Search Results

Documents authored by Räcke, Harald

Document
DOI: 10.4230/LIPIcs.ITCS.2024.55
Electrical Flows for Polylogarithmic Competitive Oblivious Routing

Authors: Gramoz Goranci, Monika Henzinger, Harald Räcke, Sushant Sachdeva, and A. R. Sricharan

Published in: LIPIcs, Volume 287, 15th Innovations in Theoretical Computer Science Conference (ITCS 2024)

Abstract
Oblivious routing is a well-studied paradigm that uses static precomputed routing tables for selecting routing paths within a network. Existing oblivious routing schemes with polylogarithmic competitive ratio for general networks are tree-based, in the sense that routing is performed according to a convex combination of trees. However, this restriction to trees leads to a construction that has time quadratic in the size of the network and does not parallelize well. In this paper we study oblivious routing schemes based on electrical routing. In particular, we show that general networks with n vertices and m edges admit a routing scheme that has competitive ratio O(log² n) and consists of a convex combination of only O(√m) electrical routings. This immediately leads to an improved construction algorithm with time Õ(m^{3/2}) that can also be implemented in parallel with Õ(√m) depth.
Cite as

Gramoz Goranci, Monika Henzinger, Harald Räcke, Sushant Sachdeva, and A. R. Sricharan. Electrical Flows for Polylogarithmic Competitive Oblivious Routing. In 15th Innovations in Theoretical Computer Science Conference (ITCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 287, pp. 55:1-55:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

Copy BibTex To Clipboard

@InProceedings{goranci_et_al:LIPIcs.ITCS.2024.55,
  author =	{Goranci, Gramoz and Henzinger, Monika and R\"{a}cke, Harald and Sachdeva, Sushant and Sricharan, A. R.},
  title =	{{Electrical Flows for Polylogarithmic Competitive Oblivious Routing}},
  booktitle =	{15th Innovations in Theoretical Computer Science Conference (ITCS 2024)},
  pages =	{55:1--55:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-309-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{287},
  editor =	{Guruswami, Venkatesan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2024.55},
  URN =		{urn:nbn:de:0030-drops-195830},
  doi =		{10.4230/LIPIcs.ITCS.2024.55},
  annote =	{Keywords: oblivious routing, electrical flows}
}
Document
DOI: 10.4230/LIPIcs.STACS.2023.36
Dynamic Maintenance of Monotone Dynamic Programs and Applications

Authors: Monika Henzinger, Stefan Neumann, Harald Räcke, and Stefan Schmid

Published in: LIPIcs, Volume 254, 40th International Symposium on Theoretical Aspects of Computer Science (STACS 2023)

Abstract
Dynamic programming (DP) is one of the fundamental paradigms in algorithm design. However, many DP algorithms have to fill in large DP tables, represented by two-dimensional arrays, which causes at least quadratic running times and space usages. This has led to the development of improved algorithms for special cases when the DPs satisfy additional properties like, e.g., the Monge property or total monotonicity. In this paper, we consider a new condition which assumes (among some other technical assumptions) that the rows of the DP table are monotone. Under this assumption, we introduce a novel data structure for computing (1+ε)-approximate DP solutions in near-linear time and space in the static setting, and with polylogarithmic update times when the DP entries change dynamically. To the best of our knowledge, our new condition is incomparable to previous conditions and is the first which allows to derive dynamic algorithms based on existing DPs. Instead of using two-dimensional arrays to store the DP tables, we store the rows of the DP tables using monotone piecewise constant functions. This allows us to store length-n DP table rows with entries in [0,W] using only polylog(n,W) bits, and to perform operations, such as (min,+)-convolution or rounding, on these functions in polylogarithmic time. We further present several applications of our data structure. For bicriteria versions of k-balanced graph partitioning and simultaneous source location, we obtain the first dynamic algorithms with subpolynomial update times, as well as the first static algorithms using only near-linear time and space. Additionally, we obtain the currently fastest algorithm for fully dynamic knapsack.
Cite as

Monika Henzinger, Stefan Neumann, Harald Räcke, and Stefan Schmid. Dynamic Maintenance of Monotone Dynamic Programs and Applications. In 40th International Symposium on Theoretical Aspects of Computer Science (STACS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 254, pp. 36:1-36:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

Copy BibTex To Clipboard

@InProceedings{henzinger_et_al:LIPIcs.STACS.2023.36,
  author =	{Henzinger, Monika and Neumann, Stefan and R\"{a}cke, Harald and Schmid, Stefan},
  title =	{{Dynamic Maintenance of Monotone Dynamic Programs and Applications}},
  booktitle =	{40th International Symposium on Theoretical Aspects of Computer Science (STACS 2023)},
  pages =	{36:1--36:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-266-2},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{254},
  editor =	{Berenbrink, Petra and Bouyer, Patricia and Dawar, Anuj and Kant\'{e}, Mamadou Moustapha},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2023.36},
  URN =		{urn:nbn:de:0030-drops-176889},
  doi =		{10.4230/LIPIcs.STACS.2023.36},
  annote =	{Keywords: Dynamic programming, dynamic algorithms, data structures}
}
Document
DOI: 10.4230/LIPIcs.ESA.2020.36
Compact Oblivious Routing in Weighted Graphs

Authors: Philipp Czerner and Harald Räcke

Published in: LIPIcs, Volume 173, 28th Annual European Symposium on Algorithms (ESA 2020)

Abstract
The space-requirement for routing-tables is an important characteristic of routing schemes. For the cost-measure of minimizing the total network load there exist a variety of results that show tradeoffs between stretch and required size for the routing tables. This paper designs compact routing schemes for the cost-measure congestion, where the goal is to minimize the maximum relative load of a link in the network (the relative load of a link is its traffic divided by its bandwidth). We show that for arbitrary undirected graphs we can obtain oblivious routing strategies with competitive ratio 𝒪̃(1) that have header length 𝒪̃(1), label size 𝒪̃(1), and require routing-tables of size 𝒪̃(deg(v)) at each vertex v in the graph. This improves a result of Räcke and Schmid who proved a similar result in unweighted graphs.
Cite as

Philipp Czerner and Harald Räcke. Compact Oblivious Routing in Weighted Graphs. In 28th Annual European Symposium on Algorithms (ESA 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 173, pp. 36:1-36:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

Copy BibTex To Clipboard

@InProceedings{czerner_et_al:LIPIcs.ESA.2020.36,
  author =	{Czerner, Philipp and R\"{a}cke, Harald},
  title =	{{Compact Oblivious Routing in Weighted Graphs}},
  booktitle =	{28th Annual European Symposium on Algorithms (ESA 2020)},
  pages =	{36:1--36:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-162-7},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{173},
  editor =	{Grandoni, Fabrizio and Herman, Grzegorz and Sanders, Peter},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2020.36},
  URN =		{urn:nbn:de:0030-drops-129024},
  doi =		{10.4230/LIPIcs.ESA.2020.36},
  annote =	{Keywords: Oblivious Routing, Compact Routing, Competitive Analysis}
}
Document
DOI: 10.4230/LIPIcs.ESA.2019.75
Compact Oblivious Routing

Authors: Harald Räcke and Stefan Schmid

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

Abstract
Oblivious routing is an attractive paradigm for large distributed systems in which centralized control and frequent reconfigurations are infeasible or undesired (e.g., costly). Over the last almost 20 years, much progress has been made in devising oblivious routing schemes that guarantee close to optimal load and also algorithms for constructing such schemes efficiently have been designed. However, a common drawback of existing oblivious routing schemes is that they are not compact: they require large routing tables (of polynomial size), which does not scale. This paper presents the first oblivious routing scheme which guarantees close to optimal load and is compact at the same time - requiring routing tables of polylogarithmic size. Our algorithm maintains the polylogarithmic competitive ratio of existing algorithms, and is hence particularly well-suited for emerging large-scale networks.
Cite as

Harald Räcke and Stefan Schmid. Compact Oblivious Routing. In 27th Annual European Symposium on Algorithms (ESA 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 144, pp. 75:1-75:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

Copy BibTex To Clipboard

@InProceedings{racke_et_al:LIPIcs.ESA.2019.75,
  author =	{R\"{a}cke, Harald and Schmid, Stefan},
  title =	{{Compact Oblivious Routing}},
  booktitle =	{27th Annual European Symposium on Algorithms (ESA 2019)},
  pages =	{75:1--75:14},
  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.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2019.75},
  URN =		{urn:nbn:de:0030-drops-111968},
  doi =		{10.4230/LIPIcs.ESA.2019.75},
  annote =	{Keywords: Oblivious Routing, Compact Routing, Competitive Analysis}
}
Document
DOI: 10.4230/LIPIcs.ICALP.2017.33
Reordering Buffer Management with a Logarithmic Guarantee in General Metric Spaces

Authors: Matthias Kohler and Harald Räcke

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

Abstract
In the reordering buffer management problem a sequence of requests arrive online in a finite metric space, and have to be processed by a single server. This server is equipped with a request buffer of size k and can decide at each point in time, which request from its buffer to serve next. Servicing of a request is simply done by moving the server to the location of the request. The goal is to process all requests while minimizing the total distance that the server is traveling inside the metric space. In this paper we present a deterministic algorithm for the reordering buffer management problem that achieves a competitive ratio of O(log Delta + min {log n,log k}) in a finite metric space of n points and aspect ratio Delta. This is the first algorithm that works for general metric spaces and has just a logarithmic dependency on the relevant parameters. The guarantee is memory-robust, i.e., the competitive ratio decreases only slightly when the buffer-size of the optimum is increased to h=(1+\epsilon)k. For memory robust guarantees our bounds are close to optimal.
Cite as

Matthias Kohler and Harald Räcke. Reordering Buffer Management with a Logarithmic Guarantee in General Metric Spaces. In 44th International Colloquium on Automata, Languages, and Programming (ICALP 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 80, pp. 33:1-33:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

Copy BibTex To Clipboard

@InProceedings{kohler_et_al:LIPIcs.ICALP.2017.33,
  author =	{Kohler, Matthias and R\"{a}cke, Harald},
  title =	{{Reordering Buffer Management with a Logarithmic Guarantee in General Metric Spaces}},
  booktitle =	{44th International Colloquium on Automata, Languages, and Programming (ICALP 2017)},
  pages =	{33:1--33:12},
  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.2017.33},
  URN =		{urn:nbn:de:0030-drops-73882},
  doi =		{10.4230/LIPIcs.ICALP.2017.33},
  annote =	{Keywords: Online algorithms, reordering buffer, metric spaces, scheduling}
}
Document
DOI: 10.4230/LIPIcs.ICALP.2016.42
Online Weighted Degree-Bounded Steiner Networks via Novel Online Mixed Packing/Covering

Authors: Sina Dehghani, Soheil Ehsani, Mohammad Taghi Hajiaghayi, Vahid Liaghat, Harald Räcke, and Saeed Seddighin

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

Abstract
We design the first online algorithm with poly-logarithmic competitive ratio for the edge-weighted degree-bounded Steiner forest (EW-DB-SF) problem and its generalized variant. We obtain our result by demonstrating a new generic approach for solving mixed packing/covering integer programs in the online paradigm. In EW-DB-SF, we are given an edge-weighted graph with a degree bound for every vertex. Given a root vertex in advance, we receive a sequence of terminal vertices in an online manner. Upon the arrival of a terminal, we need to augment our solution subgraph to connect the new terminal to the root. The goal is to minimize the total weight of the solution while respecting the degree bounds on the vertices. In the offline setting, edge-weighted degree-bounded Steiner tree (EW-DB-ST) and its many variations have been extensively studied since early eighties. Unfortunately, the recent advancements in the online network design problems are inherently difficult to adapt for degree-bounded problems. In particular, it is not known whether the fractional solution obtained by standard primal-dual techniques for mixed packing/covering LPs can be rounded online. In contrast, in this paper we obtain our result by using structural properties of the optimal solution, and reducing the EW-DB-SF problem to an exponential-size mixed packing/covering integer program in which every variable appears only once in covering constraints. We then design a generic integral algorithm for solving this restricted family of IPs. As mentioned above, we demonstrate a new technique for solving mixed packing/covering integer programs. Define the covering frequency k of a program as the maximum number of covering constraints in which a variable can participate. Let m denote the number of packing constraints. We design an online deterministic integral algorithm with competitive ratio of O(k*log(m)) for the mixed packing/covering integer programs. We prove the tightness of our result by providing a matching lower bound for any randomized algorithm. We note that our solution solely depends on m and k. Indeed, there can be exponentially many variables. Furthermore, our algorithm directly provides an integral solution, even if the integrality gap of the program is unbounded. We believe this technique can be used as an interesting alternative for the standard primal-dual techniques in solving online problems.
Cite as

Sina Dehghani, Soheil Ehsani, Mohammad Taghi Hajiaghayi, Vahid Liaghat, Harald Räcke, and Saeed Seddighin. Online Weighted Degree-Bounded Steiner Networks via Novel Online Mixed Packing/Covering. In 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 55, pp. 42:1-42:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

Copy BibTex To Clipboard

@InProceedings{dehghani_et_al:LIPIcs.ICALP.2016.42,
  author =	{Dehghani, Sina and Ehsani, Soheil and Hajiaghayi, Mohammad Taghi and Liaghat, Vahid and R\"{a}cke, Harald and Seddighin, Saeed},
  title =	{{Online Weighted Degree-Bounded Steiner Networks via Novel Online Mixed Packing/Covering}},
  booktitle =	{43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016)},
  pages =	{42:1--42:14},
  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.2016.42},
  URN =		{urn:nbn:de:0030-drops-63221},
  doi =		{10.4230/LIPIcs.ICALP.2016.42},
  annote =	{Keywords: Online, Steiner Tree, Approximation, Competitive ratio}
}
Document
DOI: 10.4230/LIPIcs.STACS.2016.58
Improved Approximation Algorithms for Balanced Partitioning Problems

Authors: Harald Räcke and Richard Stotz

Published in: LIPIcs, Volume 47, 33rd Symposium on Theoretical Aspects of Computer Science (STACS 2016)

Abstract
We present approximation algorithms for balanced partitioning problems. These problems are notoriously hard and we present new bicriteria approximation algorithms, that approximate the optimal cost and relax the balance constraint. In the first scenario, we consider Min-Max k-Partitioning, the problem of dividing a graph into k equal-sized parts while minimizing the maximum cost of edges cut by a single part. Our approximation algorithm relaxes the size of the parts by (1+epsilon) and approximates the optimal cost by O(log^{1.5}(n) * log(log(n))), for every 0 < epsilon < 1. This is the first nontrivial algorithm for this problem that relaxes the balance constraint by less than 2. In the second scenario, we consider strategies to find a minimum-cost mapping of a graph of processes to a hierarchical network with identical processors at the leaves. This Hierarchical Graph Partitioning problem has been studied recently by Hajiaghayi et al. who presented an (O(log(n)),(1+epsilon)(h+1)) approximation algorithm for constant network heights h. We use spreading metrics to give an improved (O(log(n)),(1+epsilon)h) approximation algorithm that runs in polynomial time for arbitrary network heights.
Cite as

Harald Räcke and Richard Stotz. Improved Approximation Algorithms for Balanced Partitioning Problems. In 33rd Symposium on Theoretical Aspects of Computer Science (STACS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 47, pp. 58:1-58:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

Copy BibTex To Clipboard

@InProceedings{racke_et_al:LIPIcs.STACS.2016.58,
  author =	{R\"{a}cke, Harald and Stotz, Richard},
  title =	{{Improved Approximation Algorithms for Balanced Partitioning Problems}},
  booktitle =	{33rd Symposium on Theoretical Aspects of Computer Science (STACS 2016)},
  pages =	{58:1--58:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-001-9},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{47},
  editor =	{Ollinger, Nicolas and Vollmer, Heribert},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2016.58},
  URN =		{urn:nbn:de:0030-drops-57598},
  doi =		{10.4230/LIPIcs.STACS.2016.58},
  annote =	{Keywords: graph partitioning, dynamic programming, scheduling}
}
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 About DROPS Imprint Privacy Contact