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Documents authored by Dory, Michal

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Brief Announcement
DOI: 10.4230/LIPIcs.DISC.2024.40
Brief Announcement: Distributed Maximum Flow in Planar Graphs

Authors: Yaseen Abd-Elhaleem, Michal Dory, Merav Parter, and Oren Weimann

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

Abstract
The dual of a planar graph G is a planar graph G^* that has a vertex for each face of G and an edge for each pair of adjacent faces of G. The profound relationship between a planar graph and its dual has been the algorithmic basis for solving numerous (centralized) classical problems on planar graphs involving distances, flows, and cuts. In the distributed setting however, the only use of planar duality is for finding a recursive decomposition of G [DISC 2017, STOC 2019]. In this paper, we extend the distributed algorithmic toolkit (such as recursive decompositions and minor-aggregations) to work on the dual graph G^*. These tools can then facilitate various algorithms on G by solving a suitable dual problem on G^*. Given a directed planar graph G with hop-diameter D, our key result is an Õ(D²)-round algorithm for Single Source Shortest Paths on G^*, which then implies an Õ(D²)-round algorithm for Maximum st-Flow on G. Prior to our work, no Õ(Poly(D))-round algorithm was known for Maximum st-Flow. We further obtain a D⋅ n^o(1)-rounds (1+ε)-approximation algorithm for Maximum st-Flow on G when G is undirected and s and t lie on the same face. Finally, we give a near optimal Õ(D)-round algorithm for computing the weighted girth of G. The main challenges in our work are that G^* is not the communication graph (e.g., a vertex of G is mapped to multiple vertices of G^*), and that the diameter of G^* can be much larger than D (i.e., possibly by a linear factor). We overcome these challenges by carefully defining and maintaining subgraphs of the dual graph G^* while applying the recursive decomposition on the primal graph G. The main technical difficulty, is that along the recursive decomposition, a face of G gets shattered into (disconnected) components yet we still need to treat it as a dual node.
Cite as

Yaseen Abd-Elhaleem, Michal Dory, Merav Parter, and Oren Weimann. Brief Announcement: Distributed Maximum Flow in Planar Graphs. In 38th International Symposium on Distributed Computing (DISC 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 319, pp. 40:1-40:8, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{abdelhaleem_et_al:LIPIcs.DISC.2024.40,
  author =	{Abd-Elhaleem, Yaseen and Dory, Michal and Parter, Merav and Weimann, Oren},
  title =	{{Brief Announcement: Distributed Maximum Flow in Planar Graphs}},
  booktitle =	{38th International Symposium on Distributed Computing (DISC 2024)},
  pages =	{40:1--40:8},
  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.2024.40},
  URN =		{urn:nbn:de:0030-drops-212687},
  doi =		{10.4230/LIPIcs.DISC.2024.40},
  annote =	{Keywords: Maximum flow, shortest paths, planar graphs, distributed computing}
}
Document
Track A: Algorithms, Complexity and Games
DOI: 10.4230/LIPIcs.ICALP.2024.58
New Tradeoffs for Decremental Approximate All-Pairs Shortest Paths

Authors: Michal Dory, Sebastian Forster, Yasamin Nazari, and Tijn de Vos

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

Abstract
We provide new tradeoffs between approximation and running time for the decremental all-pairs shortest paths (APSP) problem. For undirected graphs with m edges and n nodes undergoing edge deletions, we provide four new approximate decremental APSP algorithms, two for weighted and two for unweighted graphs. Our first result is (2+ε)-APSP with total update time Õ(m^{1/2}n^{3/2}) (when m = n^{1+c} for any constant 0 < c < 1). Prior to our work the fastest algorithm for weighted graphs with approximation at most 3 had total Õ(mn) update time for (1+ε)-APSP [Bernstein, SICOMP 2016]. Our second result is (2+ε, W_{u,v})-APSP with total update time Õ(nm^{3/4}), where the second term is an additive stretch with respect to W_{u,v}, the maximum weight on the shortest path from u to v. Our third result is (2+ε)-APSP for unweighted graphs in Õ(m^{7/4}) update time, which for sparse graphs (m = o(n^{8/7})) is the first subquadratic (2+ε)-approximation. Our last result for unweighted graphs is (1+ε, 2(k-1))-APSP, for k ≥ 2, with Õ(n^{2-1/k}m^{1/k}) total update time (when m = n^{1+c} for any constant c > 0). For comparison, in the special case of (1+ε, 2)-approximation, this improves over the state-of-the-art algorithm by [Henzinger, Krinninger, Nanongkai, SICOMP 2016] with total update time of Õ(n^{2.5}). All of our results are randomized, work against an oblivious adversary, and have constant query time.
Cite as

Michal Dory, Sebastian Forster, Yasamin Nazari, and Tijn de Vos. New Tradeoffs for Decremental Approximate All-Pairs Shortest Paths. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 58:1-58:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{dory_et_al:LIPIcs.ICALP.2024.58,
  author =	{Dory, Michal and Forster, Sebastian and Nazari, Yasamin and de Vos, Tijn},
  title =	{{New Tradeoffs for Decremental Approximate All-Pairs Shortest Paths}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{58:1--58:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-322-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{297},
  editor =	{Bringmann, Karl and Grohe, Martin and Puppis, Gabriele and Svensson, Ola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2024.58},
  URN =		{urn:nbn:de:0030-drops-202012},
  doi =		{10.4230/LIPIcs.ICALP.2024.58},
  annote =	{Keywords: Decremental Shortest Path, All-Pairs Shortest Paths}
}
Document
DOI: 10.4230/LIPIcs.OPODIS.2017.21
Fast Distributed Approximation for TAP and 2-Edge-Connectivity

Authors: Keren Censor-Hillel and Michal Dory

Published in: LIPIcs, Volume 95, 21st International Conference on Principles of Distributed Systems (OPODIS 2017)

Abstract
The tree augmentation problem (TAP) is a fundamental network design problem, in which the input is a graph G and a spanning tree T for it, and the goal is to augment T with a minimum set of edges Aug from G, such that T ∪ Aug is 2-edge-connected. TAP has been widely studied in the sequential setting. The best known approximation ratio of 2 for the weighted case dates back to the work of Frederickson and JáJá, SICOMP 1981. Recently, a 3/2-approximation was given for the unweighted case by Kortsarz and Nutov, TALG 2016, and recent breakthroughs by Adjiashvili, SODA 2017, and by Fiorini et al., 2017, give approximations better than 2 for bounded weights. In this paper, we provide the first fast distributed approximations for TAP. We present a distributed 2-approximation for weighted TAP which completes in O(h) rounds, where h is the height of T . When h is large, we show a much faster 4-approximation algorithm for the unweighted case, completing in O(D + (√n) log^{*} n) rounds, where n is the number of vertices and D is the diameter of G. Immediate consequences of our results are an O(D)-round 2-approximation algorithm for the minimum size 2-edge-connected spanning subgraph, which significantly improves upon the running time of previous approximation algorithms, and an O(hMST + (√n)log^{*} n)-round 3- approximation algorithm for the weighted case, where hMST is the height of the MST of the graph. Additional applications are algorithms for verifying 2-edge-connectivity and for augment- ing the connectivity of any connected spanning subgraph to 2. Finally, we complement our study with proving lower bounds for distributed approximations of TAP.
Cite as

Keren Censor-Hillel and Michal Dory. Fast Distributed Approximation for TAP and 2-Edge-Connectivity. In 21st International Conference on Principles of Distributed Systems (OPODIS 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 95, pp. 21:1-21:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)

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@InProceedings{censorhillel_et_al:LIPIcs.OPODIS.2017.21,
  author =	{Censor-Hillel, Keren and Dory, Michal},
  title =	{{Fast Distributed Approximation for TAP and 2-Edge-Connectivity}},
  booktitle =	{21st International Conference on Principles of Distributed Systems (OPODIS 2017)},
  pages =	{21:1--21:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-061-3},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{95},
  editor =	{Aspnes, James and Bessani, Alysson and Felber, Pascal and Leit\~{a}o, Jo\~{a}o},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.OPODIS.2017.21},
  URN =		{urn:nbn:de:0030-drops-86475},
  doi =		{10.4230/LIPIcs.OPODIS.2017.21},
  annote =	{Keywords: approximation algorithms, distributed network design, connectivity augmentation}
}
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