Skip to content
Free planNo credit card requiredStart writing
AI for Research home
AI for Research home
Dashboard
Sign inGet started

Search 250 million research papers

Read the abstract, see who wrote it and who cites it, and get the citation in APA, MLA, Chicago or Harvard.

About 482 papers for “Distributed minimum spanning tree”

Distributed minimum diameter spanning tree construction

Bui, Marc, Butelle, Franck, Institut National de Recherche en Informatique et en Automatique (INRIA), 78 - Rocquencourt (France). Unite de Recherche de Rocquencourt · OpenGrey (Institut de l'Information Scientifique et Technique) · 1993

Cited by 0

Awake Complexity of Distributed Minimum Spanning Tree

John Augustine, William K. Moses, Gopal Pandurangan · arXiv (Cornell University) · 2022

We study the distributed minimum spanning tree (MST) problem, a fundamental problem in distributed computing. It is well-known that distributed MST can be solved in $\tilde{O}(D+\sqrt{n})$ rounds in the standard CONGEST model (where $n$ is the network size and $D$ is the network diameter) and this is essentially the best possible round complexity (up to logarithmic factors). However, in resource-constrained networks such as ad hoc wireless and sensor networks, nodes spending so much time can lead to significant spending of resources such as energy. Motivated by the above consideration, we study distributed algorithms for MST under the \emph{sleeping model} [Chatterjee et al., PODC 2020], a model for design and analysis of resource-efficient distributed algorithms. In the sleeping model, a node can be in one of two modes in any round -- \emph{sleeping} or \emph{awake} (unlike the traditional model where nodes are always awake). Only the rounds in which a node is \emph{awake} are counted, while \emph{sleeping} rounds are ignored. A node spends resources only in the awake rounds and hence the main goal is to minimize the \emph{awake complexity} of a distributed algorithm, the worst-case number of rounds any node is awake. We present deterministic and randomized distributed MST algorithms that have an \emph{optimal} awake complexity of $O(\log n)$ time with a matching lower bound. We also show that our randomized awake-optimal algorithm has essentially the best possible round complexity by presenting a lower bound of $\tildeΩ(n)$ on the product of the awake and round complexity of any distributed algorithm (including randomized) that outputs an MST. To complement our trade-off lower bound, we present a parameterized family of distributed algorithms that gives an essentially optimal trade-off between the awake complexity and the round complexity.

Cited by 0Open access

Distributed Broadcast Minimum Spanning Tree (reliable version)

Ahmad A. Kardan, Mohammad Kajbaf · 2007

DBMST is a broadcast communication protocol that provides a distributed MST algorithm It is based on the FPS power-management protocol. This paper presents the complete version of DBMST that regards packet loss and dynamism of the network topology and provides reliable communication. The proposed method decreases the power consumption of reliable broadcasting up to 15% in comparison with the basic version. In DBMST, network structure adapts to topology variations quickly while it takes several hours for other methods to find out variations in network.

Cited by 1

Distributed Minimum Spanning Tree Maintenance for Transient Node Failures

Paola Flocchini, Tony Mesa Enriquez, Linda Pagli et al. · IEEE Transactions on Computers · 2010

In many network applications, the computation takes place on the minimum-cost spanning tree (MST) of the network G; unfortunately, a single link or node failure disconnects the tree. The ALL NODES REPLACEMENT (ANR) problem is the problem of precomputing, for each node u in G, the new MST should u fail. This problem has been extensively investigated for serial and parallel settings, and efficient solutions have been designed for those environments. The situation is surprisingly different in distributed settings. In fact, no distributed solution exists to date which performs better than the brute-force repeated application of MST construction. In this paper, we consider for the first time the problem of computing all the replacement minimum-cost spanning trees distributively. We design a solution protocol, and we prove that the total amount of communication exchanges taking place is O(n), each exchange using at most O(n) data items. Hence, the total amount of data items communicated during the computation (the data complexity) is O(n^2). We also show how the simpler problem ALL EDGES REPLACEMENT (AER) dealing with single edge failures, which can be solved with the same costs using some existing techniques. Also for the AER problem, efficient solutions exist in the serial and parallel setting but, prior to this work, no distributed solution other than brute force was known.

Cited by 18

Tight Bounds for Distributed Minimum-Weight Spanning Tree Verification

Kor, Liah, Korman, Amos, Peleg, David · arXiv (Cornell University) · 2015

This paper introduces the notion of distributed verification without preprocessing. It focuses on the Minimum-weight Spanning Tree (MST) verification problem and establishes tight upper and lower bounds for the time and message complexities of this problem. Specifically, we provide an MST verification algorithm that achieves simultaneously O(m) messages and O($\sqrt$ n+D) time, where m is the number of edges in the given graph G, n is the number of nodes, and D is G's diameter. On the other hand, we show that any MST verification algorithm must send Ω(m) messages and incur Ω($\sqrt$ n + D) time in worst case. Our upper bound result appears to indicate that the verification of an MST may be easier than its construction, since for MST construction, both lower bounds of Ω(m) messages and Ω($\sqrt$ n+D time hold, but at the moment there is no known distributed algorithm that constructs an MST and achieves simultaneously O(m) messages and O($\sqrt$ n + D) time. Specifically, the best known time-optimal algorithm (using O($\sqrt$ n + D) time) requires O(m + n 3/2) messages, and the best known message-optimal algorithm (using O(m) messages) requires O(n) time. On the other hand, our lower bound results indicate that the verification of an MST is not significantly easier than its construction.

Cited by 0Open access

Efficient Distributed Algorithms for Minimum Spanning Tree in Dense Graphs

MohammadHossein Bateni, Morteza Monemzadeh, Kees Voorintholt · 2022 IEEE International Conference on Data Mining Workshops (ICDMW) · 2022

In recent years, the Massively Parallel Computation (MPC) model capturing the MapReduce framework has become the de facto standard model for large-scale data analysis, given the ubiquity of efficient and affordable cloud implementations. In this model, an input of size <tex>$m$</tex> is initially distributed among <tex>$t$</tex> machines, each with a local space of size <tex>$s$</tex>. Computation proceeds in synchronous rounds in which each machine performs arbitrary local computation on its data and then sends messages to other machines. In this paper, we study the Minimum Spanning Tree (MST) problem for dense graphs in the MPC model. We say a graph <tex>$G(V,\ E)$</tex> is relatively dense if <tex>$m=\Theta(n^{1+c})$</tex> where <tex>$n=\vert V\vert$</tex> is the number of vertices, <tex>$m=\vert E\vert$</tex> is the number of edges in this graph, and <tex>$0 &lt; c\leq 1$</tex>. We develop the first work- and space-efficient MPC algorithm that with high probability computes an MST of <tex>$G$</tex> using <tex>$\lceil\log\frac{c}{\epsilon}\rceil+1$</tex> rounds of communication. As an MPC algorithm, our algorithm uses <tex>$t=O(n^{c-\epsilon})$</tex> machines each one having local storage of size <tex>$s=O(n^{1+\epsilon})$</tex> for any <tex>$0 &lt; \epsilon\leq c$</tex>. Indeed, not only is this algorithm very simple and easy to implement, it also simultaneously achieves optimal total work, per-machine space, and number of rounds.

Cited by 0

Efficient distributed algorithm to solve updating minimum spanning tree problem

Jung‐Ho Park, Kenichi Hagihara, Nobuki Tokura et al. · Systems and Computers in Japan · 1992

Abstract This paper proposes a distributed algorithm for reconstructing a minimum‐weight spanning tree T ′ of a network N ′ when link addition and deletion occur in a network N with a minimum‐weight spanning tree T. In this algorithm each processor uses information whose adjacent links belong to T in order to construct T ′ efficiently. The communication complexity and ideal time complexity of the algorithm are O(n log (f + t) + m) and O(n log (f + t) + n) , respectively, where n and e are the number of processors and that of links in N ′, t is the number of added links, and f represents that of deleted links belonging to T. Here, m = n + t when f = 0 and m = e otherwise. This paper also presents a distributed algorithm for reconstructing a minimum‐weight spanning tree T + when links and processors are added and deleted. The communication complexity and ideal time complexity of the algorithm are O(n log (g + h) + r and O(n log (g + h) + n) , respectively, where g is the total number of added links (including links incident to added processors) and h represents the number of deleted links belonging to T (including links incident to deleted processors). Thus, r = n + g when h = 0 and r = e when h &gt; 0.

Cited by 4

Energy-Efficient Distributed Minimum Spanning Tree Construction: Tight Bounds and Algorithms

Yongwook Choi, et al. · 2013

Traditionally, the performance of distributed algorithms has been measured in terms of running time and message complexity. However, in many settings, a more accurate and relevant measure of performance is required. In ad hoc wireless networks, energy is a very critical factor for measuring the efficiency of a distributed algorithm. Thus in addition to the traditional time and message complexity, it is also relevant to consider energy complexity that accounts for the total energy associated with the messages exchanged among the nodes in a distributed algorithm. This paper focuses on the energy complexity of distributed algorithms for the Euclidean minimum spanning tree (MST) problem, one of the most important problems in distributed computing. We show tight upper and lower bounds on the energy complexity of distributed (Euclidean) MST algorithms. We also study distributed approximation algorithms for MST that have almost optimal energy complexity, but give a constant factor approximation to the MST. We present two sets of results, one where nodes are distributed randomly in a plane, and the other where nodes can be arbitrarily distributed. For random distribution of nodes, we show that Ω(log n) is a lower bound on the energy complexity of any distributed MST algorithm. We then give a distributed algorithm that constructs an optimal MST with O(log n) energy complexity on

Cited by 0