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Brief Announcement: distributed Maximum Flow in Planar Graphs 38

Brief Announcement: Distributed Maximum Flow in Planar Graph...

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38th International symposium on distributed computing, DISC 2024

作者： Abd-Elhaleem, Yaseen Dory, Michal Parter, Merav Weimann, Oren Department of Computer Science University of Haifa Israel Department of Computer Science and Applied Mathematics Weizmann Institute of Science Rehovot Israel

ISBN: (纸本)9783959773522

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 algorithm1 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·no(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. © Yaseen Abd-Elhaleem, Michal Dory, Merav Parter, and Oren Weimann.

关键词： Approximation algorithms

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Improved Tradeoffs for Leader Election 23

Improved Tradeoffs for Leader Election

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42nd acm SIGACT-SIGOPS symposium on principles of distributed computing (PODC)

作者： Kutten, Shay Robinson, Peter Ming, Ming Zhu, Xianbin Technion Israel Inst Technol Haifa Israel Augusta Univ Sch Comp & Cyber Sci Augusta GA USA City Univ Hong Kong Dept Comp Sci Hong Kong Peoples R China

ISBN: (纸本)9798400701214

We consider leader election in clique networks, where n nodes are connected by point-to-point communication links. For the synchronous clique under simultaneous wake-up, i.e., where all nodes start executing the algorithm in round 1, we show a tradeoff between the number of messages and the amount of time. The previous lower bound side of such a tradeoff, in the seminal paper of Afek and Gafni (1991), was shown only assuming adversarial wake-up. Interestingly, our new tradeoff also improves the previous lower bounds for a large part of the spectrum, even under simultaneous wake-up. More specifically, we show that any deterministic algorithm with a message complexity of n f (n) requires Omega(log n/log f(n) + 1) rounds, for f(n) > 1. Our result holds even if the node IDs are chosen from a relatively small set of size Theta(n log n), as we are able to avoid using Ramsey's theorem, in contrast to many existing lower bounds for deterministic algorithms. We also give an upper bound that improves over the previously-best tradeoff achieved by the algorithm of Afek and Gafni. Our second contribution for the synchronous clique under simultaneous wake-up is to show that Omega(n log n) is in fact a lower bound on the message complexity that holds for any deterministic algorithm with a termination time T (n) (i.e., any function of n), for a sufficiently large ID space. We complement this result by giving a simple deterministic algorithm that achieves leader election in sublinear time while sending only o(n log n) messages, if the ID space is of at most linear size. We also show that Las Vegas algorithms (that never fail) require Theta(n) messages. This exhibits a gap between Las Vegas and Monte Carlo algorithms. For the synchronous clique under adversarial wake-up, we show that Omega(n(3/2)) is a lower bound for 2-round algorithms. Our result is the first superlinear lower bound for randomized leader election algorithms in the clique. We also give a simple algorithm that matche

关键词： distributed Algorithm Leader Election Lower Bound

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distributed Edge Coloring in Time Polylogarithmic in " 41

Distributed Edge Coloring in Time Polylogarithmic in "

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41st acm symposium on principles of distributed computing, PODC 2022

作者： Balliu, Alkida Brandt, Sebastian Kuhn, Fabian Olivetti, Dennis Gran Sasso Science Institute L'Aquila Italy Cispa Helmholtz Center for Information Security Saarbrücken Germany University of Freiburg Freiburg Germany

ISBN: (纸本)9781450392624

We provide new deterministic algorithms for the edge coloring problem, which is one of the classic and highly studied distributed local symmetry breaking problems. As our main result, we show that a (2Δ- 1)-edge coloring can be computed in time poly log Δ+ O(log∗n) in the LOCAL model. This improves a result of Balliu, Kuhn, and Olivetti [PODC '20], who gave an algorithm with a quasi-polylogarithmic dependency on ". We further show that in the CONGEST model, an (8 + ) "-edge coloring can be computed in poly log Δ+ O(log∗n) rounds. The best previous O( ")-edge coloring algorithm that can be implemented in the CONGEST model is by Barenboim and Elkin [PODC '11] and it computes a 2O(1/) "- edge coloring in time O( "+ log∗n) for any ĝ (0, 1]. © 2022 acm.

关键词： Coloring

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Near-Optimal distributed Dominating Set in Bounded Arboricity Graphs 22

Near-Optimal Distributed Dominating Set in Bounded Arboricit...

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acm symposium on principles of distributed computing (PODC)

作者： Dory, Michal Ghaffari, Mohsen Ilchi, Saeed Swiss Fed Inst Technol Zurich Switzerland

ISBN: (纸本)9781450392624

We describe a simple deterministic O(epsilon(-1) log Delta) round distributed algorithm for (2 alpha+ 1) (1 + epsilon) approximation of minimum weighted dominating set on graphs with arboricity at most alpha. Here Delta denotes the maximum degree. We also show a lower bound proving that this round complexity is nearly optimal even for the unweighted case, via a reduction from the celebrated KMW lower bound on distributed vertex cover approximation [Kuhn, Moscibroda, and Wattenhofer Jacm'16]. Our algorithm improves on all the previous results (that work only for unweighted graphs) including a randomized O(alpha(2)) approximation in O(log n) rounds [Lenzen and Wattenhofer DISC'10], a deterministic O(alpha log Delta) approximation in O(log Delta) rounds [Lenzen and Wattenhofer DISC'10], a deterministic O(alpha) approximation in O(log(2) Delta) rounds [implicit in Bansal and Umboh IPL'17 and Kuhn, Moscibroda, and Wattenhofer SODA'06], and a randomized O(alpha) approximation in O(alpha log n) rounds [Morgan, Solomon and Wein DISC'21]. We also provide a randomized O(alpha log Delta) round distributed algorithm that sharpens the approximation factor to alpha (1 + o(1)). If each node is restricted to do polynomial-time computations, our approximation factor is tight in the first order as it is NP-hard to achieve alpha - 1 - epsilon approximation [Bansal and Umboh IPL'17].

关键词： distributed computing Dominating Set Arboricity Approximation Algorithms

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Speedup of distributed Algorithms for Power Graphs in the CONGEST Model 38

Speedup of Distributed Algorithms for Power Graphs in the CO...

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38th International symposium on distributed computing, DISC 2024

作者： Barenboim, Leonid Goldenberg, Uri Open University of Israel Ra’anana Israel Ben-Gurion University of the Negev Beersheba Israel

ISBN: (纸本)9783959773522

We obtain improved distributed algorithms in the CONGEST message-passing setting for problems on power graphs of an input graph G. This includes Coloring, Maximal Independent Set, and related problems. For R = f(∆k, n), we develop a general deterministic technique that transforms R-round LOCAL model algorithms for Gk with certain properties into O(R · ∆k/2-1)-round CONGEST algorithms for Gk. This improves the previously-known running time for such transformation, which was O(R · ∆k-1). Consequently, for problems that can be solved by algorithms with the required properties and within polylogarithmic number of rounds, we obtain quadratic improvement for Gk and exponential improvement for G2. We also obtain significant improvements for problems with larger number of rounds in G. Notable implications of our technique are the following deterministic distributed algorithms: We devise a distributed algorithm for O(∆4)-coloring of G2 whose number of rounds is O(log ∆ + log∗ n). This improves exponentially (in terms of ∆) the best previously-known deterministic result of Halldorsson, Kuhn and Maus.[25] that required O(∆ + log∗ n) rounds, and the standard simulation of Linial [30] algorithm in Gk that required O(∆ · log∗ n) rounds. We devise an algorithm for O(∆2)-coloring of G2 with O(∆ · log ∆ + log∗ n) rounds, and (∆2 + 1)-coloring with O(∆1.5 · log ∆ + log∗ n) rounds. This improves quadratically, and by a power of 4/3, respectively, the best previously-known results of Halldorsson, Khun and Maus. [25]. For k > 2, our running time for O(∆2k)-coloring of Gk is O(k · ∆k/2-1 · log ∆ · log∗ n). Our running time for O(∆k)-coloring of Gk is Õ(k · ∆k-1 · log∗ n). This improves best previously-known results quadratically, and by a power of 3/2, respectively. For constant k > 2, our upper bound for O(∆2k)-coloring of Gk nearly matches the lower bound of Fraigniaud, Halldorsson and Nolin. [16] for checking the correctness of a coloring in Gk © Leonid Barenboim and Uri Goldenberg.

关键词： Message passing

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Brief Announcement: Near Optimal Bounds for Replacement Paths and Related Problems in the CONGEST Model 22

Brief Announcement: Near Optimal Bounds for Replacement Path...

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acm symposium on principles of distributed computing (PODC)

作者： Manoharan, Vignesh Ramachandran, Vijaya Univ Texas Austin Austin TX 78712 USA

ISBN: (纸本)9781450392624

We present round complexity results in the CONGEST model for Replacement Paths (RPaths), Minimum Weight Cycle (MWC), and All Nodes Shortest Cycles (ANSC). We study these fundamental problems in both directed and undirected graphs, weighted and unweighted. Many of our results are optimal to within a polylog factor: For an.. -node graph.. we establish near linear lower and upper bounds for RPaths if.. is directed andweighted, and forMWC and ANSC if.. is weighted, directed or undirected;near root n lower and upper bounds for undirected weighted RPaths;and Theta(D) bound for undirected unweighted RPaths. We also present lower and upper bounds for approximation: a (2 - ( 1/g))-approximation algorithm for undirected unweighted MWC that runs in O-similar to (root n +D) rounds, improving on the previous best bound of O-similar to (root ng +D) rounds, where.. is the MWC length, and a ( 1 +epsilon)-approximation algorithm for directed weighted RPaths and (2 +epsilon)-approximation for weighted undirected MWC, for any constant epsilon > 0, that beat the round complexity lower bound for an exact solution.

关键词： distributed algorithms CONGEST lower bounds replacement paths minimum weight cycle

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distributed Computations in Fully-Defective Networks 22

Distributed Computations in Fully-Defective Networks

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acm symposium on principles of distributed computing (PODC)

作者： Censor-Hillel, Keren Cohen, Shir Gelles, Ran Sela, Gal Technion Haifa Israel Bar Ilan Univ Ramat Gan Israel

ISBN: (纸本)9781450392624

We address fully-defective asynchronous networks, in which all links are subject to an unlimited number of alteration errors, implying that all messages in the network may be completely corrupted. Despite the possible intuition that such a setting is too harsh for any reliable communication, we show how to simulate any algorithm for a noiseless setting over any fully-defective setting, given that the network is 2-edge connected. We prove that if the network is not 2-edge connected, no non-trivial computation in the fully-defective setting is possible. The key structural property of 2-edge-connected graphs that we leverage is the existence of an oriented (non-simple) cycle that goes through all nodes [Robbins, 1939]. The core of our technical contribution is presenting a construction of such a Robbins cycle in fully-defective networks, and showing how to communicate over it despite total message corruption. These are obtained in a content-oblivious manner, since nodes must ignore the content of received messages.

关键词： Fully-defective Networks Noise Resilience Robbins' Theorem

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Encrypted distributed Systems 22

Encrypted Distributed Systems

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acm symposium on principles of distributed computing (PODC)

作者： Kamara, Seny MongoDB Atlanta GA 30305 USA Brown Univ Providence RI 02912 USA

ISBN: (纸本)9781450392624

distributed computing is at the heart of modern system architectures and infrastructures. But as security and privacy have increasingly become critical to every organization, modern cryptography is making its way into core systems. In this talk, I will describe work that focuses on using modern cryptographic techniques in large scale practical distributed systems in order to improve their security and privacy guarantees. I will show how both cryptographic techniques and distributed systems need to be adapted to make this work and how to think about the security of these new encrypted distributed systems.

关键词： Cryptography distributed systems

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A Next Generation Architecture for Internet of Things in the Automotive Supply Chain for Electric Vehicles 24

A Next Generation Architecture for Internet of Things in the...

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2024 International symposium on Theory, Algorithmic Foundations, and Protocol Design for Mobile Networks and Mobile computing, MobiHoc 2024

作者： Kapsalis, Panagiotis Rimassa, Giovanni Zeydan, Engin Via, Selva Risso, Fulvio Giovanni Chiasserini, Carla Fabiana Vivo, Giulio Martel Innovate Zürich Switzerland Castelldefels Spain Politechnico di Torino Turin Italy Centro Ricerche FIAT SCpA Turin Italy

ISBN: (纸本)9798400705212

This paper presents a next-generation architecture that focuses on the advancement of edge computing and Internet of Things (IoT) technologies in the context of the automotive supply value chain for electric vehicles (EVs). First, we outline the general architecture design, the specific layers and their goals. Based on the principles of the proposed architecture, we also give a use case for improving the traceability, monitoring and efficiency of EV battery transportation using innovative approaches in federated data spaces, AI-powered inference and orchestration of a multi-objective computational continuum. The automotive supply chain use case is presented with potential Key Performance Indicators (KPIs) while emphasizing the potential impact on operational efficiency, cost reduction and sustainability. By addressing the current limitations in distributed intelligence, data governance, and cross-domain interoperability, we emphasize the importance of real-time data processing, dynamic field governance, and energy-efficient machine learning in the context of the electric vehicle supply chain. At the end of the paper, a discussion and comparative analysis highlights the advances over existing technologies and frameworks and identifies future directions to further improve innovations and applications in this area. © 2024 Copyright held by the owner/author(s).

关键词： Edge computing

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The Landscape of distributed Complexities on Trees and Beyond 22

The Landscape of Distributed Complexities on Trees and Beyon...

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acm symposium on principles of distributed computing (PODC)

作者： Grunau, Christoph Rozhon, Vaclav Brandt, Sebastian Swiss Fed Inst Technol Zurich Switzerland CISPA Helmholtz Ctr Informat Secur Saarbrucken Germany

ISBN: (纸本)9781450392624

We study the local complexity landscape of locally checkable labeling (LCL) problems on constant-degree graphs with a focus on complexities below log* n. Our contribution is threefold: (1) Our main contribution is that we complete the classification of the complexity landscape of LCL problems on trees in the LOCAL model, by proving that every LCL problem with local complexity o (log* n) has actually complexityO(1). This result improves upon the previous speedup result from o (log log* n) to O(1) by [Chang, Pettie, FOCS 2017]. (2) In the related LCA and VOLUME models [Alon, Rubinfeld, Vardi, Xie, SODA 2012, Rubinfeld, Tamir, Vardi, Xie, 2011, Rosenbaum, Suomela, PODC 2020],we prove the same speedup from o (log* n) to O(1) for all constant-degree graphs. (3) Similarly, we complete the classification of the LOCAL complexity landscape of oriented d-dimensional grids by proving that any LCL problem with local complexity o (log* n) has actually complexity O(1). This improves upon the previous speed-up from o ((d)root log* n) by Suomela, explained in [Chang, Pettie, FOCS 2017].

关键词： graph problems LCL problems distributed complexity theory locality LOCAL model volume model gap result

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