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Documents authored by Halldórsson, Magnús M.

Found 2 Possible Name Variants:

Halldorsson, Magnus M.

Document
DOI: 10.4230/LIPIcs.DISC.2024.24
Decentralized Distributed Graph Coloring II: Degree+1-Coloring Virtual Graphs

Authors: Maxime Flin, Magnús M. Halldórsson, and Alexandre Nolin

Published in: LIPIcs, Volume 319, 38th International Symposium on Distributed Computing (DISC 2024)

Abstract
Graph coloring is fundamental to distributed computing. We give the first general treatment of the coloring of virtual graphs, where the graph H to be colored is locally embedded within the communication graph G. Besides generalizing classical distributed graph coloring (where H = G), this captures other previously studied settings, including cluster graphs and power graphs. We find that the complexity of coloring a virtual graph depends linearly on the edge congestion of its embedding. The main question of interest is how fast we can color virtual graphs of constant congestion. We find that, surprisingly, these graphs can be colored nearly as fast as ordinary graphs. Namely, we give a O(log⁴log n)-round algorithm for the deg+1-coloring problem, where each node is assigned more colors than its degree. This can be viewed as a case where a distributed graph problem can be solved even when the operation of each node is decentralized.
Cite as

Maxime Flin, Magnús M. Halldórsson, and Alexandre Nolin. Decentralized Distributed Graph Coloring II: Degree+1-Coloring Virtual Graphs. In 38th International Symposium on Distributed Computing (DISC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 319, pp. 24:1-24:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{flin_et_al:LIPIcs.DISC.2024.24,
  author =	{Flin, Maxime and Halld\'{o}rsson, Magn\'{u}s M. and Nolin, Alexandre},
  title =	{{Decentralized Distributed Graph Coloring II: Degree+1-Coloring Virtual Graphs}},
  booktitle =	{38th International Symposium on Distributed Computing (DISC 2024)},
  pages =	{24:1--24:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-352-2},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{319},
  editor =	{Alistarh, Dan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2024.24},
  URN =		{urn:nbn:de:0030-drops-212502},
  doi =		{10.4230/LIPIcs.DISC.2024.24},
  annote =	{Keywords: Graph Coloring, Distributed Algorithms, Virtual Graphs, Congestion, Dilation}
}
Document
DOI: 10.4230/LIPIcs.DISC.2024.31
Distributed Delta-Coloring Under Bandwidth Limitations

Authors: Magnús M. Halldórsson and Yannic Maus

Published in: LIPIcs, Volume 319, 38th International Symposium on Distributed Computing (DISC 2024)

Abstract
We consider the problem of coloring graphs of maximum degree Δ with Δ colors in the distributed setting with limited bandwidth. Specifically, we give a polylog log n-round randomized algorithm in the CONGEST model. This is close to the lower bound of Ω(log log n) rounds from [Brandt et al., STOC '16], which holds also in the more powerful LOCAL model. The core of our algorithm is a reduction to several special instances of the constructive Lovász local lemma (LLL) and the deg+1-list coloring problem.
Cite as

Magnús M. Halldórsson and Yannic Maus. Distributed Delta-Coloring Under Bandwidth Limitations. In 38th International Symposium on Distributed Computing (DISC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 319, pp. 31:1-31:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{halldorsson_et_al:LIPIcs.DISC.2024.31,
  author =	{Halld\'{o}rsson, Magn\'{u}s M. and Maus, Yannic},
  title =	{{Distributed Delta-Coloring Under Bandwidth Limitations}},
  booktitle =	{38th International Symposium on Distributed Computing (DISC 2024)},
  pages =	{31:1--31:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-352-2},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{319},
  editor =	{Alistarh, Dan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2024.31},
  URN =		{urn:nbn:de:0030-drops-212572},
  doi =		{10.4230/LIPIcs.DISC.2024.31},
  annote =	{Keywords: Graph problems, Graph coloring, Lov\'{a}sz local lemma, LOCAL model, CONGEST model, Distributed computing}
}
Document
DOI: 10.4230/LIPIcs.DISC.2023.19
Fast Coloring Despite Congested Relays

Authors: Maxime Flin, Magnús M. Halldórsson, and Alexandre Nolin

Published in: LIPIcs, Volume 281, 37th International Symposium on Distributed Computing (DISC 2023)

Abstract
We provide a O(log⁶ log n)-round randomized algorithm for distance-2 coloring in CONGEST with Δ²+1 colors. For Δ≫polylog n, this improves exponentially on the O(logΔ+polylog log n) algorithm of [Halldórsson, Kuhn, Maus, Nolin, DISC'20].
Cite as

Maxime Flin, Magnús M. Halldórsson, and Alexandre Nolin. Fast Coloring Despite Congested Relays. In 37th International Symposium on Distributed Computing (DISC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 281, pp. 19:1-19:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{flin_et_al:LIPIcs.DISC.2023.19,
  author =	{Flin, Maxime and Halld\'{o}rsson, Magn\'{u}s M. and Nolin, Alexandre},
  title =	{{Fast Coloring Despite Congested Relays}},
  booktitle =	{37th International Symposium on Distributed Computing (DISC 2023)},
  pages =	{19:1--19:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-301-0},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{281},
  editor =	{Oshman, Rotem},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2023.19},
  URN =		{urn:nbn:de:0030-drops-191453},
  doi =		{10.4230/LIPIcs.DISC.2023.19},
  annote =	{Keywords: CONGEST model, distributed graph coloring, power graphs}
}
Document
DOI: 10.4230/LIPIcs.DISC.2022.26
Fast Distributed Vertex Splitting with Applications

Authors: Magnús M. Halldórsson, Yannic Maus, and Alexandre Nolin

Published in: LIPIcs, Volume 246, 36th International Symposium on Distributed Computing (DISC 2022)

Abstract
We present poly log log n-round randomized distributed algorithms to compute vertex splittings, a partition of the vertices of a graph into k parts such that a node of degree d(u) has ≈ d(u)/k neighbors in each part. Our techniques can be seen as the first progress towards general poly log log n-round algorithms for the Lovász Local Lemma. As the main application of our result, we obtain a randomized poly log log n-round CONGEST algorithm for (1+ε)Δ-edge coloring n-node graphs of sufficiently large constant maximum degree Δ, for any ε > 0. Further, our results improve the computation of defective colorings and certain tight list coloring problems. All the results improve the state-of-the-art round complexity exponentially, even in the LOCAL model.
Cite as

Magnús M. Halldórsson, Yannic Maus, and Alexandre Nolin. Fast Distributed Vertex Splitting with Applications. In 36th International Symposium on Distributed Computing (DISC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 246, pp. 26:1-26:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{halldorsson_et_al:LIPIcs.DISC.2022.26,
  author =	{Halld\'{o}rsson, Magn\'{u}s M. and Maus, Yannic and Nolin, Alexandre},
  title =	{{Fast Distributed Vertex Splitting with Applications}},
  booktitle =	{36th International Symposium on Distributed Computing (DISC 2022)},
  pages =	{26:1--26:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-255-6},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{246},
  editor =	{Scheideler, Christian},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2022.26},
  URN =		{urn:nbn:de:0030-drops-172176},
  doi =		{10.4230/LIPIcs.DISC.2022.26},
  annote =	{Keywords: Graph problems, Edge coloring, List coloring, Lov\'{a}sz local lemma, LOCAL model, CONGEST model, Distributed computing}
}
Document
DOI: 10.4230/LIPIcs.DISC.2020.39
Coloring Fast Without Learning Your Neighbors' Colors

Authors: Magnús M. Halldórsson, Fabian Kuhn, Yannic Maus, and Alexandre Nolin

Published in: LIPIcs, Volume 179, 34th International Symposium on Distributed Computing (DISC 2020)

Abstract
We give an improved randomized CONGEST algorithm for distance-2 coloring that uses Δ²+1 colors and runs in O(log n) rounds, improving the recent O(log Δ ⋅ log n)-round algorithm in [Halldórsson, Kuhn, Maus; PODC '20]. We then improve the time complexity to O(log Δ) + 2^{O(√{log log n})}.
Cite as

Magnús M. Halldórsson, Fabian Kuhn, Yannic Maus, and Alexandre Nolin. Coloring Fast Without Learning Your Neighbors' Colors. In 34th International Symposium on Distributed Computing (DISC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 179, pp. 39:1-39:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{halldorsson_et_al:LIPIcs.DISC.2020.39,
  author =	{Halld\'{o}rsson, Magn\'{u}s M. and Kuhn, Fabian and Maus, Yannic and Nolin, Alexandre},
  title =	{{Coloring Fast Without Learning Your Neighbors' Colors}},
  booktitle =	{34th International Symposium on Distributed Computing (DISC 2020)},
  pages =	{39:1--39:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-168-9},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{179},
  editor =	{Attiya, Hagit},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2020.39},
  URN =		{urn:nbn:de:0030-drops-131170},
  doi =		{10.4230/LIPIcs.DISC.2020.39},
  annote =	{Keywords: distributed graph coloring, distance 2 coloring, congestion}
}
Document
DOI: 10.4230/LIPIcs.DISC.2019.14
The Capacity of Smartphone Peer-To-Peer Networks

Authors: Michael Dinitz, Magnús M. Halldórsson, Calvin Newport, and Alex Weaver

Published in: LIPIcs, Volume 146, 33rd International Symposium on Distributed Computing (DISC 2019)

Abstract
We study three capacity problems in the mobile telephone model, a network abstraction that models the peer-to-peer communication capabilities implemented in most commodity smartphone operating systems. The capacity of a network expresses how much sustained throughput can be maintained for a set of communication demands, and is therefore a fundamental bound on the usefulness of a network. Because of this importance, wireless network capacity has been active area of research for the last two decades. The three capacity problems that we study differ in the structure of the communication demands. The first problem is pairwise capacity, where the demands are (source, destination) pairs. Pairwise capacity is one of the most classical definitions, as it was analyzed in the seminal paper of Gupta and Kumar on wireless network capacity. The second problem we study is broadcast capacity, in which a single source must deliver packets to all other nodes in the network. Finally, we turn our attention to all-to-all capacity, in which all nodes must deliver packets to all other nodes. In all three of these problems we characterize the optimal achievable throughput for any given network, and design algorithms which asymptotically match this performance. We also study these problems in networks generated randomly by a process introduced by Gupta and Kumar, and fully characterize their achievable throughput. Interestingly, the techniques that we develop for all-to-all capacity also allow us to design a one-shot gossip algorithm that runs within a polylogarithmic factor of optimal in every graph. This largely resolves an open question from previous work on the one-shot gossip problem in this model.
Cite as

Michael Dinitz, Magnús M. Halldórsson, Calvin Newport, and Alex Weaver. The Capacity of Smartphone Peer-To-Peer Networks. In 33rd International Symposium on Distributed Computing (DISC 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 146, pp. 14:1-14:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{dinitz_et_al:LIPIcs.DISC.2019.14,
  author =	{Dinitz, Michael and Halld\'{o}rsson, Magn\'{u}s M. and Newport, Calvin and Weaver, Alex},
  title =	{{The Capacity of Smartphone Peer-To-Peer Networks}},
  booktitle =	{33rd International Symposium on Distributed Computing (DISC 2019)},
  pages =	{14:1--14:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-126-9},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{146},
  editor =	{Suomela, Jukka},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2019.14},
  URN =		{urn:nbn:de:0030-drops-113218},
  doi =		{10.4230/LIPIcs.DISC.2019.14},
  annote =	{Keywords: Capacity, Wireless, Mobile Telephone, Throughput}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2019.7
Query-Competitive Sorting with Uncertainty

Authors: Magnús M. Halldórsson and Murilo Santos de Lima

Published in: LIPIcs, Volume 138, 44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019)

Abstract
We study the problem of sorting under incomplete information, when queries are used to resolve uncertainties. Each of n data items has an unknown value, which is known to lie in a given interval. We can pay a query cost to learn the actual value, and we may allow an error threshold in the sorting. The goal is to find a nearly-sorted permutation by performing a minimum-cost set of queries. We show that an offline optimum query set can be found in polynomial time, and that both oblivious and adaptive problems have simple query-competitive algorithms. The query-competitiveness for the oblivious problem is n for uniform query costs, and unbounded for arbitrary costs; for the adaptive problem, the ratio is 2. We then present a unified adaptive strategy for uniform query costs that yields: (i) a 3/2-query-competitive randomized algorithm; (ii) a 5/3-query-competitive deterministic algorithm if the dependency graph has no 2-components after some preprocessing, which has query-competitive ratio 3/2 + O(1/k) if the components obtained have size at least k; (iii) an exact algorithm if the intervals constitute a laminar family. The first two results have matching lower bounds, and we have a lower bound of 7/5 for large components. We also show that the advice complexity of the adaptive problem is floor[n/2] if no error threshold is allowed, and ceil[n/3 * lg 3] for the general case.
Cite as

Magnús M. Halldórsson and Murilo Santos de Lima. Query-Competitive Sorting with Uncertainty. In 44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 138, pp. 7:1-7:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{halldorsson_et_al:LIPIcs.MFCS.2019.7,
  author =	{Halld\'{o}rsson, Magn\'{u}s M. and de Lima, Murilo Santos},
  title =	{{Query-Competitive Sorting with Uncertainty}},
  booktitle =	{44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019)},
  pages =	{7:1--7:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-117-7},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{138},
  editor =	{Rossmanith, Peter and Heggernes, Pinar and Katoen, Joost-Pieter},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2019.7},
  URN =		{urn:nbn:de:0030-drops-109519},
  doi =		{10.4230/LIPIcs.MFCS.2019.7},
  annote =	{Keywords: online algorithms, sorting, randomized algorithms, advice complexity, threshold tolerance graphs}
}
Document
DOI: 10.4230/LIPIcs.ICALP.2018.158
Spanning Trees With Edge Conflicts and Wireless Connectivity

Authors: Magnús M. Halldórsson, Guy Kortsarz, Pradipta Mitra, and Tigran Tonoyan

Published in: LIPIcs, Volume 107, 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)

Abstract
We introduce the problem of finding a spanning tree along with a partition of the tree edges into fewest number of feasible sets, where constraints on the edges define feasibility. The motivation comes from wireless networking, where we seek to model the irregularities seen in actual wireless environments. Not all node pairs may be able to communicate, even if geographically close - thus, the available pairs are specified with a link graph {L}=(V,E). Also, signal attenuation need not follow a nice geometric formula - hence, interference is modeled by a conflict (hyper)graph {C}=(E,F) on the links. The objective is to maximize the efficiency of the communication, or equivalently, to minimize the length of a schedule of the tree edges in the form of a coloring. We find that in spite of all this generality, the problem can be approximated linearly in terms of a versatile parameter, the inductive independence of the interference graph. Specifically, we give a simple algorithm that attains a O(rho log n)-approximation, where n is the number of nodes and rho is the inductive independence, and show that near-linear dependence on rho is also necessary. We also treat an extension to Steiner trees, modeling multicasting, and obtain a comparable result. Our results suggest that several canonical assumptions of geometry, regularity and "niceness" in wireless settings can sometimes be relaxed without a significant hit in algorithm performance.
Cite as

Magnús M. Halldórsson, Guy Kortsarz, Pradipta Mitra, and Tigran Tonoyan. Spanning Trees With Edge Conflicts and Wireless Connectivity. In 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 107, pp. 158:1-158:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{halldorsson_et_al:LIPIcs.ICALP.2018.158,
  author =	{Halld\'{o}rsson, Magn\'{u}s M. and Kortsarz, Guy and Mitra, Pradipta and Tonoyan, Tigran},
  title =	{{Spanning Trees With Edge Conflicts and Wireless Connectivity}},
  booktitle =	{45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)},
  pages =	{158:1--158:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-076-7},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{107},
  editor =	{Chatzigiannakis, Ioannis and Kaklamanis, Christos and Marx, D\'{a}niel and Sannella, Donald},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2018.158},
  URN =		{urn:nbn:de:0030-drops-91627},
  doi =		{10.4230/LIPIcs.ICALP.2018.158},
  annote =	{Keywords: spanning trees, wireless capacity, aggregation, approximation algorithms}
}
Document
DOI: 10.4230/LIPIcs.DISC.2017.25
An Efficient Communication Abstraction for Dense Wireless Networks

Authors: Magnús M. Halldórsson, Fabian Kuhn, Nancy Lynch, and Calvin Newport

Published in: LIPIcs, Volume 91, 31st International Symposium on Distributed Computing (DISC 2017)

Abstract
In this paper we study the problem of developing efficient distributed algorithms for dense wireless networks. For many problems in this setting, fast solutions must leverage the reality that radio signals fade with distance, which can be exploited to enable concurrent communication among multiple sender/receiver pairs. To simplify the development of these algorithms we describe a new communication abstraction called FadingMAC which exposes the benefits of this concurrent communication, but also hides the details of the underlying low-level radio signal behavior. This approach splits efforts between those who develop useful algorithms that run on the abstraction, and those who implement the abstraction in concrete low-level wireless models, or on real hardware. After defining FadingMAC, we describe and analyze an efficient implementation of the abstraction in a standard low-level SINR-style network model. We then describe solutions to the following problems that run on the abstraction: max, min, sum, and mean computed over input values; process renaming; consensus and leader election; and optimal packet scheduling. Combining our abstraction implementation with these applications that run on the abstraction, we obtain near-optimal solutions to these problems in our low-level SINR model - significantly advancing the known results for distributed algorithms in this setting. Of equal importance to these concrete bounds, however, is the general idea advanced by this paper: as wireless networks become more dense, both theoreticians and practitioners must explore new communication abstractions that can help tame this density.
Cite as

Magnús M. Halldórsson, Fabian Kuhn, Nancy Lynch, and Calvin Newport. An Efficient Communication Abstraction for Dense Wireless Networks. In 31st International Symposium on Distributed Computing (DISC 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 91, pp. 25:1-25:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{halldorsson_et_al:LIPIcs.DISC.2017.25,
  author =	{Halld\'{o}rsson, Magn\'{u}s M. and Kuhn, Fabian and Lynch, Nancy and Newport, Calvin},
  title =	{{An Efficient Communication Abstraction for Dense Wireless Networks}},
  booktitle =	{31st International Symposium on Distributed Computing (DISC 2017)},
  pages =	{25:1--25:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-053-8},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{91},
  editor =	{Richa, Andr\'{e}a},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2017.25},
  URN =		{urn:nbn:de:0030-drops-79898},
  doi =		{10.4230/LIPIcs.DISC.2017.25},
  annote =	{Keywords: wireless networks, abstractions, SINR, signal fading}
}
Document
DOI: 10.4230/LIPIcs.ICALP.2017.129
Universal Framework for Wireless Scheduling Problems

Authors: Eyjólfur I. Ásgeirsson, Magnús M. Halldórsson, and Tigran Tonoyan

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

Abstract
An overarching issue in resource management of wireless networks is assessing their capacity: How much communication can be achieved in a network, utilizing all the tools available: power control, scheduling, routing, channel assignment and rate adjustment? We propose the first framework for approximation algorithms in the physical model that addresses these questions in full, including rate control. The approximations obtained are doubly logarithmic in the link length and rate diversity. Where previous bounds are known, this gives an exponential improvement. A key contribution is showing that the complex interference relationship of the physical model can be simplified into a novel type of amenable conflict graphs, at a small cost. We also show that the approximation obtained is provably the best possible for any conflict graph formulation.
Cite as

Eyjólfur I. Ásgeirsson, Magnús M. Halldórsson, and Tigran Tonoyan. Universal Framework for Wireless Scheduling Problems. In 44th International Colloquium on Automata, Languages, and Programming (ICALP 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 80, pp. 129:1-129:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{asgeirsson_et_al:LIPIcs.ICALP.2017.129,
  author =	{\'{A}sgeirsson, Eyj\'{o}lfur I. and Halld\'{o}rsson, Magn\'{u}s M. and Tonoyan, Tigran},
  title =	{{Universal Framework for Wireless Scheduling Problems}},
  booktitle =	{44th International Colloquium on Automata, Languages, and Programming (ICALP 2017)},
  pages =	{129:1--129:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-041-5},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{80},
  editor =	{Chatzigiannakis, Ioannis and Indyk, Piotr and Kuhn, Fabian and Muscholl, Anca},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2017.129},
  URN =		{urn:nbn:de:0030-drops-74228},
  doi =		{10.4230/LIPIcs.ICALP.2017.129},
  annote =	{Keywords: Wireless, Scheduling, Physical Model, Approximation framework}
}
Document
DOI: 10.4230/LIPIcs.OPODIS.2015.11
Distributed Approximation of k-Service Assignment

Authors: Magnús M. Halldórsson, Sven Köhler, and Dror Rawitz

Published in: LIPIcs, Volume 46, 19th International Conference on Principles of Distributed Systems (OPODIS 2015)

Abstract
We consider the k-Service Assignment problem (k-SA), defined as follows. The input consists of a network that contains servers and clients, and an integer k. Each server has a finite capacity, and each client is associated with a demand and a profit. A feasible solution is an assignment of clients to neighboring servers such that (i) the total demand assigned to a server is at most its capacity, and (ii) a client is assigned either to k servers or to none. The profit of an assignment is the total profit of clients that are assigned to k servers, and the goal is to find a maximum profit assignment. In the r-restricted version of k-SA, no client requires more than an r-fraction of the capacity of any adjacent server. The k-SA problem is motivated by backup placement in networks and by resource allocation in 4G cellular networks. It can also be viewed as machine scheduling on related machines with assignment restrictions. We present a centralized polynomial time greedy (k+1-r)/(1-r)-approximation algorithm for r-restricted k-SA. We then show that a variant of this algorithm achieves an approximation ratio of k+1 using a resource augmentation factor of 1+r. We use the latter to present a (k+1)^2-approximation algorithm for k-SA. In the distributed setting, we present: (i) a (1+epsilon)*(k +1-r)/(1-r)-approximation algorithm for r-restricted k-SA, (ii) a (1+epsilon)(k+1)-approximation algorithm that uses a resource augmentation factor of 1+r for r-restricted k-SA, both for any constant epsilon>0, and (iii) an O{k^2}-approximation algorithm for k-SA (in expectation). The three distributed algorithms compute a solution with high probability and terminate in O(k^2 *log^3(n)) rounds.
Cite as

Magnús M. Halldórsson, Sven Köhler, and Dror Rawitz. Distributed Approximation of k-Service Assignment. In 19th International Conference on Principles of Distributed Systems (OPODIS 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 46, pp. 11:1-11:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{halldorsson_et_al:LIPIcs.OPODIS.2015.11,
  author =	{Halld\'{o}rsson, Magn\'{u}s M. and K\"{o}hler, Sven and Rawitz, Dror},
  title =	{{Distributed Approximation of k-Service Assignment}},
  booktitle =	{19th International Conference on Principles of Distributed Systems (OPODIS 2015)},
  pages =	{11:1--11:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-98-9},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{46},
  editor =	{Anceaume, Emmanuelle and Cachin, Christian and Potop-Butucaru, Maria},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2015.11},
  URN =		{urn:nbn:de:0030-drops-66024},
  doi =		{10.4230/LIPIcs.OPODIS.2015.11},
  annote =	{Keywords: approximation algorithms, distributed algorithms, related machines}
}
Document
DOI: 10.4230/LIPIcs.FSTTCS.2015.529
The Price of Local Power Control in Wireless Scheduling

Authors: Magnús M. Halldórsson and Tigran Tonoyan

Published in: LIPIcs, Volume 45, 35th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2015)

Abstract
We consider the problem of scheduling wireless links in the physical model, where we seek an assignment of power levels and a partition of the given set of links into the minimum number of subsets satisfying the signal-to-interference-and-noise-ratio (SINR) constraints. Specifically, we are interested in the efficiency of local power assignment schemes, or oblivious power schemes, in approximating wireless scheduling. Oblivious power schemes are motivated by networking scenarios when power levels must be decided in advance, and not as part of the scheduling computation. We present the first O(log log Delta)-approximation algorithm, which is known to be best possible (in terms of Delta) for oblivious power schemes, where Delta is the longest to shortest link length ratio. We achieve this by representing interference by a conflict graph, which allows the application of graph-theoretic results for a variety of related problems, including the weighted capacity problem. We explore further the contours of approximability and find the choice of power assignment matters; that not all metric spaces are equal; and that the presence of weak links makes the problem harder. Combined, our results resolve the price of local power for wireless scheduling, or the value of allowing unfettered power control.
Cite as

Magnús M. Halldórsson and Tigran Tonoyan. The Price of Local Power Control in Wireless Scheduling. In 35th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 45, pp. 529-542, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)

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@InProceedings{halldorsson_et_al:LIPIcs.FSTTCS.2015.529,
  author =	{Halld\'{o}rsson, Magn\'{u}s M. and Tonoyan, Tigran},
  title =	{{The Price of Local Power Control in Wireless Scheduling}},
  booktitle =	{35th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2015)},
  pages =	{529--542},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-97-2},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{45},
  editor =	{Harsha, Prahladh and Ramalingam, G.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2015.529},
  URN =		{urn:nbn:de:0030-drops-56243},
  doi =		{10.4230/LIPIcs.FSTTCS.2015.529},
  annote =	{Keywords: Wireless Scheduling, Physical Model, Oblivious Power}
}
Document
DOI: 10.4230/LIPIcs.STACS.2011.472
Online Scheduling with Interval Conflicts

Authors: Magnus M. Halldorsson, Boaz Patt-Shamir, and Dror Rawitz

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

Abstract
In the problem of Scheduling with Interval Conflicts, there is a ground set of items indexed by integers, and the input is a collection of conflicts, each containing all the items whose index lies within some interval on the real line. Conflicts arrive in an online fashion. A scheduling algorithm must select, from each conflict, at most one survivor item, and the goal is to maximize the number (or weight) of items that survive all the conflicts they are involved in. We present a centralized deterministic online algorithm whose competitive ratio is O(log sigma), where sigma is the size of the largest conflict. For the distributed setting, we present another deterministic algorithm whose competitive ratio is 2 log sigma, in the special contiguous case, in which the item indices constitute a contiguous interval of integers. Our upper bounds are complemented by two lower bounds: one that shows that even in the contiguous case, all deterministic algorithms (centralized or distributed) have competitive ratio Omega(log sigma), and that in the non-contiguous case, no deterministic oblivious algorithm (i.e., a distributed algorithm that does not use communication) can have a bounded competitive ratio.
Cite as

Magnus M. Halldorsson, Boaz Patt-Shamir, and Dror Rawitz. Online Scheduling with Interval Conflicts. In 28th International Symposium on Theoretical Aspects of Computer Science (STACS 2011). Leibniz International Proceedings in Informatics (LIPIcs), Volume 9, pp. 472-483, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2011)

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@InProceedings{halldorsson_et_al:LIPIcs.STACS.2011.472,
  author =	{Halldorsson, Magnus M. and Patt-Shamir, Boaz and Rawitz, Dror},
  title =	{{Online Scheduling with Interval Conflicts}},
  booktitle =	{28th International Symposium on Theoretical Aspects of Computer Science (STACS 2011)},
  pages =	{472--483},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-25-5},
  ISSN =	{1868-8969},
  year =	{2011},
  volume =	{9},
  editor =	{Schwentick, Thomas and D\"{u}rr, Christoph},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2011.472},
  URN =		{urn:nbn:de:0030-drops-30363},
  doi =		{10.4230/LIPIcs.STACS.2011.472},
  annote =	{Keywords: online scheduling, online set packing, interval conflicts, competitive analysis, compound tasks, distributed algorithms}
}

Halldórsson, Magnús M.

Document
DOI: 10.4230/LIPIcs.DISC.2024.24
Decentralized Distributed Graph Coloring II: Degree+1-Coloring Virtual Graphs

Authors: Maxime Flin, Magnús M. Halldórsson, and Alexandre Nolin

Published in: LIPIcs, Volume 319, 38th International Symposium on Distributed Computing (DISC 2024)

Abstract
Graph coloring is fundamental to distributed computing. We give the first general treatment of the coloring of virtual graphs, where the graph H to be colored is locally embedded within the communication graph G. Besides generalizing classical distributed graph coloring (where H = G), this captures other previously studied settings, including cluster graphs and power graphs. We find that the complexity of coloring a virtual graph depends linearly on the edge congestion of its embedding. The main question of interest is how fast we can color virtual graphs of constant congestion. We find that, surprisingly, these graphs can be colored nearly as fast as ordinary graphs. Namely, we give a O(log⁴log n)-round algorithm for the deg+1-coloring problem, where each node is assigned more colors than its degree. This can be viewed as a case where a distributed graph problem can be solved even when the operation of each node is decentralized.
Cite as

Maxime Flin, Magnús M. Halldórsson, and Alexandre Nolin. Decentralized Distributed Graph Coloring II: Degree+1-Coloring Virtual Graphs. In 38th International Symposium on Distributed Computing (DISC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 319, pp. 24:1-24:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{flin_et_al:LIPIcs.DISC.2024.24,
  author =	{Flin, Maxime and Halld\'{o}rsson, Magn\'{u}s M. and Nolin, Alexandre},
  title =	{{Decentralized Distributed Graph Coloring II: Degree+1-Coloring Virtual Graphs}},
  booktitle =	{38th International Symposium on Distributed Computing (DISC 2024)},
  pages =	{24:1--24:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-352-2},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{319},
  editor =	{Alistarh, Dan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2024.24},
  URN =		{urn:nbn:de:0030-drops-212502},
  doi =		{10.4230/LIPIcs.DISC.2024.24},
  annote =	{Keywords: Graph Coloring, Distributed Algorithms, Virtual Graphs, Congestion, Dilation}
}
Document
DOI: 10.4230/LIPIcs.DISC.2024.31
Distributed Delta-Coloring Under Bandwidth Limitations

Authors: Magnús M. Halldórsson and Yannic Maus

Published in: LIPIcs, Volume 319, 38th International Symposium on Distributed Computing (DISC 2024)

Abstract
We consider the problem of coloring graphs of maximum degree Δ with Δ colors in the distributed setting with limited bandwidth. Specifically, we give a polylog log n-round randomized algorithm in the CONGEST model. This is close to the lower bound of Ω(log log n) rounds from [Brandt et al., STOC '16], which holds also in the more powerful LOCAL model. The core of our algorithm is a reduction to several special instances of the constructive Lovász local lemma (LLL) and the deg+1-list coloring problem.
Cite as

Magnús M. Halldórsson and Yannic Maus. Distributed Delta-Coloring Under Bandwidth Limitations. In 38th International Symposium on Distributed Computing (DISC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 319, pp. 31:1-31:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{halldorsson_et_al:LIPIcs.DISC.2024.31,
  author =	{Halld\'{o}rsson, Magn\'{u}s M. and Maus, Yannic},
  title =	{{Distributed Delta-Coloring Under Bandwidth Limitations}},
  booktitle =	{38th International Symposium on Distributed Computing (DISC 2024)},
  pages =	{31:1--31:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-352-2},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{319},
  editor =	{Alistarh, Dan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2024.31},
  URN =		{urn:nbn:de:0030-drops-212572},
  doi =		{10.4230/LIPIcs.DISC.2024.31},
  annote =	{Keywords: Graph problems, Graph coloring, Lov\'{a}sz local lemma, LOCAL model, CONGEST model, Distributed computing}
}
Document
DOI: 10.4230/LIPIcs.DISC.2023.19
Fast Coloring Despite Congested Relays

Authors: Maxime Flin, Magnús M. Halldórsson, and Alexandre Nolin

Published in: LIPIcs, Volume 281, 37th International Symposium on Distributed Computing (DISC 2023)

Abstract
We provide a O(log⁶ log n)-round randomized algorithm for distance-2 coloring in CONGEST with Δ²+1 colors. For Δ≫polylog n, this improves exponentially on the O(logΔ+polylog log n) algorithm of [Halldórsson, Kuhn, Maus, Nolin, DISC'20].
Cite as

Maxime Flin, Magnús M. Halldórsson, and Alexandre Nolin. Fast Coloring Despite Congested Relays. In 37th International Symposium on Distributed Computing (DISC 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 281, pp. 19:1-19:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{flin_et_al:LIPIcs.DISC.2023.19,
  author =	{Flin, Maxime and Halld\'{o}rsson, Magn\'{u}s M. and Nolin, Alexandre},
  title =	{{Fast Coloring Despite Congested Relays}},
  booktitle =	{37th International Symposium on Distributed Computing (DISC 2023)},
  pages =	{19:1--19:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-301-0},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{281},
  editor =	{Oshman, Rotem},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2023.19},
  URN =		{urn:nbn:de:0030-drops-191453},
  doi =		{10.4230/LIPIcs.DISC.2023.19},
  annote =	{Keywords: CONGEST model, distributed graph coloring, power graphs}
}
Document
DOI: 10.4230/LIPIcs.DISC.2022.26
Fast Distributed Vertex Splitting with Applications

Authors: Magnús M. Halldórsson, Yannic Maus, and Alexandre Nolin

Published in: LIPIcs, Volume 246, 36th International Symposium on Distributed Computing (DISC 2022)

Abstract
We present poly log log n-round randomized distributed algorithms to compute vertex splittings, a partition of the vertices of a graph into k parts such that a node of degree d(u) has ≈ d(u)/k neighbors in each part. Our techniques can be seen as the first progress towards general poly log log n-round algorithms for the Lovász Local Lemma. As the main application of our result, we obtain a randomized poly log log n-round CONGEST algorithm for (1+ε)Δ-edge coloring n-node graphs of sufficiently large constant maximum degree Δ, for any ε > 0. Further, our results improve the computation of defective colorings and certain tight list coloring problems. All the results improve the state-of-the-art round complexity exponentially, even in the LOCAL model.
Cite as

Magnús M. Halldórsson, Yannic Maus, and Alexandre Nolin. Fast Distributed Vertex Splitting with Applications. In 36th International Symposium on Distributed Computing (DISC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 246, pp. 26:1-26:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{halldorsson_et_al:LIPIcs.DISC.2022.26,
  author =	{Halld\'{o}rsson, Magn\'{u}s M. and Maus, Yannic and Nolin, Alexandre},
  title =	{{Fast Distributed Vertex Splitting with Applications}},
  booktitle =	{36th International Symposium on Distributed Computing (DISC 2022)},
  pages =	{26:1--26:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-255-6},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{246},
  editor =	{Scheideler, Christian},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2022.26},
  URN =		{urn:nbn:de:0030-drops-172176},
  doi =		{10.4230/LIPIcs.DISC.2022.26},
  annote =	{Keywords: Graph problems, Edge coloring, List coloring, Lov\'{a}sz local lemma, LOCAL model, CONGEST model, Distributed computing}
}
Document
DOI: 10.4230/LIPIcs.DISC.2020.39
Coloring Fast Without Learning Your Neighbors' Colors

Authors: Magnús M. Halldórsson, Fabian Kuhn, Yannic Maus, and Alexandre Nolin

Published in: LIPIcs, Volume 179, 34th International Symposium on Distributed Computing (DISC 2020)

Abstract
We give an improved randomized CONGEST algorithm for distance-2 coloring that uses Δ²+1 colors and runs in O(log n) rounds, improving the recent O(log Δ ⋅ log n)-round algorithm in [Halldórsson, Kuhn, Maus; PODC '20]. We then improve the time complexity to O(log Δ) + 2^{O(√{log log n})}.
Cite as

Magnús M. Halldórsson, Fabian Kuhn, Yannic Maus, and Alexandre Nolin. Coloring Fast Without Learning Your Neighbors' Colors. In 34th International Symposium on Distributed Computing (DISC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 179, pp. 39:1-39:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{halldorsson_et_al:LIPIcs.DISC.2020.39,
  author =	{Halld\'{o}rsson, Magn\'{u}s M. and Kuhn, Fabian and Maus, Yannic and Nolin, Alexandre},
  title =	{{Coloring Fast Without Learning Your Neighbors' Colors}},
  booktitle =	{34th International Symposium on Distributed Computing (DISC 2020)},
  pages =	{39:1--39:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-168-9},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{179},
  editor =	{Attiya, Hagit},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2020.39},
  URN =		{urn:nbn:de:0030-drops-131170},
  doi =		{10.4230/LIPIcs.DISC.2020.39},
  annote =	{Keywords: distributed graph coloring, distance 2 coloring, congestion}
}
Document
DOI: 10.4230/LIPIcs.DISC.2019.14
The Capacity of Smartphone Peer-To-Peer Networks

Authors: Michael Dinitz, Magnús M. Halldórsson, Calvin Newport, and Alex Weaver

Published in: LIPIcs, Volume 146, 33rd International Symposium on Distributed Computing (DISC 2019)

Abstract
We study three capacity problems in the mobile telephone model, a network abstraction that models the peer-to-peer communication capabilities implemented in most commodity smartphone operating systems. The capacity of a network expresses how much sustained throughput can be maintained for a set of communication demands, and is therefore a fundamental bound on the usefulness of a network. Because of this importance, wireless network capacity has been active area of research for the last two decades. The three capacity problems that we study differ in the structure of the communication demands. The first problem is pairwise capacity, where the demands are (source, destination) pairs. Pairwise capacity is one of the most classical definitions, as it was analyzed in the seminal paper of Gupta and Kumar on wireless network capacity. The second problem we study is broadcast capacity, in which a single source must deliver packets to all other nodes in the network. Finally, we turn our attention to all-to-all capacity, in which all nodes must deliver packets to all other nodes. In all three of these problems we characterize the optimal achievable throughput for any given network, and design algorithms which asymptotically match this performance. We also study these problems in networks generated randomly by a process introduced by Gupta and Kumar, and fully characterize their achievable throughput. Interestingly, the techniques that we develop for all-to-all capacity also allow us to design a one-shot gossip algorithm that runs within a polylogarithmic factor of optimal in every graph. This largely resolves an open question from previous work on the one-shot gossip problem in this model.
Cite as

Michael Dinitz, Magnús M. Halldórsson, Calvin Newport, and Alex Weaver. The Capacity of Smartphone Peer-To-Peer Networks. In 33rd International Symposium on Distributed Computing (DISC 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 146, pp. 14:1-14:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{dinitz_et_al:LIPIcs.DISC.2019.14,
  author =	{Dinitz, Michael and Halld\'{o}rsson, Magn\'{u}s M. and Newport, Calvin and Weaver, Alex},
  title =	{{The Capacity of Smartphone Peer-To-Peer Networks}},
  booktitle =	{33rd International Symposium on Distributed Computing (DISC 2019)},
  pages =	{14:1--14:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-126-9},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{146},
  editor =	{Suomela, Jukka},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2019.14},
  URN =		{urn:nbn:de:0030-drops-113218},
  doi =		{10.4230/LIPIcs.DISC.2019.14},
  annote =	{Keywords: Capacity, Wireless, Mobile Telephone, Throughput}
}
Document
DOI: 10.4230/LIPIcs.MFCS.2019.7
Query-Competitive Sorting with Uncertainty

Authors: Magnús M. Halldórsson and Murilo Santos de Lima

Published in: LIPIcs, Volume 138, 44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019)

Abstract
We study the problem of sorting under incomplete information, when queries are used to resolve uncertainties. Each of n data items has an unknown value, which is known to lie in a given interval. We can pay a query cost to learn the actual value, and we may allow an error threshold in the sorting. The goal is to find a nearly-sorted permutation by performing a minimum-cost set of queries. We show that an offline optimum query set can be found in polynomial time, and that both oblivious and adaptive problems have simple query-competitive algorithms. The query-competitiveness for the oblivious problem is n for uniform query costs, and unbounded for arbitrary costs; for the adaptive problem, the ratio is 2. We then present a unified adaptive strategy for uniform query costs that yields: (i) a 3/2-query-competitive randomized algorithm; (ii) a 5/3-query-competitive deterministic algorithm if the dependency graph has no 2-components after some preprocessing, which has query-competitive ratio 3/2 + O(1/k) if the components obtained have size at least k; (iii) an exact algorithm if the intervals constitute a laminar family. The first two results have matching lower bounds, and we have a lower bound of 7/5 for large components. We also show that the advice complexity of the adaptive problem is floor[n/2] if no error threshold is allowed, and ceil[n/3 * lg 3] for the general case.
Cite as

Magnús M. Halldórsson and Murilo Santos de Lima. Query-Competitive Sorting with Uncertainty. In 44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 138, pp. 7:1-7:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{halldorsson_et_al:LIPIcs.MFCS.2019.7,
  author =	{Halld\'{o}rsson, Magn\'{u}s M. and de Lima, Murilo Santos},
  title =	{{Query-Competitive Sorting with Uncertainty}},
  booktitle =	{44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019)},
  pages =	{7:1--7:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-117-7},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{138},
  editor =	{Rossmanith, Peter and Heggernes, Pinar and Katoen, Joost-Pieter},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2019.7},
  URN =		{urn:nbn:de:0030-drops-109519},
  doi =		{10.4230/LIPIcs.MFCS.2019.7},
  annote =	{Keywords: online algorithms, sorting, randomized algorithms, advice complexity, threshold tolerance graphs}
}
Document
DOI: 10.4230/LIPIcs.ICALP.2018.158
Spanning Trees With Edge Conflicts and Wireless Connectivity

Authors: Magnús M. Halldórsson, Guy Kortsarz, Pradipta Mitra, and Tigran Tonoyan

Published in: LIPIcs, Volume 107, 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)

Abstract
We introduce the problem of finding a spanning tree along with a partition of the tree edges into fewest number of feasible sets, where constraints on the edges define feasibility. The motivation comes from wireless networking, where we seek to model the irregularities seen in actual wireless environments. Not all node pairs may be able to communicate, even if geographically close - thus, the available pairs are specified with a link graph {L}=(V,E). Also, signal attenuation need not follow a nice geometric formula - hence, interference is modeled by a conflict (hyper)graph {C}=(E,F) on the links. The objective is to maximize the efficiency of the communication, or equivalently, to minimize the length of a schedule of the tree edges in the form of a coloring. We find that in spite of all this generality, the problem can be approximated linearly in terms of a versatile parameter, the inductive independence of the interference graph. Specifically, we give a simple algorithm that attains a O(rho log n)-approximation, where n is the number of nodes and rho is the inductive independence, and show that near-linear dependence on rho is also necessary. We also treat an extension to Steiner trees, modeling multicasting, and obtain a comparable result. Our results suggest that several canonical assumptions of geometry, regularity and "niceness" in wireless settings can sometimes be relaxed without a significant hit in algorithm performance.
Cite as

Magnús M. Halldórsson, Guy Kortsarz, Pradipta Mitra, and Tigran Tonoyan. Spanning Trees With Edge Conflicts and Wireless Connectivity. In 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 107, pp. 158:1-158:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{halldorsson_et_al:LIPIcs.ICALP.2018.158,
  author =	{Halld\'{o}rsson, Magn\'{u}s M. and Kortsarz, Guy and Mitra, Pradipta and Tonoyan, Tigran},
  title =	{{Spanning Trees With Edge Conflicts and Wireless Connectivity}},
  booktitle =	{45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)},
  pages =	{158:1--158:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-076-7},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{107},
  editor =	{Chatzigiannakis, Ioannis and Kaklamanis, Christos and Marx, D\'{a}niel and Sannella, Donald},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2018.158},
  URN =		{urn:nbn:de:0030-drops-91627},
  doi =		{10.4230/LIPIcs.ICALP.2018.158},
  annote =	{Keywords: spanning trees, wireless capacity, aggregation, approximation algorithms}
}
Document
DOI: 10.4230/LIPIcs.DISC.2017.25
An Efficient Communication Abstraction for Dense Wireless Networks

Authors: Magnús M. Halldórsson, Fabian Kuhn, Nancy Lynch, and Calvin Newport

Published in: LIPIcs, Volume 91, 31st International Symposium on Distributed Computing (DISC 2017)

Abstract
In this paper we study the problem of developing efficient distributed algorithms for dense wireless networks. For many problems in this setting, fast solutions must leverage the reality that radio signals fade with distance, which can be exploited to enable concurrent communication among multiple sender/receiver pairs. To simplify the development of these algorithms we describe a new communication abstraction called FadingMAC which exposes the benefits of this concurrent communication, but also hides the details of the underlying low-level radio signal behavior. This approach splits efforts between those who develop useful algorithms that run on the abstraction, and those who implement the abstraction in concrete low-level wireless models, or on real hardware. After defining FadingMAC, we describe and analyze an efficient implementation of the abstraction in a standard low-level SINR-style network model. We then describe solutions to the following problems that run on the abstraction: max, min, sum, and mean computed over input values; process renaming; consensus and leader election; and optimal packet scheduling. Combining our abstraction implementation with these applications that run on the abstraction, we obtain near-optimal solutions to these problems in our low-level SINR model - significantly advancing the known results for distributed algorithms in this setting. Of equal importance to these concrete bounds, however, is the general idea advanced by this paper: as wireless networks become more dense, both theoreticians and practitioners must explore new communication abstractions that can help tame this density.
Cite as

Magnús M. Halldórsson, Fabian Kuhn, Nancy Lynch, and Calvin Newport. An Efficient Communication Abstraction for Dense Wireless Networks. In 31st International Symposium on Distributed Computing (DISC 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 91, pp. 25:1-25:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{halldorsson_et_al:LIPIcs.DISC.2017.25,
  author =	{Halld\'{o}rsson, Magn\'{u}s M. and Kuhn, Fabian and Lynch, Nancy and Newport, Calvin},
  title =	{{An Efficient Communication Abstraction for Dense Wireless Networks}},
  booktitle =	{31st International Symposium on Distributed Computing (DISC 2017)},
  pages =	{25:1--25:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-053-8},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{91},
  editor =	{Richa, Andr\'{e}a},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2017.25},
  URN =		{urn:nbn:de:0030-drops-79898},
  doi =		{10.4230/LIPIcs.DISC.2017.25},
  annote =	{Keywords: wireless networks, abstractions, SINR, signal fading}
}
Document
DOI: 10.4230/LIPIcs.ICALP.2017.129
Universal Framework for Wireless Scheduling Problems

Authors: Eyjólfur I. Ásgeirsson, Magnús M. Halldórsson, and Tigran Tonoyan

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

Abstract
An overarching issue in resource management of wireless networks is assessing their capacity: How much communication can be achieved in a network, utilizing all the tools available: power control, scheduling, routing, channel assignment and rate adjustment? We propose the first framework for approximation algorithms in the physical model that addresses these questions in full, including rate control. The approximations obtained are doubly logarithmic in the link length and rate diversity. Where previous bounds are known, this gives an exponential improvement. A key contribution is showing that the complex interference relationship of the physical model can be simplified into a novel type of amenable conflict graphs, at a small cost. We also show that the approximation obtained is provably the best possible for any conflict graph formulation.
Cite as

Eyjólfur I. Ásgeirsson, Magnús M. Halldórsson, and Tigran Tonoyan. Universal Framework for Wireless Scheduling Problems. In 44th International Colloquium on Automata, Languages, and Programming (ICALP 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 80, pp. 129:1-129:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{asgeirsson_et_al:LIPIcs.ICALP.2017.129,
  author =	{\'{A}sgeirsson, Eyj\'{o}lfur I. and Halld\'{o}rsson, Magn\'{u}s M. and Tonoyan, Tigran},
  title =	{{Universal Framework for Wireless Scheduling Problems}},
  booktitle =	{44th International Colloquium on Automata, Languages, and Programming (ICALP 2017)},
  pages =	{129:1--129:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-041-5},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{80},
  editor =	{Chatzigiannakis, Ioannis and Indyk, Piotr and Kuhn, Fabian and Muscholl, Anca},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2017.129},
  URN =		{urn:nbn:de:0030-drops-74228},
  doi =		{10.4230/LIPIcs.ICALP.2017.129},
  annote =	{Keywords: Wireless, Scheduling, Physical Model, Approximation framework}
}
Document
DOI: 10.4230/LIPIcs.OPODIS.2015.11
Distributed Approximation of k-Service Assignment

Authors: Magnús M. Halldórsson, Sven Köhler, and Dror Rawitz

Published in: LIPIcs, Volume 46, 19th International Conference on Principles of Distributed Systems (OPODIS 2015)

Abstract
We consider the k-Service Assignment problem (k-SA), defined as follows. The input consists of a network that contains servers and clients, and an integer k. Each server has a finite capacity, and each client is associated with a demand and a profit. A feasible solution is an assignment of clients to neighboring servers such that (i) the total demand assigned to a server is at most its capacity, and (ii) a client is assigned either to k servers or to none. The profit of an assignment is the total profit of clients that are assigned to k servers, and the goal is to find a maximum profit assignment. In the r-restricted version of k-SA, no client requires more than an r-fraction of the capacity of any adjacent server. The k-SA problem is motivated by backup placement in networks and by resource allocation in 4G cellular networks. It can also be viewed as machine scheduling on related machines with assignment restrictions. We present a centralized polynomial time greedy (k+1-r)/(1-r)-approximation algorithm for r-restricted k-SA. We then show that a variant of this algorithm achieves an approximation ratio of k+1 using a resource augmentation factor of 1+r. We use the latter to present a (k+1)^2-approximation algorithm for k-SA. In the distributed setting, we present: (i) a (1+epsilon)*(k +1-r)/(1-r)-approximation algorithm for r-restricted k-SA, (ii) a (1+epsilon)(k+1)-approximation algorithm that uses a resource augmentation factor of 1+r for r-restricted k-SA, both for any constant epsilon>0, and (iii) an O{k^2}-approximation algorithm for k-SA (in expectation). The three distributed algorithms compute a solution with high probability and terminate in O(k^2 *log^3(n)) rounds.
Cite as

Magnús M. Halldórsson, Sven Köhler, and Dror Rawitz. Distributed Approximation of k-Service Assignment. In 19th International Conference on Principles of Distributed Systems (OPODIS 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 46, pp. 11:1-11:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{halldorsson_et_al:LIPIcs.OPODIS.2015.11,
  author =	{Halld\'{o}rsson, Magn\'{u}s M. and K\"{o}hler, Sven and Rawitz, Dror},
  title =	{{Distributed Approximation of k-Service Assignment}},
  booktitle =	{19th International Conference on Principles of Distributed Systems (OPODIS 2015)},
  pages =	{11:1--11:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-98-9},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{46},
  editor =	{Anceaume, Emmanuelle and Cachin, Christian and Potop-Butucaru, Maria},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2015.11},
  URN =		{urn:nbn:de:0030-drops-66024},
  doi =		{10.4230/LIPIcs.OPODIS.2015.11},
  annote =	{Keywords: approximation algorithms, distributed algorithms, related machines}
}
Document
DOI: 10.4230/LIPIcs.FSTTCS.2015.529
The Price of Local Power Control in Wireless Scheduling

Authors: Magnús M. Halldórsson and Tigran Tonoyan

Published in: LIPIcs, Volume 45, 35th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2015)

Abstract
We consider the problem of scheduling wireless links in the physical model, where we seek an assignment of power levels and a partition of the given set of links into the minimum number of subsets satisfying the signal-to-interference-and-noise-ratio (SINR) constraints. Specifically, we are interested in the efficiency of local power assignment schemes, or oblivious power schemes, in approximating wireless scheduling. Oblivious power schemes are motivated by networking scenarios when power levels must be decided in advance, and not as part of the scheduling computation. We present the first O(log log Delta)-approximation algorithm, which is known to be best possible (in terms of Delta) for oblivious power schemes, where Delta is the longest to shortest link length ratio. We achieve this by representing interference by a conflict graph, which allows the application of graph-theoretic results for a variety of related problems, including the weighted capacity problem. We explore further the contours of approximability and find the choice of power assignment matters; that not all metric spaces are equal; and that the presence of weak links makes the problem harder. Combined, our results resolve the price of local power for wireless scheduling, or the value of allowing unfettered power control.
Cite as

Magnús M. Halldórsson and Tigran Tonoyan. The Price of Local Power Control in Wireless Scheduling. In 35th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 45, pp. 529-542, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)

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@InProceedings{halldorsson_et_al:LIPIcs.FSTTCS.2015.529,
  author =	{Halld\'{o}rsson, Magn\'{u}s M. and Tonoyan, Tigran},
  title =	{{The Price of Local Power Control in Wireless Scheduling}},
  booktitle =	{35th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2015)},
  pages =	{529--542},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-97-2},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{45},
  editor =	{Harsha, Prahladh and Ramalingam, G.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2015.529},
  URN =		{urn:nbn:de:0030-drops-56243},
  doi =		{10.4230/LIPIcs.FSTTCS.2015.529},
  annote =	{Keywords: Wireless Scheduling, Physical Model, Oblivious Power}
}
Document
DOI: 10.4230/LIPIcs.STACS.2011.472
Online Scheduling with Interval Conflicts

Authors: Magnus M. Halldorsson, Boaz Patt-Shamir, and Dror Rawitz

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

Abstract
In the problem of Scheduling with Interval Conflicts, there is a ground set of items indexed by integers, and the input is a collection of conflicts, each containing all the items whose index lies within some interval on the real line. Conflicts arrive in an online fashion. A scheduling algorithm must select, from each conflict, at most one survivor item, and the goal is to maximize the number (or weight) of items that survive all the conflicts they are involved in. We present a centralized deterministic online algorithm whose competitive ratio is O(log sigma), where sigma is the size of the largest conflict. For the distributed setting, we present another deterministic algorithm whose competitive ratio is 2 log sigma, in the special contiguous case, in which the item indices constitute a contiguous interval of integers. Our upper bounds are complemented by two lower bounds: one that shows that even in the contiguous case, all deterministic algorithms (centralized or distributed) have competitive ratio Omega(log sigma), and that in the non-contiguous case, no deterministic oblivious algorithm (i.e., a distributed algorithm that does not use communication) can have a bounded competitive ratio.
Cite as

Magnus M. Halldorsson, Boaz Patt-Shamir, and Dror Rawitz. Online Scheduling with Interval Conflicts. In 28th International Symposium on Theoretical Aspects of Computer Science (STACS 2011). Leibniz International Proceedings in Informatics (LIPIcs), Volume 9, pp. 472-483, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2011)

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@InProceedings{halldorsson_et_al:LIPIcs.STACS.2011.472,
  author =	{Halldorsson, Magnus M. and Patt-Shamir, Boaz and Rawitz, Dror},
  title =	{{Online Scheduling with Interval Conflicts}},
  booktitle =	{28th International Symposium on Theoretical Aspects of Computer Science (STACS 2011)},
  pages =	{472--483},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-25-5},
  ISSN =	{1868-8969},
  year =	{2011},
  volume =	{9},
  editor =	{Schwentick, Thomas and D\"{u}rr, Christoph},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2011.472},
  URN =		{urn:nbn:de:0030-drops-30363},
  doi =		{10.4230/LIPIcs.STACS.2011.472},
  annote =	{Keywords: online scheduling, online set packing, interval conflicts, competitive analysis, compound tasks, distributed algorithms}
}
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