Distributed and Massively Parallel Graph Algorithms

Project Information

DistMaP

Grant agreement ID: 853109

DOI

10.3030/853109

Project terminated on 31 October 2024

EC signature date 7 October 2019

Start date 1 November 2019

End date 31 October 2024

Funded under

• EXCELLENT SCIENCE - European Research Council (ERC)

Total cost

€ 1 498 250,00

EU contribution

€ 1 498 250,00

Coordinated by

MAX-PLANCK-GESELLSCHAFT ZUR FORDERUNG DER WISSENSCHAFTEN EV
Germany

Periodic Reporting for period 4 - DistMaP (Distributed and Massively Parallel Graph Algorithms)

Reporting period: 2024-01-01 to 2024-10-31

Summary of the context and overall objectives of the project

This project studies foundational aspects of computation in distributed or massively parallel systems. With the rapid increase in the data sizes and their spatial spread, computations of the future will rely more and more on decentralized formats --- concretely distributed computing and parallel computing. This project investigates principles of computation in these settings, through a theoretical lens. For instance, a key direction is to understand whether, and if yes to what extent, randomness is necessary for efficient computation in distributed settings, in particular, for distributed graph algorithms. The second direction is to develop methods for some of the central graph problems which break the longstanding barrier of logarithmic time. The third direction is to develop more efficient methods for some of the same graph problems in the setting of massively parallel computation, where numerous machines cooperate together to solve the problem faster.

Work performed from the beginning of the project to the end of the period covered by the report and main results achieved so far

Direction I:

- Mohsen Ghaffari, Christoph Grunau: Near-Optimal Deterministic Network Decomposition and Ruling Set, and Improved MIS, IEEE Symposium on Foundations of Computer Science (FOCS) 2024
- Václav Rozhoň ® Bernhard Haeupler ® Anders Martinsson ® Christoph Grunau ® Goran Zuzic: Parallel Breadth-First Search and Exact Shortest Paths and Stronger Notions for Approximate Distances, ACM Symposium on Theory of Computing (STOC) 2023;
- Václav Rozhoň ® Bernhard Haeupler ® Christoph Grunau: A Simple Deterministic Distributed Low-Diameter Clustering, ACM-SIAM Symposium on Simplicity in Algorithms (SOSA) 2023;
- Mohsen Ghaffari, Christoph Grunau, Bernhard Haeupler, Saeed Ilchi, Václav Rozhoň: Improved Distributed Network Decomposition, Hitting Sets, and Spanners, via Derandomization, ACM-SIAM Symposium on Discrete Algorithms (SODA) 2023;
- Salwa Faour, Mohsen Ghaffari, Christoph Grunau, Fabian Kuhn, Václav Rozhoň: Local Distributed Rounding: Generalized to MIS, Matching, Set Cover, and Beyond, ACM-SIAM Symposium on Discrete Algorithms (SODA) 2023;
- Michael Elkin ® Bernhard Haeupler ® Václav Rozhoň ® Christoph Grunau: Deterministic Low-Diameter Decompositions for Weighted Graphs and Distributed and Parallel Applications, IEEE Symposium on Foundations of Computer Science (FOCS) 2022;
- Marcel Bezdrighin, Michael Elkin, Mohsen Ghaffari, Christoph Grunau, Bernhard Haeupler, Saeed Ilchi, Václav Rozhoň : Deterministic Distributed Sparse and Ultra-Sparse Spanners and Connectivity Certificates, ACM Symposium on Parallelism in Algorithms and Architectures (SPAA) 2022;
- Mohsen Ghaffari, Christoph Grunau, Václav Rozhoň: Improved Deterministic Network Decomposition, ACM-SIAM Symposium on Discrete Algorithms (SODA) 2021;
- Václav Rozhoň, Mohsen Ghaffari: Polylogarithmic-Time Deterministic Network Decomposition and Distributed Derandomization, Symposium on Theory of Computing (STOC) 2020;


Direction II:

- Manuela Fischer, Jeff Giliberti, Christoph Grunau: Deterministic Massively Parallel Symmetry Breaking for Sparse Graphs, ACM Symposium on Parallelism in Algorithms and Architectures (SPAA) 2023;
- Mohsen Ghaffari and Julian Portmann Distributed MIS with Low Energy and Time Complexities, ACM Symposium on Principles of Distributed Computing (PODC) 2023.
- Jan Grebík, Václav Rozhoň: Local Problems on Grids from the Perspective of Distributed Algorithms, Finitary Factors, and Descriptive Combinatorics, Advances in Mathematics Journal 2023
- Michal Dory, Mohsen Ghaffari, and Saeed Ilchi: Near-Optimal Distributed Dominating Set in Bounded Arboricity Graphs, ACM Symposium on Principles of Distributed Computing (PODC) 2022.
- Christoph Grunau ® Václav Rozhoň ® Sebastian Brandt: The Landscape of Distributed Complexities on Trees and Beyond, Principles of Distributed Computing (PODC) 2022;
- Sebastian Brandt, Yi-Jun Chang, Jan Grebík, Christoph Grunau, Václav Rozhoň, Zoltán Vidnyánszky: Local Problems on Trees from the Perspectives of Distributed Algorithms, Finitary Factors, and Descriptive Combinatorics, Innovations of Theoretical Computer Science (ITCS) 2022;
- Sebastian Brandt, Christoph Grunau, Václav Rozhoň: The Randomized Local Computation Complexity of the Lovász Local Lemma, Principles of Distributed Computing (PODC) 2021;
- Jan Grebík, Václav Rozhoň: Classification of Local Problems on Paths from the Perspective of Descriptive Combinatorics EUROCOMB 2020
- Sebastian Brandt, Christoph Grunau, Václav Rozhoň: Generalizing the Sharp Threshold Phenomenon for the Distributed Complexity of the Lovász Local Lemma, Principles of Distributed Computing (PODC) 2020;


Direction III:
- Manuela Fischer, Jeff Giliberti, Christoph Grunau: Improved Deterministic Connectivity in Massively Parallel Computation, International Symposium on Distributed Computing (DISC) 2022;
- Mohsen Ghaffari, Christoph Grunau, and Slobodan Mitrovic : Massively Parallel Algorithms for b-Matching, ACM Symposium on Parallelism in Algorithms and Architectures (SPAA) 2022;
- Mohsen Ghaffari, Christoph Grunau, Ce Jin: Improved MPC Algorithms for MIS, Matching, and Coloring on Trees and Beyond, International Symposium on DIStributed Computing (DISC) 2020;

Results that stemmed from the tools and techniques of the project, but do not fall into the above three categories, are not summarized here, due to the space limits. See other tabs

Progress beyond the state of the art and expected potential impact (including the socio-economic impact and the wider societal implications of the project so far)

The results mentioned above (especially the three highlighted) go well beyond the state of the art in distributed graph algorithms. Below, we highlight three key achievements, which resolve several central problems that had remained open for three or more decades.

Paper [A] gave a near-optimal algorithm for network decomposition, essentially settling a line of research that had been pursued since the 1990s, and it received the best paper award of FOCS 2024, which is regarded as the top most recognition for a paper in theoretical computer science. Paper [B] developed a novel technique called "local rounding", which results in significantly improved distributed algorithms for a range of problems, in a systematic manner. Paper [C] gave the first efficient distributed method for derandomizing distributed graph algorithms, and therefore the first polylogarithmic time deterministic distributed algorithm for several well-studied problems, including maximal independent set and coloring. This paper resolved problems that had remained open since 1985 (e.g. Linial's open problem from 1987, which was called "the most outstanding open problem" in the area), and is thus widely viewed as a major breakthrough (and is cited as such explicitly quite a few times).



[A] Mohsen Ghaffari, Christoph Grunau: Near-Optimal Deterministic Network Decomposition and Ruling Set, and Improved MIS, IEEE Symposium on Foundations of Computer Science (FOCS) 2024. The paper received the best paper award of FOCS 2024.


[B] Salwa Faour, Mohsen Ghaffari, Christoph Grunau, Fabian Kuhn, Václav Rozhoň: Local Distributed Rounding: Generalized to MIS, Matching, Set Cover, and Beyond, ACM-SIAM Symposium on Discrete Algorithms (SODA) 2023.


[C] Václav Rozhoň, Mohsen Ghaffari: Polylogarithmic-Time Deterministic Network Decomposition and Distributed Derandomization, Symposium on Theory of Computing (STOC) 2020.

wola-without-name-prime.png