22 Search Results for "Dinitz, Michael"

Document
DOI: 10.4230/LIPIcs.ITCS.2023.20
Epic Fail: Emulators Can Tolerate Polynomially Many Edge Faults for Free

Authors: Greg Bodwin, Michael Dinitz, and Yasamin Nazari

Published in: LIPIcs, Volume 251, 14th Innovations in Theoretical Computer Science Conference (ITCS 2023)

Abstract
A t-emulator of a graph G is a graph H that approximates its pairwise shortest path distances up to multiplicative t error. We study fault tolerant t-emulators, under the model recently introduced by Bodwin, Dinitz, and Nazari [ITCS 2022] for vertex failures. In this paper we consider the version for edge failures, and show that they exhibit surprisingly different behavior. In particular, our main result is that, for (2k-1)-emulators with k odd, we can tolerate a polynomial number of edge faults for free. For example: for any n-node input graph, we construct a 5-emulator (k = 3) on O(n^{4/3}) edges that is robust to f = O(n^{2/9}) edge faults. It is well known that Ω(n^{4/3}) edges are necessary even if the 5-emulator does not need to tolerate any faults. Thus we pay no extra cost in the size to gain this fault tolerance. We leave open the precise range of free fault tolerance for odd k, and whether a similar phenomenon can be proved for even k.
Cite as

Greg Bodwin, Michael Dinitz, and Yasamin Nazari. Epic Fail: Emulators Can Tolerate Polynomially Many Edge Faults for Free. In 14th Innovations in Theoretical Computer Science Conference (ITCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 251, pp. 20:1-20:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{bodwin_et_al:LIPIcs.ITCS.2023.20,
  author =	{Bodwin, Greg and Dinitz, Michael and Nazari, Yasamin},
  title =	{{Epic Fail: Emulators Can Tolerate Polynomially Many Edge Faults for Free}},
  booktitle =	{14th Innovations in Theoretical Computer Science Conference (ITCS 2023)},
  pages =	{20:1--20:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-263-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{251},
  editor =	{Tauman Kalai, Yael},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2023.20},
  URN =		{urn:nbn:de:0030-drops-175231},
  doi =		{10.4230/LIPIcs.ITCS.2023.20},
  annote =	{Keywords: Emulators, Fault Tolerance, Girth Conjecture}
}
Document
DOI: 10.4230/LIPIcs.DISC.2022.18
Smoothed Analysis of Information Spreading in Dynamic Networks

Authors: Michael Dinitz, Jeremy Fineman, Seth Gilbert, and Calvin Newport

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

Abstract
The best known solutions for k-message broadcast in dynamic networks of size n require Ω(nk) rounds. In this paper, we see if these bounds can be improved by smoothed analysis. To do so, we study perhaps the most natural randomized algorithm for disseminating tokens in this setting: at every time step, choose a token to broadcast randomly from the set of tokens you know. We show that with even a small amount of smoothing (i.e., one random edge added per round), this natural strategy solves k-message broadcast in Õ(n+k³) rounds, with high probability, beating the best known bounds for k = o(√n) and matching the Ω(n+k) lower bound for static networks for k = O(n^{1/3}) (ignoring logarithmic factors). In fact, the main result we show is even stronger and more general: given 𝓁-smoothing (i.e., 𝓁 random edges added per round), this simple strategy terminates in O(kn^{2/3}log^{1/3}(n)𝓁^{-1/3}) rounds. We then prove this analysis close to tight with an almost-matching lower bound. To better understand the impact of smoothing on information spreading, we next turn our attention to static networks, proving a tight bound of Õ(k√n) rounds to solve k-message broadcast, which is better than what our strategy can achieve in the dynamic setting. This confirms the intuition that although smoothed analysis reduces the difficulties induced by changing graph structures, it does not eliminate them altogether. Finally, we apply tools developed to support our smoothed analysis to prove an optimal result for k-message broadcast in so-called well-mixed networks in the absence of smoothing. By comparing this result to an existing lower bound for well-mixed networks, we establish a formal separation between oblivious and strongly adaptive adversaries with respect to well-mixed token spreading, partially resolving an open question on the impact of adversary strength on the k-message broadcast problem.
Cite as

Michael Dinitz, Jeremy Fineman, Seth Gilbert, and Calvin Newport. Smoothed Analysis of Information Spreading in Dynamic Networks. In 36th International Symposium on Distributed Computing (DISC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 246, pp. 18:1-18:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{dinitz_et_al:LIPIcs.DISC.2022.18,
  author =	{Dinitz, Michael and Fineman, Jeremy and Gilbert, Seth and Newport, Calvin},
  title =	{{Smoothed Analysis of Information Spreading in Dynamic Networks}},
  booktitle =	{36th International Symposium on Distributed Computing (DISC 2022)},
  pages =	{18:1--18:22},
  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-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2022.18},
  URN =		{urn:nbn:de:0030-drops-172094},
  doi =		{10.4230/LIPIcs.DISC.2022.18},
  annote =	{Keywords: Smoothed Analysis, Dynamic networks, Gossip}
}
Document
Brief Announcement
DOI: 10.4230/LIPIcs.DISC.2022.42
Brief Announcement: Minimizing Congestion in Hybrid Demand-Aware Network Topologies

Authors: Wenkai Dai, Michael Dinitz, Klaus-Tycho Foerster, and Stefan Schmid

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

Abstract
Emerging reconfigurable optical communication technologies enable demand-aware networks: networks whose static topology can be enhanced with demand-aware links optimized towards the traffic pattern the network serves. This paper studies the algorithmic problem of how to jointly optimize the topology and the routing in such demand-aware networks, to minimize congestion. We investigate this problem along two dimensions: (1) whether flows are splittable or unsplittable, and (2) whether routing on the hybrid topology is segregated or not, i.e., whether or not flows either have to use exclusively either the static network or the demand-aware connections. For splittable and segregated routing, we show that the problem is 2-approximable in general, but APX-hard even for uniform demands induced by a bipartite demand graph. For unsplittable and segregated routing, we show an upper bound of O(log m/ log log m) and a lower bound of Ω(log m/ log log m) for polynomial-time approximation algorithms, where m is the number of static links. Under splittable (resp., unsplittable) and non-segregated routing, even for demands of a single source (resp., destination), the problem cannot be approximated better than Ω(c_{max}/c_{min}) unless P=NP, where c_{max} (resp., c_{min}) denotes the maximum (resp., minimum) capacity. It is still NP-hard for uniform capacities, but can be solved efficiently for a single commodity and uniform capacities.
Cite as

Wenkai Dai, Michael Dinitz, Klaus-Tycho Foerster, and Stefan Schmid. Brief Announcement: Minimizing Congestion in Hybrid Demand-Aware Network Topologies. In 36th International Symposium on Distributed Computing (DISC 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 246, pp. 42:1-42:3, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{dai_et_al:LIPIcs.DISC.2022.42,
  author =	{Dai, Wenkai and Dinitz, Michael and Foerster, Klaus-Tycho and Schmid, Stefan},
  title =	{{Brief Announcement: Minimizing Congestion in Hybrid Demand-Aware Network Topologies}},
  booktitle =	{36th International Symposium on Distributed Computing (DISC 2022)},
  pages =	{42:1--42:3},
  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-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2022.42},
  URN =		{urn:nbn:de:0030-drops-172330},
  doi =		{10.4230/LIPIcs.DISC.2022.42},
  annote =	{Keywords: Congestion, Reconfigurable Networks, Algorithms, Complexity}
}
Document
APPROX
DOI: 10.4230/LIPIcs.APPROX/RANDOM.2022.41
Relative Survivable Network Design

Authors: Michael Dinitz, Ama Koranteng, and Guy Kortsarz

Published in: LIPIcs, Volume 245, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2022)

Abstract
One of the most important and well-studied settings for network design is edge-connectivity requirements. This encompasses uniform demands such as the Minimum k-Edge-Connected Spanning Subgraph problem (k-ECSS), as well as nonuniform demands such as the Survivable Network Design problem. A weakness of these formulations, though, is that we are not able to ask for fault-tolerance larger than the connectivity. Taking inspiration from recent definitions and progress in graph spanners, we introduce and study new variants of these problems under a notion of relative fault-tolerance. Informally, we require not that two nodes are connected if there are a bounded number of faults (as in the classical setting), but that two nodes are connected if there are a bounded number of faults and the two nodes are connected in the underlying graph post-faults. That is, the subgraph we build must "behave" identically to the underlying graph with respect to connectivity after bounded faults. We define and introduce these problems, and provide the first approximation algorithms: a (1+4/k)-approximation for the unweighted relative version of k-ECSS, a 2-approximation for the weighted relative version of k-ECSS, and a 27/4-approximation for the special case of Relative Survivable Network Design with only a single demand with a connectivity requirement of 3. To obtain these results, we introduce a number of technical ideas that may of independent interest. First, we give a generalization of Jain’s iterative rounding analysis that works even when the cut-requirement function is not weakly supermodular, but instead satisfies a weaker definition we introduce and term local weak supermodularity. Second, we prove a structure theorem and design an approximation algorithm utilizing a new decomposition based on important separators, which are structures commonly used in fixed-parameter algorithms that have not commonly been used in approximation algorithms.
Cite as

Michael Dinitz, Ama Koranteng, and Guy Kortsarz. Relative Survivable Network Design. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 245, pp. 41:1-41:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{dinitz_et_al:LIPIcs.APPROX/RANDOM.2022.41,
  author =	{Dinitz, Michael and Koranteng, Ama and Kortsarz, Guy},
  title =	{{Relative Survivable Network Design}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2022)},
  pages =	{41:1--41:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-249-5},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{245},
  editor =	{Chakrabarti, Amit and Swamy, Chaitanya},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX/RANDOM.2022.41},
  URN =		{urn:nbn:de:0030-drops-171632},
  doi =		{10.4230/LIPIcs.APPROX/RANDOM.2022.41},
  annote =	{Keywords: Fault Tolerance, Network Design}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2022.86
Near-Optimal Decremental Hopsets with Applications

Authors: Jakub Łącki and Yasamin Nazari

Published in: LIPIcs, Volume 229, 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)

Abstract
Given a weighted undirected graph G = (V,E,w), a hopset H of hopbound β and stretch (1+ε) is a set of edges such that for any pair of nodes u, v ∈ V, there is a path in G ∪ H of at most β hops, whose length is within a (1+ε) factor from the distance between u and v in G. We show the first efficient decremental algorithm for maintaining hopsets with a polylogarithmic hopbound. The update time of our algorithm matches the best known static algorithm up to polylogarithmic factors. All the previous decremental hopset constructions had a superpolylogarithmic (but subpolynomial) hopbound of 2^{log^{Ω(1)} n} [Bernstein, FOCS'09; HKN, FOCS'14; Chechik, FOCS'18]. By applying our decremental hopset construction, we get improved or near optimal bounds for several distance problems. Most importantly, we show how to decrementally maintain (2k-1)(1+ε)-approximate all-pairs shortest paths (for any constant k ≥ 2), in Õ(n^{1/k}) amortized update time and O(k) query time. This improves (by a polynomial factor) over the update-time of the best previously known decremental algorithm in the constant query time regime. Moreover, it improves over the result of [Chechik, FOCS'18] that has a query time of O(log log(nW)), where W is the aspect ratio, and the amortized update time is n^{1/k}⋅(1/ε)^{Õ(√{log n})}). For sparse graphs our construction nearly matches the best known static running time / query time tradeoff. We also obtain near-optimal bounds for maintaining approximate multi-source shortest paths and distance sketches, and get improved bounds for approximate single-source shortest paths. Our algorithms are randomized and our bounds hold with high probability against an oblivious adversary.
Cite as

Jakub Łącki and Yasamin Nazari. Near-Optimal Decremental Hopsets with Applications. In 49th International Colloquium on Automata, Languages, and Programming (ICALP 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 229, pp. 86:1-86:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{lacki_et_al:LIPIcs.ICALP.2022.86,
  author =	{{\L}\k{a}cki, Jakub and Nazari, Yasamin},
  title =	{{Near-Optimal Decremental Hopsets with Applications}},
  booktitle =	{49th International Colloquium on Automata, Languages, and Programming (ICALP 2022)},
  pages =	{86:1--86:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-235-8},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{229},
  editor =	{Boja\'{n}czyk, Miko{\l}aj and Merelli, Emanuela and Woodruff, David P.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2022.86},
  URN =		{urn:nbn:de:0030-drops-164277},
  doi =		{10.4230/LIPIcs.ICALP.2022.86},
  annote =	{Keywords: Dynamic Algorithms, Data Structures, Shortest Paths, Hopsets}
}
Document
DOI: 10.4230/LIPIcs.ITCS.2022.25
Vertex Fault-Tolerant Emulators

Authors: Greg Bodwin, Michael Dinitz, and Yasamin Nazari

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

Abstract
A k-spanner of a graph G is a sparse subgraph that preserves its shortest path distances up to a multiplicative stretch factor of k, and a k-emulator is similar but not required to be a subgraph of G. A classic theorem by Althöfer et al. [Disc. Comp. Geom. '93] and Thorup and Zwick [JACM '05] shows that, despite the extra flexibility available to emulators, the size/stretch tradeoffs for spanners and emulators are equivalent. Our main result is that this equivalence in tradeoffs no longer holds in the commonly-studied setting of graphs with vertex failures. That is: we introduce a natural definition of vertex fault-tolerant emulators, and then we show a three-way tradeoff between size, stretch, and fault-tolerance for these emulators that polynomially surpasses the tradeoff known to be optimal for spanners. We complement our emulator upper bound with a lower bound construction that is essentially tight (within log n factors of the upper bound) when the stretch is 2k-1 and k is either a fixed odd integer or 2. We also show constructions of fault-tolerant emulators with additive error, demonstrating that these also enjoy significantly improved tradeoffs over those available for fault-tolerant additive spanners.
Cite as

Greg Bodwin, Michael Dinitz, and Yasamin Nazari. Vertex Fault-Tolerant Emulators. In 13th Innovations in Theoretical Computer Science Conference (ITCS 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 215, pp. 25:1-25:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{bodwin_et_al:LIPIcs.ITCS.2022.25,
  author =	{Bodwin, Greg and Dinitz, Michael and Nazari, Yasamin},
  title =	{{Vertex Fault-Tolerant Emulators}},
  booktitle =	{13th Innovations in Theoretical Computer Science Conference (ITCS 2022)},
  pages =	{25:1--25:22},
  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.2022.25},
  URN =		{urn:nbn:de:0030-drops-156217},
  doi =		{10.4230/LIPIcs.ITCS.2022.25},
  annote =	{Keywords: Emulators, Fault Tolerance, Girth Conjecture}
}
Document
DOI: 10.4230/LIPIcs.OPODIS.2019.34
Sparse Hopsets in Congested Clique

Authors: Yasamin Nazari

Published in: LIPIcs, Volume 153, 23rd International Conference on Principles of Distributed Systems (OPODIS 2019)

Abstract
We give the first Congested Clique algorithm that computes a sparse hopset with polylogarithmic hopbound in polylogarithmic time. Given a graph G=(V,E), a (β,ε)-hopset H with "hopbound" β, is a set of edges added to G such that for any pair of nodes u and v in G there is a path with at most β hops in G ∪ H with length within (1+ε) of the shortest path between u and v in G. Our hopsets are significantly sparser than the recent construction of [Censor-Hillel et al., 2019], that constructs a hopset of size Õ (n^{3/2}), but with a smaller polylogarithmic hopbound. On the other hand, the previously known construction of sparse hopsets with polylogarithmic hopbound in the Congested Clique model, proposed by [Elkin and Neiman, 2018; Elkin and Neiman, 2019; Elkin and Neiman, 2019], all require polynomial rounds. One tool that we use is an efficient algorithm that constructs an l-limited neighborhood cover, that may be of independent interest. Finally, as a side result, we also give a hopset construction in a variant of the low-memory Massively Parallel Computation model, with improved running time over existing algorithms.
Cite as

Yasamin Nazari. Sparse Hopsets in Congested Clique. In 23rd International Conference on Principles of Distributed Systems (OPODIS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 153, pp. 34:1-34:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{nazari:LIPIcs.OPODIS.2019.34,
  author =	{Nazari, Yasamin},
  title =	{{Sparse Hopsets in Congested Clique}},
  booktitle =	{23rd International Conference on Principles of Distributed Systems (OPODIS 2019)},
  pages =	{34:1--34:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-133-7},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{153},
  editor =	{Felber, Pascal and Friedman, Roy and Gilbert, Seth and Miller, Avery},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2019.34},
  URN =		{urn:nbn:de:0030-drops-118207},
  doi =		{10.4230/LIPIcs.OPODIS.2019.34},
  annote =	{Keywords: Hopsets, Congested Clique, Shortest Paths, Massively Parallel Computation}
}
Document
DOI: 10.4230/LIPIcs.OPODIS.2019.35
Massively Parallel Approximate Distance Sketches

Authors: Michael Dinitz and Yasamin Nazari

Published in: LIPIcs, Volume 153, 23rd International Conference on Principles of Distributed Systems (OPODIS 2019)

Abstract
Data structures that allow efficient distance estimation (distance oracles, distance sketches, etc.) have been extensively studied, and are particularly well studied in centralized models and classical distributed models such as CONGEST. We initiate their study in newer (and arguably more realistic) models of distributed computation: the Congested Clique model and the Massively Parallel Computation (MPC) model. We provide efficient constructions in both of these models, but our core results are for MPC. In MPC we give two main results: an algorithm that constructs stretch/space optimal distance sketches but takes a (small) polynomial number of rounds, and an algorithm that constructs distance sketches with worse stretch but that only takes polylogarithmic rounds. Along the way, we show that other useful combinatorial structures can also be computed in MPC. In particular, one key component we use to construct distance sketches are an MPC construction of the hopsets of [Elkin and Neiman, 2016]. This result has additional applications such as the first polylogarithmic time algorithm for constant approximate single-source shortest paths for weighted graphs in the low memory MPC setting.
Cite as

Michael Dinitz and Yasamin Nazari. Massively Parallel Approximate Distance Sketches. In 23rd International Conference on Principles of Distributed Systems (OPODIS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 153, pp. 35:1-35:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)

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@InProceedings{dinitz_et_al:LIPIcs.OPODIS.2019.35,
  author =	{Dinitz, Michael and Nazari, Yasamin},
  title =	{{Massively Parallel Approximate Distance Sketches}},
  booktitle =	{23rd International Conference on Principles of Distributed Systems (OPODIS 2019)},
  pages =	{35:1--35:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-133-7},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{153},
  editor =	{Felber, Pascal and Friedman, Roy and Gilbert, Seth and Miller, Avery},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2019.35},
  URN =		{urn:nbn:de:0030-drops-118216},
  doi =		{10.4230/LIPIcs.OPODIS.2019.35},
  annote =	{Keywords: Distance Sketches, Massively Parallel Computation, Distance Oracles, Single-Source Shortest Paths}
}
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-dev.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
Brief Announcement
DOI: 10.4230/LIPIcs.DISC.2019.42
Brief Announcement: Massively Parallel Approximate Distance Sketches

Authors: Michael Dinitz and Yasamin Nazari

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

Abstract
Data structures that allow efficient distance estimation have been extensively studied both in centralized models and classical distributed models. We initiate their study in newer (and arguably more realistic) models of distributed computation: the Congested Clique model and the Massively Parallel Computation (MPC) model. In MPC we give two main results: an algorithm that constructs stretch/space optimal distance sketches but takes a (small) polynomial number of rounds, and an algorithm that constructs distance sketches with worse stretch but that only takes polylogarithmic rounds. Along the way, we show that other useful combinatorial structures can also be computed in MPC. In particular, one key component we use is an MPC construction of the hopsets of Elkin and Neiman (2016). This result has additional applications such as the first polylogarithmic time algorithm for constant approximate single-source shortest paths for weighted graphs in the low memory MPC setting.
Cite as

Michael Dinitz and Yasamin Nazari. Brief Announcement: Massively Parallel Approximate Distance Sketches. In 33rd International Symposium on Distributed Computing (DISC 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 146, pp. 42:1-42:3, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{dinitz_et_al:LIPIcs.DISC.2019.42,
  author =	{Dinitz, Michael and Nazari, Yasamin},
  title =	{{Brief Announcement: Massively Parallel Approximate Distance Sketches}},
  booktitle =	{33rd International Symposium on Distributed Computing (DISC 2019)},
  pages =	{42:1--42:3},
  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-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.DISC.2019.42},
  URN =		{urn:nbn:de:0030-drops-113491},
  doi =		{10.4230/LIPIcs.DISC.2019.42},
  annote =	{Keywords: Distance Sketches, Massively Parallel Computation, Congested Clique}
}
Document
APPROX
DOI: 10.4230/LIPIcs.APPROX-RANDOM.2019.11
Approximating the Norms of Graph Spanners

Authors: Eden Chlamtáč, Michael Dinitz, and Thomas Robinson

Published in: LIPIcs, Volume 145, Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2019)

Abstract
The l_p-norm of the degree vector was recently introduced by [Chlamtáč, Dinitz, Robinson ICALP '19] as a new cost metric for graph spanners, as it interpolates between two traditional notions of cost (the sparsity l_1 and the max degree l_infty) and is well-motivated from applications. We study this from an approximation algorithms point of view, analyzing old algorithms and designing new algorithms for this new context, as well as providing hardness results. Our main results are for the l_2-norm and stretch 3, where we give a tight analysis of the greedy algorithm and a new algorithm specifically tailored to this setting which gives an improved approximation ratio.
Cite as

Eden Chlamtáč, Michael Dinitz, and Thomas Robinson. Approximating the Norms of Graph Spanners. In Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 145, pp. 11:1-11:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{chlamtac_et_al:LIPIcs.APPROX-RANDOM.2019.11,
  author =	{Chlamt\'{a}\v{c}, Eden and Dinitz, Michael and Robinson, Thomas},
  title =	{{Approximating the Norms of Graph Spanners}},
  booktitle =	{Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques (APPROX/RANDOM 2019)},
  pages =	{11:1--11:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-125-2},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{145},
  editor =	{Achlioptas, Dimitris and V\'{e}gh, L\'{a}szl\'{o} A.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.APPROX-RANDOM.2019.11},
  URN =		{urn:nbn:de:0030-drops-112261},
  doi =		{10.4230/LIPIcs.APPROX-RANDOM.2019.11},
  annote =	{Keywords: Spanners, Approximations}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2019.40
The Norms of Graph Spanners

Authors: Eden Chlamtáč, Michael Dinitz, and Thomas Robinson

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

Abstract
A t-spanner of a graph G is a subgraph H in which all distances are preserved up to a multiplicative t factor. A classical result of Althöfer et al. is that for every integer k and every graph G, there is a (2k-1)-spanner of G with at most O(n^{1+1/k}) edges. But for some settings the more interesting notion is not the number of edges, but the degrees of the nodes. This spurred interest in and study of spanners with small maximum degree. However, this is not necessarily a robust enough objective: we would like spanners that not only have small maximum degree, but also have "few" nodes of "large" degree. To interpolate between these two extremes, in this paper we initiate the study of graph spanners with respect to the l_p-norm of their degree vector, thus simultaneously modeling the number of edges (the l_1-norm) and the maximum degree (the l_{infty}-norm). We give precise upper bounds for all ranges of p and stretch t: we prove that the greedy (2k-1)-spanner has l_p norm of at most max(O(n), O(n^{{k+p}/{kp}})), and that this bound is tight (assuming the Erdős girth conjecture). We also study universal lower bounds, allowing us to give "generic" guarantees on the approximation ratio of the greedy algorithm which generalize and interpolate between the known approximations for the l_1 and l_{infty} norm. Finally, we show that at least in some situations, the l_p norm behaves fundamentally differently from l_1 or l_{infty}: there are regimes (p=2 and stretch 3 in particular) where the greedy spanner has a provably superior approximation to the generic guarantee.
Cite as

Eden Chlamtáč, Michael Dinitz, and Thomas Robinson. The Norms of Graph Spanners. In 46th International Colloquium on Automata, Languages, and Programming (ICALP 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 132, pp. 40:1-40:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{chlamtac_et_al:LIPIcs.ICALP.2019.40,
  author =	{Chlamt\'{a}\v{c}, Eden and Dinitz, Michael and Robinson, Thomas},
  title =	{{The Norms of Graph Spanners}},
  booktitle =	{46th International Colloquium on Automata, Languages, and Programming (ICALP 2019)},
  pages =	{40:1--40:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-109-2},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{132},
  editor =	{Baier, Christel and Chatzigiannakis, Ioannis and Flocchini, Paola and Leonardi, Stefano},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2019.40},
  URN =		{urn:nbn:de:0030-drops-106163},
  doi =		{10.4230/LIPIcs.ICALP.2019.40},
  annote =	{Keywords: spanners, approximations}
}
Document
DOI: 10.4230/LIPIcs.FSTTCS.2018.33
Characterizing Demand Graphs for (Fixed-Parameter) Shallow-Light Steiner Network

Authors: Amy Babay, Michael Dinitz, and Zeyu Zhang

Published in: LIPIcs, Volume 122, 38th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2018)

Abstract
We consider the Shallow-Light Steiner Network problem from a fixed-parameter perspective. Given a graph G, a distance bound L, and p pairs of vertices (s_1,t_1),...,(s_p,t_p), the objective is to find a minimum-cost subgraph G' such that s_i and t_i have distance at most L in G' (for every i in [p]). Our main result is on the fixed-parameter tractability of this problem for parameter p. We exactly characterize the demand structures that make the problem "easy", and give FPT algorithms for those cases. In all other cases, we show that the problem is W[1]-hard. We also extend our results to handle general edge lengths and costs, precisely characterizing which demands allow for good FPT approximation algorithms and which demands remain W[1]-hard even to approximate.
Cite as

Amy Babay, Michael Dinitz, and Zeyu Zhang. Characterizing Demand Graphs for (Fixed-Parameter) Shallow-Light Steiner Network. In 38th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 122, pp. 33:1-33:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{babay_et_al:LIPIcs.FSTTCS.2018.33,
  author =	{Babay, Amy and Dinitz, Michael and Zhang, Zeyu},
  title =	{{Characterizing Demand Graphs for (Fixed-Parameter) Shallow-Light Steiner Network}},
  booktitle =	{38th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2018)},
  pages =	{33:1--33:22},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-093-4},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{122},
  editor =	{Ganguly, Sumit and Pandya, Paritosh},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2018.33},
  URN =		{urn:nbn:de:0030-drops-99329},
  doi =		{10.4230/LIPIcs.FSTTCS.2018.33},
  annote =	{Keywords: fixed-parameter tractable, network design, shallow-light steiner network, demand graphs}
}
Document
DOI: 10.4230/LIPIcs.ESA.2018.71
Large Low-Diameter Graphs are Good Expanders

Authors: Michael Dinitz, Michael Schapira, and Gal Shahaf

Published in: LIPIcs, Volume 112, 26th Annual European Symposium on Algorithms (ESA 2018)

Abstract
We revisit the classical question of the relationship between the diameter of a graph and its expansion properties. One direction is well understood: expander graphs exhibit essentially the lowest possible diameter. We focus on the reverse direction, showing that "sufficiently large" graphs of fixed diameter and degree must be "good" expanders. We prove this statement for various definitions of "sufficiently large" (multiplicative/additive factor from the largest possible size), for different forms of expansion (edge, vertex, and spectral expansion), and for both directed and undirected graphs. A recurring theme is that the lower the diameter of the graph and (more importantly) the larger its size, the better the expansion guarantees. Aside from inherent theoretical interest, our motivation stems from the domain of network design. Both low-diameter networks and expanders are prominent approaches to designing high-performance networks in parallel computing, HPC, datacenter networking, and beyond. Our results establish that these two approaches are, in fact, inextricably intertwined. We leave the reader with many intriguing questions for future research.
Cite as

Michael Dinitz, Michael Schapira, and Gal Shahaf. Large Low-Diameter Graphs are Good Expanders. In 26th Annual European Symposium on Algorithms (ESA 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 112, pp. 71:1-71:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{dinitz_et_al:LIPIcs.ESA.2018.71,
  author =	{Dinitz, Michael and Schapira, Michael and Shahaf, Gal},
  title =	{{Large Low-Diameter Graphs are Good Expanders}},
  booktitle =	{26th Annual European Symposium on Algorithms (ESA 2018)},
  pages =	{71:1--71:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-081-1},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{112},
  editor =	{Azar, Yossi and Bast, Hannah and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops-dev.dagstuhl.de/entities/document/10.4230/LIPIcs.ESA.2018.71},
  URN =		{urn:nbn:de:0030-drops-95348},
  doi =		{10.4230/LIPIcs.ESA.2018.71},
  annote =	{Keywords: Network design, Expander graphs, Spectral graph theory}
}
Document
Brief Announcement
DOI: 10.4230/LIPIcs.ICALP.2018.104
Brief Announcement: Characterizing Demand Graphs for (Fixed-Parameter) Shallow-Light Steiner Network

Authors: Amy Babay, Michael Dinitz, and Zeyu Zhang

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

Abstract
We consider the Shallow-Light Steiner Network problem from a fixed-parameter perspective. Given a graph G, a distance bound L, and p pairs of vertices {(s_i,t_i)}_{i in [p]}, the objective is to find a minimum-cost subgraph G' such that s_i and t_i have distance at most L in G' (for every i in [p]). Our main result is on the fixed-parameter tractability of this problem for parameter p. We exactly characterize the demand structures that make the problem "easy", and give FPT algorithms for those cases. In all other cases, we show that the problem is W[1]-hard. We also extend our results to handle general edge lengths and costs, precisely characterizing which demands allow for good FPT approximation algorithms and which demands remain W[1]-hard even to approximate.
Cite as

Amy Babay, Michael Dinitz, and Zeyu Zhang. Brief Announcement: Characterizing Demand Graphs for (Fixed-Parameter) Shallow-Light Steiner Network. In 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 107, pp. 104:1-104:4, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{babay_et_al:LIPIcs.ICALP.2018.104,
  author =	{Babay, Amy and Dinitz, Michael and Zhang, Zeyu},
  title =	{{Brief Announcement: Characterizing Demand Graphs for (Fixed-Parameter) Shallow-Light Steiner Network}},
  booktitle =	{45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)},
  pages =	{104:1--104:4},
  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.2018.104},
  URN =		{urn:nbn:de:0030-drops-91083},
  doi =		{10.4230/LIPIcs.ICALP.2018.104},
  annote =	{Keywords: Shallow-Light, Steiner Network, Fixed-Parameter Tractability}
}
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