6 Search Results for "Hanauer, Kathrin"

Document
DOI: 10.4230/LIPIcs.SEA.2024.12
Streaming Matching and Edge Cover in Practice

Authors: S M Ferdous, Alex Pothen, and Mahantesh Halappanavar

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

Abstract
Graph algorithms with polynomial space and time requirements often become infeasible for massive graphs with billions of edges or more. State-of-the-art approaches therefore employ approximate serial, parallel, and distributed algorithms to tackle these challenges. However, such approaches require storing the entire graph in memory and thus need access to costly computing resources such as clusters and supercomputers. In this paper, we present practical streaming approaches for solving massive graph problems using limited memory for two prototypical graph problems: maximum weighted matching and minimum weighted edge cover. For matching, we conduct a thorough computational study on two of the semi-streaming algorithms including a recent breakthrough result that achieves a 1/(2+ε)-approximation of the weight while using O(n log W /ε) memory (here n is the number of vertices and W is the maximum edge weight), designed by Paz and Schwartzman [SODA, 2017]. Empirically, we show that the semi-streaming algorithms produce matchings whose weight is close to the best 1/2-approximate offline algorithm while requiring less time and an order-of-magnitude less memory. For minimum weighted edge cover, we develop three novel semi-streaming algorithms. Two of these algorithms require a single pass through the input graph, require O(n log n) memory, and provide a 2-approximation guarantee on the objective. We also leverage a relationship between approximate maximum weighted matching and approximate minimum weighted edge cover to develop a two-pass 3/2+ε-approximate algorithm with the memory requirement of Paz and Schwartzman’s semi-streaming matching algorithm. These streaming approaches are compared against the state-of-the-art 3/2-approximate offline algorithm. The semi-streaming matching and the novel edge cover algorithms proposed in this paper can process graphs with several billions of edges in under 30 minutes using 6 GB of memory, which is at least an order of magnitude improvement from the offline (non-streaming) algorithms. For the largest graph, the best alternative offline parallel approximation algorithm (GPA+ROMA) could not finish in three hours even while employing hundreds of processors and 1 TB of memory. We also demonstrate an application of semi-streaming algorithm by computing a matching using linearly bounded memory on intersection graphs derived from three machine learning datasets, while the existing offline algorithms could not complete on one of these datasets since its memory requirement exceeded 1TB.
Cite as

S M Ferdous, Alex Pothen, and Mahantesh Halappanavar. Streaming Matching and Edge Cover in Practice. In 22nd International Symposium on Experimental Algorithms (SEA 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 301, pp. 12:1-12:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

Copy BibTex To Clipboard

@InProceedings{ferdous_et_al:LIPIcs.SEA.2024.12,
  author =	{Ferdous, S M and Pothen, Alex and Halappanavar, Mahantesh},
  title =	{{Streaming Matching and Edge Cover in Practice}},
  booktitle =	{22nd International Symposium on Experimental Algorithms (SEA 2024)},
  pages =	{12:1--12:22},
  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.2024.12},
  URN =		{urn:nbn:de:0030-drops-203773},
  doi =		{10.4230/LIPIcs.SEA.2024.12},
  annote =	{Keywords: Matching, Edge Cover, Semi-Streaming Algorithm, Parallel Algorithms, Algorithm Engineering}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2024.120
Caching Connections in Matchings

Authors: Yaniv Sadeh and Haim Kaplan

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

Abstract
Motivated by the desire to utilize a limited number of configurable optical switches by recent advances in Software Defined Networks (SDNs), we define an online problem which we call the Caching in Matchings problem. This problem has a natural combinatorial structure and therefore may find additional applications in theory and practice. In the Caching in Matchings problem our cache consists of k matchings of connections between servers that form a bipartite graph. To cache a connection we insert it into one of the k matchings possibly evicting at most two other connections from this matching. This problem resembles the problem known as Connection Caching [Cohen et al., 2000], where we also cache connections but our only restriction is that they form a graph with bounded degree k. Our results show a somewhat surprising qualitative separation between the problems: The competitive ratio of any online algorithm for caching in matchings must depend on the size of the graph. Specifically, we give a deterministic O(nk) competitive and randomized O(n log k) competitive algorithms for caching in matchings, where n is the number of servers and k is the number of matchings. We also show that the competitive ratio of any deterministic algorithm is Ω(max(n/k,k)) and of any randomized algorithm is Ω(log (n/(k² log k)) ⋅ log k). In particular, the lower bound for randomized algorithms is Ω(log n) regardless of k, and can be as high as Ω(log² n) if k = n^{1/3}, for example. We also show that if we allow the algorithm to use at least 2k-1 matchings compared to k used by the optimum then we match the competitive ratios of connection catching which are independent of n. Interestingly, we also show that even a single extra matching for the algorithm allows to get substantially better bounds.
Cite as

Yaniv Sadeh and Haim Kaplan. Caching Connections in Matchings. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 120:1-120:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

Copy BibTex To Clipboard

@InProceedings{sadeh_et_al:LIPIcs.ICALP.2024.120,
  author =	{Sadeh, Yaniv and Kaplan, Haim},
  title =	{{Caching Connections in Matchings}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{120:1--120:20},
  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.2024.120},
  URN =		{urn:nbn:de:0030-drops-202639},
  doi =		{10.4230/LIPIcs.ICALP.2024.120},
  annote =	{Keywords: Caching, Matchings, Caching in Matchings, Edge Coloring, Online Algorithms}
}
Document
DOI: 10.4230/LIPIcs.SAND.2022.18
Fully Dynamic Four-Vertex Subgraph Counting

Authors: Kathrin Hanauer, Monika Henzinger, and Qi Cheng Hua

Published in: LIPIcs, Volume 221, 1st Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2022)

Abstract
This paper presents a comprehensive study of algorithms for maintaining the number of all connected four-vertex subgraphs in a dynamic graph. Specifically, our algorithms maintain the number of paths of length three in deterministic amortized O(m^{1/2}) update time, and any other connected four-vertex subgraph which is not a clique in deterministic amortized update time O(m^{2/3}). Queries can be answered in constant time. We also study the query times for subgraphs containing an arbitrary edge that is supplied only with the query as well as the case where only subgraphs containing a vertex s that is fixed beforehand are considered. For length-3 paths, paws, 4-cycles, and diamonds our bounds match or are not far from (conditional) lower bounds: Based on the OMv conjecture we show that any dynamic algorithm that detects the existence of paws, diamonds, or 4-cycles or that counts length-3 paths takes update time Ω(m^{1/2-δ}). Additionally, for 4-cliques and all connected induced subgraphs, we show a lower bound of Ω(m^{1-δ}) for any small constant δ > 0 for the amortized update time, assuming the static combinatorial 4-clique conjecture holds. This shows that the O(m) algorithm by Eppstein et al. [David Eppstein et al., 2012] for these subgraphs cannot be improved by a polynomial factor.
Cite as

Kathrin Hanauer, Monika Henzinger, and Qi Cheng Hua. Fully Dynamic Four-Vertex Subgraph Counting. In 1st Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 221, pp. 18:1-18:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

Copy BibTex To Clipboard

@InProceedings{hanauer_et_al:LIPIcs.SAND.2022.18,
  author =	{Hanauer, Kathrin and Henzinger, Monika and Hua, Qi Cheng},
  title =	{{Fully Dynamic Four-Vertex Subgraph Counting}},
  booktitle =	{1st Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2022)},
  pages =	{18:1--18:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-224-2},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{221},
  editor =	{Aspnes, James and Michail, Othon},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAND.2022.18},
  URN =		{urn:nbn:de:0030-drops-159608},
  doi =		{10.4230/LIPIcs.SAND.2022.18},
  annote =	{Keywords: Dynamic Graph Algorithms, Subgraph Counting, Motif Search}
}
Document
Invited Talk
DOI: 10.4230/LIPIcs.SAND.2022.1
Recent Advances in Fully Dynamic Graph Algorithms (Invited Talk)

Authors: Kathrin Hanauer, Monika Henzinger, and Christian Schulz

Published in: LIPIcs, Volume 221, 1st Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2022)

Abstract
In recent years, significant advances have been made in the design and analysis of fully dynamic algorithms. However, these theoretical results have received very little attention from the practical perspective. Few of the algorithms are implemented and tested on real datasets, and their practical potential is far from understood. Here, we present a quick reference guide to recent engineering and theory results in the area of fully dynamic graph algorithms.
Cite as

Kathrin Hanauer, Monika Henzinger, and Christian Schulz. Recent Advances in Fully Dynamic Graph Algorithms (Invited Talk). In 1st Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 221, pp. 1:1-1:47, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2022)

Copy BibTex To Clipboard

@InProceedings{hanauer_et_al:LIPIcs.SAND.2022.1,
  author =	{Hanauer, Kathrin and Henzinger, Monika and Schulz, Christian},
  title =	{{Recent Advances in Fully Dynamic Graph Algorithms}},
  booktitle =	{1st Symposium on Algorithmic Foundations of Dynamic Networks (SAND 2022)},
  pages =	{1:1--1:47},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-224-2},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{221},
  editor =	{Aspnes, James and Michail, Othon},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAND.2022.1},
  URN =		{urn:nbn:de:0030-drops-159434},
  doi =		{10.4230/LIPIcs.SAND.2022.1},
  annote =	{Keywords: fully dynamic graph algorithms, survey}
}
Document
DOI: 10.4230/LIPIcs.SEA.2021.13
O'Reach: Even Faster Reachability in Large Graphs

Authors: Kathrin Hanauer, Christian Schulz, and Jonathan Trummer

Published in: LIPIcs, Volume 190, 19th International Symposium on Experimental Algorithms (SEA 2021)

Abstract
One of the most fundamental problems in computer science is the reachability problem: Given a directed graph and two vertices s and t, can s reach t via a path? We revisit existing techniques and combine them with new approaches to support a large portion of reachability queries in constant time using a linear-sized reachability index. Our new algorithm O'Reach can be easily combined with previously developed solutions for the problem or run standalone. In a detailed experimental study, we compare a variety of algorithms with respect to their index-building and query times as well as their memory footprint on a diverse set of instances. Our experiments indicate that the query performance often depends strongly not only on the type of graph, but also on the result, i.e., reachable or unreachable. Furthermore, we show that previous algorithms are significantly sped up when combined with our new approach in almost all scenarios. Surprisingly, due to cache effects, a higher investment in space doesn't necessarily pay off: Reachability queries can often be answered even faster than single memory accesses in a precomputed full reachability matrix.
Cite as

Kathrin Hanauer, Christian Schulz, and Jonathan Trummer. O'Reach: Even Faster Reachability in Large Graphs. In 19th International Symposium on Experimental Algorithms (SEA 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 190, pp. 13:1-13:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

Copy BibTex To Clipboard

@InProceedings{hanauer_et_al:LIPIcs.SEA.2021.13,
  author =	{Hanauer, Kathrin and Schulz, Christian and Trummer, Jonathan},
  title =	{{O'Reach: Even Faster Reachability in Large Graphs}},
  booktitle =	{19th International Symposium on Experimental Algorithms (SEA 2021)},
  pages =	{13:1--13:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-185-6},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{190},
  editor =	{Coudert, David and Natale, Emanuele},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2021.13},
  URN =		{urn:nbn:de:0030-drops-137856},
  doi =		{10.4230/LIPIcs.SEA.2021.13},
  annote =	{Keywords: Reachability, Static Graphs, Graph Algorithms, Reachability Index, Algorithm Engineering}
}
Document
DOI: 10.4230/LIPIcs.SEA.2020.14
Faster Fully Dynamic Transitive Closure in Practice

Authors: Kathrin Hanauer, Monika Henzinger, and Christian Schulz

Published in: LIPIcs, Volume 160, 18th International Symposium on Experimental Algorithms (SEA 2020)

Abstract
The fully dynamic transitive closure problem asks to maintain reachability information in a directed graph between arbitrary pairs of vertices, while the graph undergoes a sequence of edge insertions and deletions. The problem has been thoroughly investigated in theory and many specialized algorithms for solving it have been proposed in the last decades. In two large studies [Frigioni ea, 2001; Krommidas and Zaroliagis, 2008], a number of these algorithms have been evaluated experimentally against simple, static algorithms for graph traversal, showing the competitiveness and even superiority of the simple algorithms in practice, except for very dense random graphs or very high ratios of queries. A major drawback of those studies is that only small and mostly randomly generated graphs are considered. In this paper, we engineer new algorithms to maintain all-pairs reachability information which are simple and space-efficient. Moreover, we perform an extensive experimental evaluation on both generated and real-world instances that are several orders of magnitude larger than those in the previous studies. Our results indicate that our new algorithms outperform all state-of-the-art algorithms on all types of input considerably in practice.
Cite as

Kathrin Hanauer, Monika Henzinger, and Christian Schulz. Faster Fully Dynamic Transitive Closure in Practice. In 18th International Symposium on Experimental Algorithms (SEA 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 160, pp. 14:1-14:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

Copy BibTex To Clipboard

@InProceedings{hanauer_et_al:LIPIcs.SEA.2020.14,
  author =	{Hanauer, Kathrin and Henzinger, Monika and Schulz, Christian},
  title =	{{Faster Fully Dynamic Transitive Closure in Practice}},
  booktitle =	{18th International Symposium on Experimental Algorithms (SEA 2020)},
  pages =	{14:1--14:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-148-1},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{160},
  editor =	{Faro, Simone and Cantone, Domenico},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SEA.2020.14},
  URN =		{urn:nbn:de:0030-drops-120887},
  doi =		{10.4230/LIPIcs.SEA.2020.14},
  annote =	{Keywords: Dynamic Graph Algorithms, Reachability, Transitive Closure}
}
  • Refine by Author
  • 4 Hanauer, Kathrin
  • 3 Henzinger, Monika
  • 3 Schulz, Christian
  • 1 Ferdous, S M
  • 1 Halappanavar, Mahantesh
  • Show More...

  • Refine by Classification
  • 2 Mathematics of computing → Graph algorithms
  • 2 Theory of computation → Dynamic graph algorithms
  • 2 Theory of computation → Graph algorithms analysis
  • 1 Computing methodologies
  • 1 Computing methodologies → Shared memory algorithms
  • Show More...

  • Refine by Keyword
  • 2 Algorithm Engineering
  • 2 Dynamic Graph Algorithms
  • 2 Reachability
  • 1 Caching
  • 1 Caching in Matchings
  • Show More...

  • Refine by Type
  • 6 document

  • Refine by Publication Year
  • 2 2022
  • 2 2024
  • 1 2020
  • 1 2021

© 2023-2024 Schloss Dagstuhl – LZI GmbH Imprint Privacy Contact