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@InProceedings{tromp:DagSemProc.06051.4,
  author =	{Tromp, John},
  title =	{{Binary Lambda Calculus and Combinatory Logic}},
  booktitle =	{Kolmogorov Complexity and Applications},
  pages =	{1--20},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2006},
  volume =	{6051},
  editor =	{Marcus Hutter and Wolfgang Merkle and Paul M.B. Vitanyi},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DagSemProc.06051.4},
  URN =		{urn:nbn:de:0030-drops-6289},
  doi =		{10.4230/DagSemProc.06051.4},
  annote =	{Keywords: Concrete, program size complexity, ambda calculus, combinatory logic, encoding, self-delimiting, binary strings}
}
Document
DOI: 10.4230/DagSemProc.06051.5
Combinatorial proof of Muchnik's theorem

Authors: Alexander Shen

Published in: Dagstuhl Seminar Proceedings, Volume 6051, Kolmogorov Complexity and Applications (2006)

Abstract
Original proof of Muchnik's theorem on conditional descriptions can be modified and split into two parts: 1) we construct a graph that allows large online matchings (main part) 2) we use this graph to prove the theorem The question about online matching could be interesting in itself.
Cite as

Alexander Shen. Combinatorial proof of Muchnik's theorem. In Kolmogorov Complexity and Applications. Dagstuhl Seminar Proceedings, Volume 6051, pp. 1-5, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2006)

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@InProceedings{shen:DagSemProc.06051.5,
  author =	{Shen, Alexander},
  title =	{{Combinatorial proof of Muchnik's theorem}},
  booktitle =	{Kolmogorov Complexity and Applications},
  pages =	{1--5},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2006},
  volume =	{6051},
  editor =	{Marcus Hutter and Wolfgang Merkle and Paul M.B. Vitanyi},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DagSemProc.06051.5},
  URN =		{urn:nbn:de:0030-drops-6258},
  doi =		{10.4230/DagSemProc.06051.5},
  annote =	{Keywords: Matching conditional descriptions Kolmogorov complexity}
}
Document
DOI: 10.4230/DagSemProc.06051.6
Complexity Monotone in Conditions and Future Prediction Errors

Authors: Alexey Chernov, Marcus Hutter, and Jürgen Schmidhuber

Published in: Dagstuhl Seminar Proceedings, Volume 6051, Kolmogorov Complexity and Applications (2006)

Abstract
We bound the future loss when predicting any (computably) stochastic sequence online. Solomonoff finitely bounded the total deviation of his universal predictor $M$ from the true distribution $mu$ by the algorithmic complexity of $mu$. Here we assume we are at a time $t>1$ and already observed $x=x_1...x_t$. We bound the future prediction performance on $x_{t+1}x_{t+2}...$ by a new variant of algorithmic complexity of $mu$ given $x$, plus the complexity of the randomness deficiency of $x$. The new complexity is monotone in its condition in the sense that this complexity can only decrease if the condition is prolonged. We also briefly discuss potential generalizations to Bayesian model classes and to classification problems.
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Alexey Chernov, Marcus Hutter, and Jürgen Schmidhuber. Complexity Monotone in Conditions and Future Prediction Errors. In Kolmogorov Complexity and Applications. Dagstuhl Seminar Proceedings, Volume 6051, pp. 1-20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2006)

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@InProceedings{chernov_et_al:DagSemProc.06051.6,
  author =	{Chernov, Alexey and Hutter, Marcus and Schmidhuber, J\"{u}rgen},
  title =	{{Complexity Monotone in Conditions and Future Prediction Errors}},
  booktitle =	{Kolmogorov Complexity and Applications},
  pages =	{1--20},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2006},
  volume =	{6051},
  editor =	{Marcus Hutter and Wolfgang Merkle and Paul M.B. Vitanyi},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DagSemProc.06051.6},
  URN =		{urn:nbn:de:0030-drops-6327},
  doi =		{10.4230/DagSemProc.06051.6},
  annote =	{Keywords: Kolmogorov complexity, posterior bounds, online sequential prediction, Solomonoff prior, monotone conditional complexity, total error, future loss, ra}
}
Document
DOI: 10.4230/DagSemProc.06051.7
Error in Enumerable Sequence Prediction

Authors: Nick Hay

Published in: Dagstuhl Seminar Proceedings, Volume 6051, Kolmogorov Complexity and Applications (2006)

Abstract
We outline a method for quantifying the error of a sequence prediction. With sequence predictions represented by semimeasures $ u(x)$ we define their error to be $-log_2 u(x)$. We note that enumerable semimeasures are those which model the sequence as the output of a computable system given unknown input. Using this we define the simulation complexity of a computable system $C$ relative to another $U$ giving an emph{exact} bound on their difference in error. This error in turn gives an exact upper bound on the number of predictions $ u$ gets incorrect.
Cite as

Nick Hay. Error in Enumerable Sequence Prediction. In Kolmogorov Complexity and Applications. Dagstuhl Seminar Proceedings, Volume 6051, pp. 1-5, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2006)

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@InProceedings{hay:DagSemProc.06051.7,
  author =	{Hay, Nick},
  title =	{{Error in Enumerable Sequence Prediction}},
  booktitle =	{Kolmogorov Complexity and Applications},
  pages =	{1--5},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2006},
  volume =	{6051},
  editor =	{Marcus Hutter and Wolfgang Merkle and Paul M.B. Vitanyi},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/DagSemProc.06051.7},
  URN =		{urn:nbn:de:0030-drops-6331},
  doi =		{10.4230/DagSemProc.06051.7},
  annote =	{Keywords: Sequence prediction, Solomonoff induction, enumerable semimeasures}
}
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