We show that graphs excluding K2,t as a minor admit a f(t)-round 50-approximation deterministic distributed algorithm for Minimum Dominating Set. The result extends to Minimum Vertex Cover. Though fast and approximate...
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ISBN:
(纸本)9798400718854
We show that graphs excluding K2,t as a minor admit a f(t)-round 50-approximation deterministic distributed algorithm for Minimum Dominating Set. The result extends to Minimum Vertex Cover. Though fast and approximate distributed algorithms for such problems were already known for H-minor-free graphs, all of them have an approximation ratio depending on the size of H. To the best of our knowledge, this is the first example of a large non-trivial excluded minor leading to fast and constant-approximation distributed algorithms, where the ratio is independent of the size of H. A new key ingredient in the analysis of these distributed algorithms is the use of asymptotic dimension.
We study the replacement paths problem in the CONGEST model of distributedcomputing. Given an s-t shortest path P, the goal is to compute, for every edge e in P, the shortest-path distance from s to t avoiding e. For...
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ISBN:
(纸本)9798400718854
We study the replacement paths problem in the CONGEST model of distributedcomputing. Given an s-t shortest path P, the goal is to compute, for every edge e in P, the shortest-path distance from s to t avoiding e. For unweighted directed graphs, we establish the tight randomized round complexity bound for this problem as [EQUATION] by showing matching upper and lower bounds. Our upper bound extends to (1 + ϵ)-approximation for weighted directed graphs. Our lower bound applies even to the second simple shortest path problem, which asks only for the smallest replacement path length. These results improve upon the very recent work of Manoharan and Ramachandran (SIROCCO 2024), who showed a lower bound of [EQUATION] and an upper bound of [EQUATION], where hst is the number of hops in the given s-t shortest path P.
distributed consensus algorithms such as Paxos have been studied extensively. Many different liveness properties and assumptions have been stated for them, but there are no systematic comparisons for better understand...
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ISBN:
(纸本)9781450385480
distributed consensus algorithms such as Paxos have been studied extensively. Many different liveness properties and assumptions have been stated for them, but there are no systematic comparisons for better understanding of these properties. This paper systematically studies and compares different liveness properties stated for over 30 prominent consensus algorithms and variants. We introduced a precise high-level language and formally specified these properties in the language. We then create a hierarchy of liveness properties combining two hierarchies of the assumptions used and a hierarchy of the assertions made, and compare the strengths and weaknesses of algorithms that ensure these properties. Our formal specifications and systematic comparisons led to the discovery of a range of problems in various stated liveness properties. We also developed TLA+ specifications of these liveness properties, and we used model checking of execution steps to illustrate liveness patterns for Paxos.
We study fault-tolerant consensus in a variant of the synchronous message passing model, where, in each round, every node can choose to be awake or asleep. This is known as the sleeping model (Chatterjee, Gmyr, Pandur...
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ISBN:
(纸本)9798400718854
We study fault-tolerant consensus in a variant of the synchronous message passing model, where, in each round, every node can choose to be awake or asleep. This is known as the sleeping model (Chatterjee, Gmyr, Pandurangan PODC 2020) and defines the awake complexity (also called energy complexity), which measures the maximum number of rounds that any node is awake throughout the execution. Only awake nodes can send and receive messages in a given round and all messages sent to sleeping nodes are lost. We present new deterministic consensus algorithms that tolerate up to f < n crash failures, where n is the number of nodes. Our algorithms match the optimal time complexity lower bound of f + 1 rounds. For multi-value consensus, where the input values are chosen from some possibly large set, we achieve an energy complexity of [EQUATION] rounds, whereas for binary consensus, we show that [EQUATION] rounds are possible.
The Freeze-Tag Problem consists in waking up a swarm of robots starting with one initially awake robot. While there exists a wide literature on the centralized setting, where the locations of the robots are known in a...
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ISBN:
(纸本)9798400718854
The Freeze-Tag Problem consists in waking up a swarm of robots starting with one initially awake robot. While there exists a wide literature on the centralized setting, where the locations of the robots are known in advance, we focus on the distributed version where the locations of the robots, P, are unknown, and where awake robots only detect other robots up to distance 1. Assuming that moving at distance δ takes a time δ, we show that waking up the whole swarm takes O(ρ + ℓ2 log(ρ/ℓ)), where ρ is the largest distance from the initial robot to any point of P, and ℓ is the connectivity threshold of P. Moreover, the result is complemented by a matching lower bound. We also provide other distributed algorithms, complemented with lower bounds, whenever each robot has a bounded amount of energy.
Esparza and Reiter have recently conducted a systematic comparative study of models of distributedcomputing consisting of a network of identical finite-state automata that cooperate to decide if the underlying graph ...
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ISBN:
(纸本)9781450385480
Esparza and Reiter have recently conducted a systematic comparative study of models of distributedcomputing consisting of a network of identical finite-state automata that cooperate to decide if the underlying graph of the network satisfies a given property. The study classifies models according to four criteria, and shows that twenty-four initially possible combinations collapse into seven equivalence classes with respect to their decision power, i.e. the properties that the automata of each class can decide. However, Esparza and Reiter only show (proper) inclusions between the classes, and so do not characterise their decision power. In this paper we do so for labelling properties, i.e. properties that depend only on the labels of the nodes, but not on the structure of the graph. In particular, majority (whether more nodes carry label a than b) is a labelling property. Our results show that only one of the seven equivalence classes identified by Esparza and Reiter can decide majority for arbitrary networks. We then study the expressive power of the classes on bounded-degree networks, and show that three classes can. In particular, we present an algorithm for majority that works for all bounded-degree networks under adversarial schedulers, i.e. even if the scheduler must only satisfy that every node makes a move infinitely often, and prove that no such algorithm can work for arbitrary networks.
Given a graph G = (V, E), a β-ruling set is a subset S ⊆ V that is i) independent, and ii) every node υ ∈ V has a node of S within distance β. In this paper we present almost optimal distributed algorithms for fin...
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ISBN:
(纸本)9798400718854
Given a graph G = (V, E), a β-ruling set is a subset S ⊆ V that is i) independent, and ii) every node υ ∈ V has a node of S within distance β. In this paper we present almost optimal distributed algorithms for finding ruling sets in trees and high girth graphs in the classic LOCAL model. As our first contribution we present an O(log log n)-round randomized algorithm for computing 2-ruling sets on trees, almost matching the Ω (log log n/log log log n) lower bound given by Balliu et al. [FOCS'20]. Second, we show that 2-ruling sets can be solved in Õ(log5/3 log n) rounds in high-girth graphs. Lastly, we show that O(log log log n)-ruling sets can be computed in Õ(log log n) rounds in high-girth graphs matching the lower bound up to triple-log factors. All of these results either improve polynomially or exponentially on the previously best algorithms and use a smaller domination distance β.
The restoration lemma by Afek, Bremler-Barr, Kaplan, Cohen, and Merritt [Dist. Comp. '02] proves that, in an undirected unweighted graph, any replacement shortest path avoiding a failing edge can be expressed as t...
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ISBN:
(纸本)9781450385480
The restoration lemma by Afek, Bremler-Barr, Kaplan, Cohen, and Merritt [Dist. Comp. '02] proves that, in an undirected unweighted graph, any replacement shortest path avoiding a failing edge can be expressed as the concatenation of two original shortest paths. However, the lemma is tiebreaking-sensitive: if one selects a particular canonical shortest path for each node pair, it is no longer guaranteed that one can build replacement paths by concatenating two selected shortest paths. They left as an open problem whether a method of shortest path tiebreaking with this desirable property is generally possible. We settle this question affirmatively with the first general construction of restorable tiebreaking schemes. We then show applications to various problems in fault-tolerant network design. These include a faster algorithm for subset replacement paths, more efficient fault-tolerant (exact) distance labeling schemes, fault-tolerant subset distance preservers and +4 additive spanners with improved sparsity, and fast distributed algorithms that construct these objects. For example, an almost immediate corollary of our restorable tiebreaking scheme is the first nontrivial distributed construction of sparse fault-tolerant distance preservers resilient to three faults.
The tutorial will include an introduction to (i) distributed optimization and distributed machine learning, (ii) security or fault-tolerance for distributed optimization and learning, and (iii) privacy in distributed ...
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ISBN:
(纸本)9781450385480
The tutorial will include an introduction to (i) distributed optimization and distributed machine learning, (ii) security or fault-tolerance for distributed optimization and learning, and (iii) privacy in distributed optimization and learning. The presentation will cover the basic principles, and some representative solutions. Server-based and peer-to-peer solutions will be discussed. In particular, Byzantine fault-tolerant algorithms for distributed optimization and learning will be discussed. Privacy mechanisms to be discussed include differential privacy and its variations for systems based on multiple servers.
One of the most basic techniques in algorithm design consists of breaking a problem into subproblems and then proceeding recursively. In the case of graph algorithms, one way to implement this approach is through sepa...
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ISBN:
(纸本)9798400718854
One of the most basic techniques in algorithm design consists of breaking a problem into subproblems and then proceeding recursively. In the case of graph algorithms, one way to implement this approach is through separator sets. Given a graph G = (V, E), a subset of nodes S ⊆ V is called a separator set of G if the size of each connected component of G - S is at most 2/3 · |V|. The most useful separator sets are those that satisfy certain restrictions of cardinality or *** this work, we present the first deterministic algorithm in the distributed CONGEST model that recursively computes a cycle separator over planar graphs in Õ(D) rounds. This result, as in the centralized setting, has significant implications in the area of distributed planar algorithms. In fact, from this result, we can construct a deterministic algorithm that computes a DFS tree in Õ(D) rounds. This matches both the best-known randomized algorithm of Ghaffari and Parter (DISC, 2017) and, up to polylogarithmic factors, the trivial lower bound of Ω(D) rounds.
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