9 Search Results for "Kosowski, Adrian"

Document
DOI: 10.4230/LIPIcs.ESA.2024.84
Insights into (k, ρ)-Shortcutting Algorithms

Authors: Alexander Leonhardt, Ulrich Meyer, and Manuel Penschuck

Published in: LIPIcs, Volume 308, 32nd Annual European Symposium on Algorithms (ESA 2024)

Abstract
A graph is called a (k, ρ)-graph iff every node can reach ρ of its nearest neighbors in at most k hops. This property has proven useful in the analysis and design of parallel shortest-path algorithms [Blelloch et al., 2016; Dong et al., 2021]. Any graph can be transformed into a (k, ρ)-graph by adding shortcuts. Formally, the (k,ρ)-Minimum-Shortcut-Problem (kρ-MSP) asks to find an appropriate shortcut set of minimal cardinality. We show that kρ-MSP is NP-complete in the practical regime of k ≥ 3 and ρ = Θ(n^ε) for ε > 0. With a related construction, we bound the approximation factor of known kρ-MSP heuristics [Blelloch et al., 2016] from below and propose algorithmic countermeasures improving the approximation quality. Further, we describe an integer linear problem (ILP) that optimally solves kρ-MSP. Finally, we compare the practical performance and quality of all algorithms empirically.
Cite as

Alexander Leonhardt, Ulrich Meyer, and Manuel Penschuck. Insights into (k, ρ)-Shortcutting Algorithms. In 32nd Annual European Symposium on Algorithms (ESA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 308, pp. 84:1-84:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

Copy BibTex To Clipboard

@InProceedings{leonhardt_et_al:LIPIcs.ESA.2024.84,
  author =	{Leonhardt, Alexander and Meyer, Ulrich and Penschuck, Manuel},
  title =	{{Insights into (k, \rho)-Shortcutting Algorithms}},
  booktitle =	{32nd Annual European Symposium on Algorithms (ESA 2024)},
  pages =	{84:1--84:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-338-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{308},
  editor =	{Chan, Timothy and Fischer, Johannes and Iacono, John and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2024.84},
  URN =		{urn:nbn:de:0030-drops-211554},
  doi =		{10.4230/LIPIcs.ESA.2024.84},
  annote =	{Keywords: Complexity, Approximation, Optimal algorithms, Parallel shortest path}
}
Document
DOI: 10.4230/LIPIcs.AofA.2024.22
The Recurrence/Transience of Random Walks on a Bounded Grid in an Increasing Dimension

Authors: Shuma Kumamoto, Shuji Kijima, and Tomoyuki Shirai

Published in: LIPIcs, Volume 302, 35th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2024)

Abstract
It is celebrated that a simple random walk on ℤ and ℤ² returns to the initial vertex v infinitely many times during infinitely many transitions, which is said recurrent, while it returns to v only finite times on ℤ^d for d ≥ 3, which is said transient. It is also known that a simple random walk on a growing region on ℤ^d can be recurrent depending on growing speed for any fixed d. This paper shows that a simple random walk on {0,1,…,N}ⁿ with an increasing n and a fixed N can be recurrent depending on the increasing speed of n. Precisely, we are concerned with a specific model of a random walk on a growing graph (RWoGG) and show a phase transition between the recurrence and transience of the random walk regarding the growth speed of the graph. For the proof, we develop a pausing coupling argument introducing the notion of weakly less homesick as graph growing (weakly LHaGG).
Cite as

Shuma Kumamoto, Shuji Kijima, and Tomoyuki Shirai. The Recurrence/Transience of Random Walks on a Bounded Grid in an Increasing Dimension. In 35th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 302, pp. 22:1-22:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

Copy BibTex To Clipboard

@InProceedings{kumamoto_et_al:LIPIcs.AofA.2024.22,
  author =	{Kumamoto, Shuma and Kijima, Shuji and Shirai, Tomoyuki},
  title =	{{The Recurrence/Transience of Random Walks on a Bounded Grid in an Increasing Dimension}},
  booktitle =	{35th International Conference on Probabilistic, Combinatorial and Asymptotic Methods for the Analysis of Algorithms (AofA 2024)},
  pages =	{22:1--22:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-329-4},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{302},
  editor =	{Mailler, C\'{e}cile and Wild, Sebastian},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.AofA.2024.22},
  URN =		{urn:nbn:de:0030-drops-204577},
  doi =		{10.4230/LIPIcs.AofA.2024.22},
  annote =	{Keywords: Random walk, dynamic graph, recurrence, transience, coupling}
}
Document
DOI: 10.4230/LIPIcs.SEA.2024.6
Faster Treewidth-Based Approximations for Wiener Index

Authors: Giovanna Kobus Conrado, Amir Kafshdar Goharshady, Pavel Hudec, Pingjiang Li, and Harshit Jitendra Motwani

Published in: LIPIcs, Volume 301, 22nd International Symposium on Experimental Algorithms (SEA 2024)

Abstract
The Wiener index of a graph G is the sum of distances between all pairs of its vertices. It is a widely-used graph property in chemistry, initially introduced to examine the link between boiling points and structural properties of alkanes, which later found notable applications in drug design. Thus, computing or approximating the Wiener index of molecular graphs, i.e. graphs in which every vertex models an atom of a molecule and every edge models a bond, is of significant interest to the computational chemistry community. In this work, we build upon the observation that molecular graphs are sparse and tree-like and focus on developing efficient algorithms parameterized by treewidth to approximate the Wiener index. We present a new randomized approximation algorithm using a combination of tree decompositions and centroid decompositions. Our algorithm approximates the Wiener index within any desired multiplicative factor (1 ± ε) in time O(n ⋅ log n ⋅ k³ + √n ⋅ k/ε²), where n is the number of vertices of the graph and k is the treewidth. This time bound is almost-linear in n. Finally, we provide experimental results over standard benchmark molecules from PubChem and the Protein Data Bank, showcasing the applicability and scalability of our approach on real-world chemical graphs and comparing it with previous methods.
Cite as

Giovanna Kobus Conrado, Amir Kafshdar Goharshady, Pavel Hudec, Pingjiang Li, and Harshit Jitendra Motwani. Faster Treewidth-Based Approximations for Wiener Index. In 22nd International Symposium on Experimental Algorithms (SEA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 301, pp. 6:1-6:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

Copy BibTex To Clipboard

@InProceedings{conrado_et_al:LIPIcs.SEA.2024.6,
  author =	{Conrado, Giovanna Kobus and Goharshady, Amir Kafshdar and Hudec, Pavel and Li, Pingjiang and Motwani, Harshit Jitendra},
  title =	{{Faster Treewidth-Based Approximations for Wiener Index}},
  booktitle =	{22nd International Symposium on Experimental Algorithms (SEA 2024)},
  pages =	{6:1--6:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-325-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{301},
  editor =	{Liberti, Leo},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2024.6},
  URN =		{urn:nbn:de:0030-drops-203718},
  doi =		{10.4230/LIPIcs.SEA.2024.6},
  annote =	{Keywords: Computational Chemistry, Treewidth, Wiener Index}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2024.55
Exploiting Automorphisms of Temporal Graphs for Fast Exploration and Rendezvous

Authors: Konstantinos Dogeas, Thomas Erlebach, Frank Kammer, Johannes Meintrup, and William K. Moses Jr.

Published in: LIPIcs, Volume 297, 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)

Abstract
Temporal graphs are dynamic graphs where the edge set can change in each time step, while the vertex set stays the same. Exploration of temporal graphs whose snapshot in each time step is a connected graph, called connected temporal graphs, has been widely studied. In this paper, we extend the concept of graph automorphisms from static graphs to temporal graphs and show for the first time that symmetries enable faster exploration: We prove that a connected temporal graph with n vertices and orbit number r (i.e., r is the number of automorphism orbits) can be explored in O(r n^{1+ε}) time steps, for any fixed ε > 0. For r = O(n^c) for constant c < 1, this is a significant improvement over the known tight worst-case bound of Θ(n²) time steps for arbitrary connected temporal graphs. We also give two lower bounds for temporal exploration, showing that Ω(n log n) time steps are required for some inputs with r = O(1) and that Ω(rn) time steps are required for some inputs for any r with 1 ≤ r ≤ n. Moreover, we show that the techniques we develop for fast exploration can be used to derive the following result for rendezvous: Two agents with different programs and without communication ability are placed by an adversary at arbitrary vertices and given full information about the connected temporal graph, except that they do not have consistent vertex labels. Then the two agents can meet at a common vertex after O(n^{1+ε}) time steps, for any constant ε > 0. For some connected temporal graphs with the orbit number being a constant, we also present a complementary lower bound of Ω(nlog n) time steps.
Cite as

Konstantinos Dogeas, Thomas Erlebach, Frank Kammer, Johannes Meintrup, and William K. Moses Jr.. Exploiting Automorphisms of Temporal Graphs for Fast Exploration and Rendezvous. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 55:1-55:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

Copy BibTex To Clipboard

@InProceedings{dogeas_et_al:LIPIcs.ICALP.2024.55,
  author =	{Dogeas, Konstantinos and Erlebach, Thomas and Kammer, Frank and Meintrup, Johannes and Moses Jr., William K.},
  title =	{{Exploiting Automorphisms of Temporal Graphs for Fast Exploration and Rendezvous}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{55:1--55:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-322-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{297},
  editor =	{Bringmann, Karl and Grohe, Martin and Puppis, Gabriele and Svensson, Ola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2024.55},
  URN =		{urn:nbn:de:0030-drops-201989},
  doi =		{10.4230/LIPIcs.ICALP.2024.55},
  annote =	{Keywords: dynamic graphs, parameterized algorithms, algorithmic graph theory, graph automorphism, orbit number}
}
Document
DOI: 10.4230/LIPIcs.OPODIS.2020.19
Approximate Majority with Catalytic Inputs

Authors: Talley Amir, James Aspnes, and John Lazarsfeld

Published in: LIPIcs, Volume 184, 24th International Conference on Principles of Distributed Systems (OPODIS 2020)

Abstract
Population protocols [Dana Angluin et al., 2006] are a class of algorithms for modeling distributed computation in networks of finite-state agents communicating through pairwise interactions. Their suitability for analyzing numerous chemical processes has motivated the adaptation of the original population protocol framework to better model these chemical systems. In this paper, we further the study of two such adaptations in the context of solving approximate majority: persistent-state agents (or catalysts) and spontaneous state changes (or leaks). Based on models considered in recent protocols for populations with persistent-state agents [Bartlomiej Dudek and Adrian Kosowski, 2018; Alistarh et al., 2017; Dan Alistarh et al., 2020], we assume a population with n catalytic input agents and m worker agents, and the goal of the worker agents is to compute some predicate over the states of the catalytic inputs. We call this model the Catalytic Input (CI) model. For m = Θ(n), we show that computing the parity of the input population with high probability requires at least Ω(n²) total interactions, demonstrating a strong separation between the CI model and the standard population protocol model. On the other hand, we show that the simple third-state dynamics [Angluin et al., 2008; Perron et al., 2009] for approximate majority in the standard model can be naturally adapted to the CI model: we present such a constant-state protocol for the CI model that solves approximate majority in O(n log n) total steps with high probability when the input margin is Ω(√{n log n}). We then show the robustness of third-state dynamics protocols to the transient leaks events introduced by [Alistarh et al., 2017; Dan Alistarh et al., 2020]. In both the original and CI models, these protocols successfully compute approximate majority with high probability in the presence of leaks occurring at each step with probability β ≤ O(√{n log n}/n). The resilience of these dynamics to leaks exhibits similarities to previous work involving Byzantine agents, and we define and prove a notion of equivalence between the two.
Cite as

Talley Amir, James Aspnes, and John Lazarsfeld. Approximate Majority with Catalytic Inputs. In 24th International Conference on Principles of Distributed Systems (OPODIS 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 184, pp. 19:1-19:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

Copy BibTex To Clipboard

@InProceedings{amir_et_al:LIPIcs.OPODIS.2020.19,
  author =	{Amir, Talley and Aspnes, James and Lazarsfeld, John},
  title =	{{Approximate Majority with Catalytic Inputs}},
  booktitle =	{24th International Conference on Principles of Distributed Systems (OPODIS 2020)},
  pages =	{19:1--19:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-176-4},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{184},
  editor =	{Bramas, Quentin and Oshman, Rotem and Romano, Paolo},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2020.19},
  URN =		{urn:nbn:de:0030-drops-135040},
  doi =		{10.4230/LIPIcs.OPODIS.2020.19},
  annote =	{Keywords: population protocols, approximate majority, catalysts, leaks, lower bound}
}
Document
Track C: Foundations of Networks and Multi-Agent Systems: Models, Algorithms and Information Management
DOI: 10.4230/LIPIcs.ICALP.2019.143
Exploiting Hopsets: Improved Distance Oracles for Graphs of Constant Highway Dimension and Beyond

Authors: Siddharth Gupta, Adrian Kosowski, and Laurent Viennot

Published in: LIPIcs, Volume 132, 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)

Abstract
For fixed h >= 2, we consider the task of adding to a graph G a set of weighted shortcut edges on the same vertex set, such that the length of a shortest h-hop path between any pair of vertices in the augmented graph is exactly the same as the original distance between these vertices in G. A set of shortcut edges with this property is called an exact h-hopset and may be applied in processing distance queries on graph G. In particular, a 2-hopset directly corresponds to a distributed distance oracle known as a hub labeling. In this work, we explore centralized distance oracles based on 3-hopsets and display their advantages in several practical scenarios. In particular, for graphs of constant highway dimension, and more generally for graphs of constant skeleton dimension, we show that 3-hopsets require exponentially fewer shortcuts per node than any previously described distance oracle, and also offer a speedup in query time when compared to simple oracles based on a direct application of 2-hopsets. Finally, we consider the problem of computing minimum-size h-hopset (for any h >= 2) for a given graph G, showing a polylogarithmic-factor approximation for the case of unique shortest path graphs. When h=3, for a given bound on the space used by the distance oracle, we provide a construction of hopset achieving polylog approximation both for space and query time compared to the optimal 3-hopset oracle given the space bound.
Cite as

Siddharth Gupta, Adrian Kosowski, and Laurent Viennot. Exploiting Hopsets: Improved Distance Oracles for Graphs of Constant Highway Dimension and Beyond. In 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 132, pp. 143:1-143:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

Copy BibTex To Clipboard

@InProceedings{gupta_et_al:LIPIcs.ICALP.2019.143,
  author =	{Gupta, Siddharth and Kosowski, Adrian and Viennot, Laurent},
  title =	{{Exploiting Hopsets: Improved Distance Oracles for Graphs of Constant Highway Dimension and Beyond}},
  booktitle =	{46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)},
  pages =	{143:1--143:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-109-2},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{132},
  editor =	{Baier, Christel and Chatzigiannakis, Ioannis and Flocchini, Paola and Leonardi, Stefano},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2019.143},
  URN =		{urn:nbn:de:0030-drops-107199},
  doi =		{10.4230/LIPIcs.ICALP.2019.143},
  annote =	{Keywords: Hopsets, Distance Oracles, Graph Algorithms, Data Structures}
}
Document
DOI: 10.4230/LIPIcs.ICALP.2017.84
Approximation Strategies for Generalized Binary Search in Weighted Trees

Authors: Dariusz Dereniowski, Adrian Kosowski, Przemyslaw Uznanski, and Mengchuan Zou

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

Abstract
We consider the following generalization of the binary search problem. A search strategy is required to locate an unknown target node t in a given tree T. Upon querying a node v of the tree, the strategy receives as a reply an indication of the connected component of T\{v} containing the target t. The cost of querying each node is given by a known non-negative weight function, and the considered objective is to minimize the total query cost for a worst-case choice of the target. Designing an optimal strategy for a weighted tree search instance is known to be strongly NP-hard, in contrast to the unweighted variant of the problem which can be solved optimally in linear time. Here, we show that weighted tree search admits a quasi-polynomial time approximation scheme (QPTAS): for any 0 < epsilon < 1, there exists a (1+epsilon)-approximation strategy with a computation time of n^O(log n / epsilon^2). Thus, the problem is not APX-hard, unless NP is contained in DTIME(n^O(log n)). By applying a generic reduction, we obtain as a corollary that the studied problem admits a polynomial-time O(sqrt(log n))-approximation. This improves previous tilde-O(log n)-approximation approaches, where the tilde-O-notation disregards O(poly log log n)-factors.
Cite as

Dariusz Dereniowski, Adrian Kosowski, Przemyslaw Uznanski, and Mengchuan Zou. Approximation Strategies for Generalized Binary Search in Weighted Trees. In 44th International Colloquium on Automata, Languages, and Programming (ICALP 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 80, pp. 84:1-84:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

Copy BibTex To Clipboard

@InProceedings{dereniowski_et_al:LIPIcs.ICALP.2017.84,
  author =	{Dereniowski, Dariusz and Kosowski, Adrian and Uznanski, Przemyslaw and Zou, Mengchuan},
  title =	{{Approximation Strategies for Generalized Binary Search in Weighted Trees}},
  booktitle =	{44th International Colloquium on Automata, Languages, and Programming (ICALP 2017)},
  pages =	{84:1--84:14},
  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.2017.84},
  URN =		{urn:nbn:de:0030-drops-74507},
  doi =		{10.4230/LIPIcs.ICALP.2017.84},
  annote =	{Keywords: Approximation Algorithm, Adaptive Algorithm, Graph Search, Binary Search, Vertex Ranking, Trees}
}
Document
DOI: 10.4230/LIPIcs.STACS.2017.44
Multiple Random Walks on Paths and Grids

Authors: Andrej Ivaskovic, Adrian Kosowski, Dominik Pajak, and Thomas Sauerwald

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

Abstract
We derive several new results on multiple random walks on "low dimensional" graphs. First, inspired by an example of a weighted random walk on a path of three vertices given by Efremenko and Reingold, we prove the following dichotomy: as the path length n tends to infinity, we have a super-linear speed-up w.r.t. the cover time if and only if the number of walks k is equal to 2. An important ingredient of our proofs is the use of a continuous-time analogue of multiple random walks, which might be of independent interest. Finally, we also present the first tight bounds on the speed-up of the cover time for any d-dimensional grid with d >= 2 being an arbitrary constant, and reveal a sharp transition between linear and logarithmic speed-up.
Cite as

Andrej Ivaskovic, Adrian Kosowski, Dominik Pajak, and Thomas Sauerwald. Multiple Random Walks on Paths and Grids. In 34th Symposium on Theoretical Aspects of Computer Science (STACS 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 66, pp. 44:1-44:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

Copy BibTex To Clipboard

@InProceedings{ivaskovic_et_al:LIPIcs.STACS.2017.44,
  author =	{Ivaskovic, Andrej and Kosowski, Adrian and Pajak, Dominik and Sauerwald, Thomas},
  title =	{{Multiple Random Walks on Paths and Grids}},
  booktitle =	{34th Symposium on Theoretical Aspects of Computer Science (STACS 2017)},
  pages =	{44:1--44:14},
  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.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2017.44},
  URN =		{urn:nbn:de:0030-drops-69897},
  doi =		{10.4230/LIPIcs.STACS.2017.44},
  annote =	{Keywords: random walks, randomized algorithms, parallel computing}
}
Document
DOI: 10.4230/LIPIcs.STACS.2014.263
Bounds on the Cover Time of Parallel Rotor Walks

Authors: Dariusz Dereniowski, Adrian Kosowski, Dominik Pajak, and Przemyslaw Uznanski

Published in: LIPIcs, Volume 25, 31st International Symposium on Theoretical Aspects of Computer Science (STACS 2014)

Abstract
The rotor-router mechanism was introduced as a deterministic alternative to the random walk in undirected graphs. In this model, a set of k identical walkers is deployed in parallel, starting from a chosen subset of nodes, and moving around the graph in synchronous steps. During the process, each node maintains a cyclic ordering of its outgoing arcs, and successively propagates walkers which visit it along its outgoing arcs in round-robin fashion, according to the fixed ordering. We consider the cover time of such a system, i.e., the number of steps after which each node has been visited by at least one walk, regardless of the starting locations of the walks. In the case of k=1, [Yanovski et al., 2003] and [Bampas et al., 2009] showed that a single walk achieves a cover time of exactly Theta(mD) for any n-node graph with m edges and diameter D, and that the walker eventually stabilizes to a traversal of an Eulerian circuit on the set of all directed edges of the graph. For k>1 parallel walks, no similar structural behaviour can be observed. In this work we provide tight bounds on the cover time of k parallel rotor walks in a graph. We show that this cover time is at most (mD/log(k)) and at least Theta(mD/k) for any graph, which corresponds to a speedup of between Theta(log(k)) and Theta(k) with respect to the cover time of a single walk. Both of these extremal values of speedup are achieved for some graph classes. Our results hold for up to a polynomially large number of walks, k=O(poly(n)).
Cite as

Dariusz Dereniowski, Adrian Kosowski, Dominik Pajak, and Przemyslaw Uznanski. Bounds on the Cover Time of Parallel Rotor Walks. In 31st International Symposium on Theoretical Aspects of Computer Science (STACS 2014). Leibniz International Proceedings in Informatics (LIPIcs), Volume 25, pp. 263-275, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2014)

Copy BibTex To Clipboard

@InProceedings{dereniowski_et_al:LIPIcs.STACS.2014.263,
  author =	{Dereniowski, Dariusz and Kosowski, Adrian and Pajak, Dominik and Uznanski, Przemyslaw},
  title =	{{Bounds on the Cover Time of Parallel Rotor Walks}},
  booktitle =	{31st International Symposium on Theoretical Aspects of Computer Science (STACS 2014)},
  pages =	{263--275},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-65-1},
  ISSN =	{1868-8969},
  year =	{2014},
  volume =	{25},
  editor =	{Mayr, Ernst W. and Portier, Natacha},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2014.263},
  URN =		{urn:nbn:de:0030-drops-44637},
  doi =		{10.4230/LIPIcs.STACS.2014.263},
  annote =	{Keywords: Distributed graph exploration, Rotor-Router, Collaborative robots, Parallel random walks, Derandomization}
}
  • Refine by Author
  • 4 Kosowski, Adrian
  • 2 Dereniowski, Dariusz
  • 2 Pajak, Dominik
  • 2 Uznanski, Przemyslaw
  • 1 Amir, Talley
  • Show More...

  • Refine by Classification
  • 2 Theory of computation → Graph algorithms analysis
  • 1 Computing methodologies → Distributed algorithms
  • 1 Mathematics of computing → Graph algorithms
  • 1 Theory of computation → Data structures design and analysis
  • 1 Theory of computation → Dynamic graph algorithms
  • Show More...

  • Refine by Keyword
  • 1 Adaptive Algorithm
  • 1 Approximation
  • 1 Approximation Algorithm
  • 1 Binary Search
  • 1 Collaborative robots
  • Show More...

  • Refine by Type
  • 9 document

  • Refine by Publication Year
  • 4 2024
  • 2 2017
  • 1 2014
  • 1 2019
  • 1 2021

Questions / Remarks / Feedback
X

Feedback for Dagstuhl Publishing


Thanks for your feedback!

Feedback submitted

Could not send message

Please try again later or send an E-mail
© 2023-2024 Schloss Dagstuhl – LZI GmbH Imprint Privacy Contact