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"distributed algorithms"
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Distributed $(\\Delta+1)$-Coloring in Linear (in $\\Delta$) Time
The distributed$(\\Delta + 1)$ -coloring problem is one of the most fundamental and well-studied problems in distributed algorithms. Starting with the work of Cole and Vishkin in 1986, a long line of gradually improving algorithms has been published. The state-of-the-art running time, prior to our work, is$O(\\Delta \\log \\Delta + \\log^* n)$ , due to Kuhn and Wattenhofer [Proceedings of the$25$ th Annual ACM Symposium on Principles of Distributed Computing, Denver, CO, 2006, pp. 7--15]. Linial [Proceedings of the$28$ th Annual IEEE Symposium on Foundation of Computer Science, Los Angeles, CA, 1987, pp. 331--335] proved a lower bound of$\\frac{1}{2} \\log^* n$for the problem, and Szegedy and Vishwanathan [Proceedings of the 25th Annual ACM Symposium on Theory of Computing, San Diego, CA, 1993, pp. 201--207] provided a heuristic argument that shows that algorithms from a wide family of locally iterative algorithms are unlikely to achieve a running time smaller than$\\Theta(\\Delta \\log \\Delta)$ . We present a deterministic$(\\Delta + 1)$ -coloring distributed algorithm with running time$O(\\Delta) + \\frac{1}{2} \\log^* n$ . We also present a trade-off between the running time and the number of colors, and devise an$O(\\lambda\\cdot\\Delta)$ -coloring algorithm, with running time$O(\\Delta / \\lambda + \\log^* n)$ , for any parameter$\\lambda > 1$ . Our algorithm breaks the heuristic barrier of Szegedy and Vishwanathan and achieves running time which is linear in the maximum degree$\\Delta$ . On the other hand, the conjecture of Szegedy and Vishwanathan may still be true, as our algorithm does not belong to the family of locally iterative algorithms. On the way to this result we study a generalization of the notion of graph coloring, which is called defective coloring [L. Cowen, R. Cowen, and D. Woodall, J. Graph Theory, 10 (1986), pp. 187--195]. In an$m$ -defective$p$ -coloring the vertices are colored with$p$colors so that each vertex has up to$m$neighbors with the same color. We show that an$m$ -defective$p$ -coloring with reasonably small$m$and$p$can be computed very efficiently in the distributed setting. We also develop a technique to employ multiple defective colorings of various subgraphs of the original graph$G$for computing a$(\\Delta+1)$ -coloring of$G$ . We believe that these techniques are of independent interest. [PUBLICATION ABSTRACT]
Journal Article
Distributed algorithms from arboreal ants for the shortest path problem
Colonies of the arboreal turtle ant create networks of trails that link nests and food sources on the graph formed by branches and vines in the canopy of the tropical forest. Ants put down a volatile pheromone on the edges as they traverse them. At each vertex, the next edge to traverse is chosen using a decision rule based on the current pheromone level. There is a bidirectional flow of ants around the network. In a previous field study, it was observed that the trail networks approximately minimize the number of vertices, thus solving a variant of the popular shortest path problem without any central control and with minimal computational resources. We propose a biologically plausible model, based on a variant of the reinforced random walk on a graph, which explains this observation and suggests surprising algorithms for the shortest path problem and its variants. Through simulations and analysis, we show that when the rate of flow of ants does not change, the dynamics converges to the path with the minimum number of vertices, as observed in the field. The dynamics converges to the shortest path when the rate of flow increases with time, so the colony can solve the shortest path problem merely by increasing the flow rate. We also show that to guarantee convergence to the shortest path, bidirectional flow and a decision rule dividing the flow in proportion to the pheromone level are necessary, but convergence to approximately short paths is possible with other decision rules.
Journal Article
Distributed Verification and Hardness of Distributed Approximation
We study the verification problem in distributed networks, stated as follows. Let$H$be a subgraph of a network$G$where each vertex of$G$knows which edges incident on it are in$H$ . We would like to verify whether$H$has some properties, e.g., if it is a tree or if it is connected (every node knows at the end of the process whether$H$has the specified property or not). We would like to perform this verification in a decentralized fashion via a distributed algorithm. The time complexity of verification is measured as the number of rounds of distributed communication. In this paper we initiate a systematic study of distributed verification and give almost tight lower bounds on the running time of distributed verification algorithms for many fundamental problems such as connectivity, spanning connected subgraph, and$s$ - $t$cut verification. We then show applications of these results in deriving strong unconditional time lower bounds on the hardness of distributed approximation for many classical optimization problems including minimum spanning tree (MST), shortest paths, and minimum cut. Many of these results are the first nontrivial lower bounds for both exact and approximate distributed computation, and they resolve previous open questions. Moreover, our unconditional lower bound of approximating MST subsumes and improves upon the previous hardness of approximation bound of Elkin [M. Elkin, SIAM J. Comput., 36 (2006), pp. 433--456] as well as the lower bound for (exact) MST computation of Peleg and Rubinovich [D. Peleg and V. Rubinovich, SIAM J. Comput., 30 (2000), pp. 1427--1442]. Our result implies that there can be no distributed approximation algorithm for MST that is significantly faster than the current exact algorithm for any approximation factor. Our lower bound proofs show an interesting connection between communication complexity and distributed computing which turns out to be useful in establishing the time complexity of exact and approximate distributed computation of many problems. [PUBLICATION ABSTRACT]
Journal Article
Information‐Theoretically Private Federated Submodel Learning With Byzantine Local Updates
In federated submodel learning (FSL), the aggregator has multiple submodels to train, and each local machine chooses a specific submodel to update with its local training data. Therefore, a local machine may want to conceal which submodel was accessed by the local machine against the aggregator, as well as its local training data. However, Byzantine local updates during the upload phase pose a fundamental threat, as a single adversary can corrupt multiple submodels simultaneously. In this paper, an information‐theoretically private FSL scheme for protecting the multiple submodels stored in aggregators against the Byzantine local updates of the upload phase is considered, which has not been considered in previous works. This paper proposes an information‐theoretically private federated submodel learning (FSL) scheme that protects the identity of the submodel accessed by each local machine and its local training data from the aggregator. It also addresses the challenge of protecting multiple submodels stored in aggregators against Byzantine updates during the upload phase, a topic not previously explored.
Journal Article
Waterfall: Gozalandia. Distributed protocol with fast finality and proven safety and liveness
A consensus protocol is a crucial mechanism of distributed networks by which nodes can coordinate their actions and the current state of data. This article describes a BlockDAG consensus algorithm based on the Proof of Stake approach. The protocol provides network participants with cross‐voting for the order of blocks, which, in the case of a fair vote, guarantees a quick consensus. Under conditions of dishonest behavior, cross‐voting ensures that violations will be quickly detected. In addition, the protocol assumes the existence of a Coordinating network containing information about the approved ordering, which qualitatively increases security and also serves to improve network synchronization.
Journal Article
Second-order consensus of multi-agent systems with noise
This study studies second-order consensus of multi-agent systems with noise in a leaderless architecture. Two distributed consensus algorithms are designed and sufficient conditions are established, which character how much the noise intensity or the delay multi-agent systems can stand such that second-order consensus can be reached almost surely for a given coupling strength and topology structure. Simulations are given to illustrate the effectiveness of the proposed consensus algorithms.
Journal Article
A Hybrid Intelligent Simulation System for Building IoT Networks: Performance Comparison of Different Router Replacement Methods for WMNs Considering Stadium Distribution of IoT Devices
As the Internet of Things (IoT) devices and applications proliferate, it becomes increasingly important to design robust networks that can continue to meet user demands at a high level. Wireless local area networks (WLANs) can be a good choice as IoT infrastructure when high throughput is required. On the other hand, wireless mesh networks (WMNs), which are WLANs with mesh topology following the IEEE802.11s standard, have many advantages compared to conventional WLANs. Nevertheless, there are some problems that need solutions. One of them is the node placement problem. In this work, we propose and implement a hybrid intelligent system that solves this problem by determining the position of mesh nodes by maximizing the mesh connectivity and the coverage of IoT devices. The system is based on particle swarm optimization (PSO), simulated annealing (SA), and distributed genetic algorithm (DGA). We compare the performance of three router replacement methods: constriction method (CM), random inertia weight method (RIWM), and rational decrement of Vmax method (RDVM). The simulation results show that RIWM achieves better performance compared to CM and RDVM because it achieves the highest connectivity while covering more clients than the other two methods.
Journal Article
The canonical amoebot model: algorithms and concurrency control
The amoebot model abstracts active programmable matter as a collection of simple computational elements called amoebots that interact locally to collectively achieve tasks of coordination and movement. Since its introduction at SPAA 2014, a growing body of literature has adapted its assumptions for a variety of problems; however, without a standardized hierarchy of assumptions, precise systematic comparison of results under the amoebot model is difficult. We propose the canonical amoebot model, an updated formalization that distinguishes between core model features and families of assumption variants. A key improvement addressed by the canonical amoebot model is concurrency. Much of the existing literature implicitly assumes amoebot actions are isolated and reliable, reducing analysis to the sequential setting where at most one amoebot is active at a time. However, real programmable matter systems are concurrent. The canonical amoebot model formalizes all amoebot communication as message passing, leveraging adversarial activation models of concurrent executions. Under this granular treatment of time, we take two complementary approaches to concurrent algorithm design. We first establish a set of sufficient conditions for algorithm correctness under any concurrent execution, embedding concurrency control directly in algorithm design. We then present a concurrency control framework that uses locks to convert amoebot algorithms that terminate in the sequential setting and satisfy certain conventions into algorithms that exhibit equivalent behavior in the concurrent setting. As a case study, we demonstrate both approaches using a simple algorithm for hexagon formation. Together, the canonical amoebot model and these complementary approaches to concurrent algorithm design open new directions for distributed computing research on programmable matter.
Journal Article