6 Search Results for "Tonoyan, Tigran"

Document
DOI: 10.4230/LIPIcs.ITCS.2022.36
Distributed Vertex Cover Reconfiguration

Authors: Keren Censor-Hillel, Yannic Maus, Shahar Romem-Peled, and Tigran Tonoyan

Published in: LIPIcs, Volume 215, 13th Innovations in Theoretical Computer Science Conference (ITCS 2022)

Abstract
Reconfiguration schedules, i.e., sequences that gradually transform one solution of a problem to another while always maintaining feasibility, have been extensively studied. Most research has dealt with the decision problem of whether a reconfiguration schedule exists, and the complexity of finding one. A prime example is the reconfiguration of vertex covers. We initiate the study of batched vertex cover reconfiguration, which allows to reconfigure multiple vertices concurrently while requiring that any adversarial reconfiguration order within a batch maintains feasibility. The latter provides robustness, e.g., if the simultaneous reconfiguration of a batch cannot be guaranteed. The quality of a schedule is measured by the number of batches until all nodes are reconfigured, and its cost, i.e., the maximum size of an intermediate vertex cover. To set a baseline for batch reconfiguration, we show that for graphs belonging to one of the classes {{cycles, trees, forests, chordal, cactus, even-hole-free, claw-free}}, there are schedules that use O(ε^{-1}) batches and incur only a 1+ε multiplicative increase in cost over the best sequential schedules. Our main contribution is to compute such batch schedules in a distributed setting O(ε^{-1} {log^*} n) rounds, which we also show to be tight. Further, we show that once we step out of these graph classes we face a very different situation. There are graph classes on which no efficient distributed algorithm can obtain the best (or almost best) existing schedule. Moreover, there are classes of bounded degree graphs which do not admit any reconfiguration schedules without incurring a large multiplicative increase in the cost at all.
Cite as

Keren Censor-Hillel, Yannic Maus, Shahar Romem-Peled, and Tigran Tonoyan. Distributed Vertex Cover Reconfiguration. In 13th Innovations in Theoretical Computer Science Conference (ITCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 215, pp. 36:1-36:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{censorhillel_et_al:LIPIcs.ITCS.2022.36,
  author =	{Censor-Hillel, Keren and Maus, Yannic and Romem-Peled, Shahar and Tonoyan, Tigran},
  title =	{{Distributed Vertex Cover Reconfiguration}},
  booktitle =	{13th Innovations in Theoretical Computer Science Conference (ITCS 2022)},
  pages =	{36:1--36:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-217-4},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{215},
  editor =	{Braverman, Mark},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2022.36},
  URN =		{urn:nbn:de:0030-drops-156327},
  doi =		{10.4230/LIPIcs.ITCS.2022.36},
  annote =	{Keywords: reconfiguration, vertex cover, network decomposition}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2021.46
Fault Tolerant Max-Cut

Authors: Keren Censor-Hillel, Noa Marelly, Roy Schwartz, and Tigran Tonoyan

Published in: LIPIcs, Volume 198, 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)

Abstract
In this work, we initiate the study of fault tolerant Max-Cut, where given an edge-weighted undirected graph G = (V,E), the goal is to find a cut S ⊆ V that maximizes the total weight of edges that cross S even after an adversary removes k vertices from G. We consider two types of adversaries: an adaptive adversary that sees the outcome of the random coin tosses used by the algorithm, and an oblivious adversary that does not. For any constant number of failures k we present an approximation of (0.878-ε) against an adaptive adversary and of α_{GW}≈ 0.8786 against an oblivious adversary (here α_{GW} is the approximation achieved by the random hyperplane algorithm of [Goemans-Williamson J. ACM `95]). Additionally, we present a hardness of approximation of α_{GW} against both types of adversaries, rendering our results (virtually) tight. The non-linear nature of the fault tolerant objective makes the design and analysis of algorithms harder when compared to the classic Max-Cut. Hence, we employ approaches ranging from multi-objective optimization to LP duality and the ellipsoid algorithm to obtain our results.
Cite as

Keren Censor-Hillel, Noa Marelly, Roy Schwartz, and Tigran Tonoyan. Fault Tolerant Max-Cut. In 48th International Colloquium on Automata, Languages, and Programming (ICALP 2021). Leibniz International Proceedings in Informatics (LIPIcs), Volume 198, pp. 46:1-46:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2021)

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@InProceedings{censorhillel_et_al:LIPIcs.ICALP.2021.46,
  author =	{Censor-Hillel, Keren and Marelly, Noa and Schwartz, Roy and Tonoyan, Tigran},
  title =	{{Fault Tolerant Max-Cut}},
  booktitle =	{48th International Colloquium on Automata, Languages, and Programming (ICALP 2021)},
  pages =	{46:1--46:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-195-5},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{198},
  editor =	{Bansal, Nikhil and Merelli, Emanuela and Worrell, James},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2021.46},
  URN =		{urn:nbn:de:0030-drops-141158},
  doi =		{10.4230/LIPIcs.ICALP.2021.46},
  annote =	{Keywords: fault-tolerance, max-cut, approximation}
}
Document
DOI: 10.4230/LIPIcs.DISC.2020.16
Local Conflict Coloring Revisited: Linial for Lists

Authors: Yannic Maus and Tigran Tonoyan

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

Abstract
Linial’s famous color reduction algorithm reduces a given m-coloring of a graph with maximum degree Δ to a O(Δ²log m)-coloring, in a single round in the LOCAL model. We show a similar result when nodes are restricted to choose their color from a list of allowed colors: given an m-coloring in a directed graph of maximum outdegree β, if every node has a list of size Ω(β² (log β+log log m + log log |𝒞|)) from a color space 𝒞 then they can select a color in two rounds in the LOCAL model. Moreover, the communication of a node essentially consists of sending its list to the neighbors. This is obtained as part of a framework that also contains Linial’s color reduction (with an alternative proof) as a special case. Our result also leads to a defective list coloring algorithm. As a corollary, we improve the state-of-the-art truly local (deg+1)-list coloring algorithm from Barenboim et al. [PODC'18] by slightly reducing the runtime to O(√{ΔlogΔ})+log^* n and significantly reducing the message size (from huge to roughly Δ). Our techniques are inspired by the local conflict coloring framework of Fraigniaud et al. [FOCS'16].
Cite as

Yannic Maus and Tigran Tonoyan. Local Conflict Coloring Revisited: Linial for Lists. In 34th International Symposium on Distributed Computing (DISC 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 179, pp. 16:1-16:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{maus_et_al:LIPIcs.DISC.2020.16,
  author =	{Maus, Yannic and Tonoyan, Tigran},
  title =	{{Local Conflict Coloring Revisited: Linial for Lists}},
  booktitle =	{34th International Symposium on Distributed Computing (DISC 2020)},
  pages =	{16:1--16:18},
  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-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2020.16},
  URN =		{urn:nbn:de:0030-drops-130944},
  doi =		{10.4230/LIPIcs.DISC.2020.16},
  annote =	{Keywords: distributed graph coloring, list coloring, low intersecting set families}
}
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-dev.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.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-dev.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.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-dev.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}
}
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