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24
A sublinear time distributed algorithm for minimumweight spanning trees
 SIAM J. Comput
, 1998
"... (Extended Abstract) ..."
Fast Distributed Construction of Small kDominating Sets and Applications
, 2000
"... This paper presents a fast distributed algorithm to compute a small kdominating set D (for any xed k) and its induced graph partition (breaking the graph into radius k clusters centered around the vertices of D). The time complexity of the algorithm is O(k log n). ..."
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Cited by 48 (7 self)
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This paper presents a fast distributed algorithm to compute a small kdominating set D (for any xed k) and its induced graph partition (breaking the graph into radius k clusters centered around the vertices of D). The time complexity of the algorithm is O(k log n).
A Faster Distributed Protocol for Constructing a Minimum Spanning Tree
 In Proc. of the 15 th Annual ACMSIAM Symposium on Discrete Algorithms (SODA
, 2004
"... Abstract This paper studies the problem of constructing a minimumweight spanning tree (MST) in a distributed network. This is one of the most important problems in the area of distributed computing. There is a long line of gradually improving protocols for this problem, and the state of the art to ..."
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Cited by 38 (3 self)
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Abstract This paper studies the problem of constructing a minimumweight spanning tree (MST) in a distributed network. This is one of the most important problems in the area of distributed computing. There is a long line of gradually improving protocols for this problem, and the state of the art today isa protocol with running time O(\Lambda (G) + pn * log * n) due to Kutten and Peleg [22], where \Lambda (G) denotesthe diameter of the graph G. Peleg and Rubinovich [29] have shown that ~\Omega (pn) time is required forconstructing an MST even on graphs of small diameter, and claimed that their result &quot;establishes the asymptotic nearoptimality &quot; of the protocol of [22].In this paper we refine this claim, and devise a protocol that constructs the MST in ~ O(u(G,!)+pn)rounds, where u(G,!) is the MSTradius of the graph. The ratio between the diameter and the MSTradius may be as large as \Theta ( n), and, consequently, on some inputs our protocol is faster than theprotocol of [22] by a factor of ~\Omega (p n). Also, on every input, the running time of our protocol is nevergreater than twice the running time of the protocol of [22].
Time and Message Bounds for Election in Synchronous and Asynchronous Complete Networks
 SIAM Journal on Computing
, 1991
"... This paper addresses the problem of distributively electing a leader in both synchronous and asynchronous complete networks. We present O(n log n) messages synchronous and asynchronous algorithms. The time complexity of the synchronous algorithm is O(log n), while that of the asynchronous algorithm ..."
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Cited by 26 (1 self)
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This paper addresses the problem of distributively electing a leader in both synchronous and asynchronous complete networks. We present O(n log n) messages synchronous and asynchronous algorithms. The time complexity of the synchronous algorithm is O(log n), while that of the asynchronous algorithm is O(n). In the synchronous case, we prove a lower bound of \Omega\Gamma n log n) on the message complexity. We also prove that any messageoptimal synchronous algorithm requires\Omega\Gammaqui n) time. In proving these bounds we do not restrict the type of operations performed by nodes. The bounds thus apply to general algorithms and not just to comparison based algorithms. 1 Introduction In the election problem, a single node, called the leader, is to be selected from a set of nodes which initially differ only in their identifiers (ids), with no node being aware of any other id. An arbitrary subset of nodes wakes up spontaneously at arbitrary times and starts the A preliminary version...
Optimal Distributed Algorithm for Minimum Spanning Trees Revisited
 in Proceedings of the 14th Annual ACM Symposium on Principles of Distributed Computing
, 1995
"... In an earlier paper, Awerbuch presented an innovative distributed algorithm for solving minimum spanning tree (MST) problems that achieved optimal time and message complexity through the introduction of several advanced features. In this paper, we show that there are some cases where his algorithm ..."
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Cited by 24 (3 self)
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In an earlier paper, Awerbuch presented an innovative distributed algorithm for solving minimum spanning tree (MST) problems that achieved optimal time and message complexity through the introduction of several advanced features. In this paper, we show that there are some cases where his algorithm can create cycles or fail to achieve optimal time complexity. We then show how to modify the algorithm to avoid these problems, and demonstrate both the correctness and optimality of the revised algorithm. 1 Introduction Given an undirected graph G with N nodes and E edges, with weights assigned to each edge, we want to find a spanning tree for which the combined weight of all its edges is minimized, denoted an MST in the sequel. Furthermore, we want to use a distributed algorithm to find that MST by placing a processor at each node and treating each edge as a bidirectional and errorfree communication channel, over which the nodes can exchange messages among themselves. We assume that ini...
A fast distributed approximation algorithm for minimum spanning trees
 IN PROCEEDINGS OF THE 20TH INTERNATIONAL SYMPOSIUM ON DISTRIBUTED COMPUTING (DISC
, 2006
"... We present a distributed algorithm that constructs an O(log n)approximate minimum spanning tree (MST) in any arbitrary network. This algorithm runs in time Õ(D(G) + L(G, w)) where L(G, w) is a parameter called the local shortest path diameter and D(G) is the (unweighted) diameter of the graph. Our ..."
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Cited by 24 (7 self)
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We present a distributed algorithm that constructs an O(log n)approximate minimum spanning tree (MST) in any arbitrary network. This algorithm runs in time Õ(D(G) + L(G, w)) where L(G, w) is a parameter called the local shortest path diameter and D(G) is the (unweighted) diameter of the graph. Our algorithm is existentially optimal (up to polylogarithmic factors), i.e., there exists graphs which need Ω(D(G) + L(G, w)) time to compute an Happroximation to the MST for any H ∈ [1, Θ(log n)]. Our result also shows that there can be a significant time gap between exact and approximate MST computation: there exists graphs in which the running time of our approximation algorithm is exponentially faster than the timeoptimal distributed algorithm that computes the MST. Finally, we show that our algorithm can be used to find an approximate MST in wireless networks and in random weighted networks in almost optimal Õ(D(G)) time.
Local MST Computation with Short Advice
 SPAA
, 2007
"... We use the recently introduced advising scheme framework for measuring the difficulty of locally distributively computing a Minimum Spanning Tree (MST). An (m, t)advising scheme for a distributed problem P is a way, for every possible input I of P, to provide an ”advice” (i.e., a bit string) about ..."
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Cited by 16 (9 self)
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We use the recently introduced advising scheme framework for measuring the difficulty of locally distributively computing a Minimum Spanning Tree (MST). An (m, t)advising scheme for a distributed problem P is a way, for every possible input I of P, to provide an ”advice” (i.e., a bit string) about I to each node so that: (1) the maximum size of the advices is at most m bits, and (2) the problem P can be solved distributively in at most t rounds using the advices as inputs. In case of MST, the output returned by each node of a weighted graph G is the edge leading to its parent in some rooted MST T of G. Clearly, there is a trivial (⌈log n⌉, 0)advising scheme for MST (each node is given the local port number of the edge leading to the root of some MST T), and it is known that any (0, t)advising scheme satisfies t ≥ ˜ Ω ( √ n). Our main result is the construction of an (O(1), O(log n))advising scheme for MST. That is, by only giving a constant number of bits of advice to each node, one can decrease exponentially the distributed computation time of MST in arbitrary graph, compared to algorithms dealing with the problem in absence of any a priori information. We also consider the average size of the advices. On the one hand, we show that any (m, 0)advising scheme for MST gives advices of average size Ω(log n). On the other hand we design an (m, 1)advising scheme for MST with advices of constant average size, that is one round is enough to decrease the average size of the advices from log n to constant.
A LatticeStructured Proof Technique Applied to a Minimum Spanning Tree Algorithm (Extended Abstract)
 Laboratory for Computer Science, Massachusetts Institute of Technology
, 1988
"... Jennifer Lundelius Welch Leslie Lamport Digital Equipment Corporation, Systems Research Center Abstract: rithms are often hard to prove correct because they have no natural decomposition into separately provable parts. This paper presents a proof technique for the modular verification of su ..."
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Cited by 12 (3 self)
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Jennifer Lundelius Welch Leslie Lamport Digital Equipment Corporation, Systems Research Center Abstract: rithms are often hard to prove correct because they have no natural decomposition into separately provable parts. This paper presents a proof technique for the modular verification of such nonmodular algorithms. It generalizes existing verification techniques based on a totallyordered hierarchy of refinements to allow a partiallyordered hierarchythat is; a lattice of different views of the algorithm. The technique is applied to the wellknown distributed minimum spanning tree algorithm of Gallager, Humblet and Spira, which has until recently lacked a rigorous proof. 1.
Creating Optimal Distributed Algorithms for Minimum Spanning Trees
, 1995
"... This paper examines the complexity of distributed algorithms for finding a Minimum Spanning Tree in undirected graphs; the goal is to create algorithms optimal with respect to both communication O(E +N log N ) and time O(N ), where E; N is the number of edges and nodes respectively. A fundamental ..."
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Cited by 10 (1 self)
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This paper examines the complexity of distributed algorithms for finding a Minimum Spanning Tree in undirected graphs; the goal is to create algorithms optimal with respect to both communication O(E +N log N ) and time O(N ), where E; N is the number of edges and nodes respectively. A fundamental bad case that leads to nonoptimal performance and the proposed techniques to overcome this problem are presented. We introduce new techniques based on the the idea that we call Distributed Information; nodes store information that summarizes properties of groups of nodes. The techniques (and the corresponding algorithms) are classified in communication optimal and time optimal ones. Finally, the structure of the algorithm proposed in [Awe87] and the above classification can lead to a pattern for creating optimal algorithms. In addition, a simple O(E) messages and O(N ) time algorithm for counting the nodes of the network is introduced; It can be used as part of the optimal algorithm...
M.R.: A learning automatabased heuristic algorithm for solving the minimum spanning tree problem in stochastic graphs
, 2010
"... During the last decades, a host of efficient algorithms have been developed for solving the minimum spanning tree problem in deterministic graphs, where the weight associated with the graph edges is assumed to be fixed. Though it is clear that the edge weight varies with time in realistic applicatio ..."
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Cited by 8 (4 self)
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During the last decades, a host of efficient algorithms have been developed for solving the minimum spanning tree problem in deterministic graphs, where the weight associated with the graph edges is assumed to be fixed. Though it is clear that the edge weight varies with time in realistic applications and such an assumption is wrong, finding the minimum spanning tree of a stochastic graph has not received the attention it merits. This is due to the fact that the minimum spanning tree problem becomes incredibly hard to solve when the edge weight is assumed to be a random variable. This becomes more difficult, if we assume that the probability distribution function of the edge weight is unknown. In this paper, we propose a learning automata‐based heuristic algorithm to solve the minimum spanning tree problem in stochastic graphs wherein the probability distribution function of the edge weight is unknown. The proposed algorithm taking advantage of learning automata determines the edges that must be sampled at each stage. As the presented algorithm proceeds, the sampling process is concentrated on the edges that constitute the spanning tree with the minimum expected weight. The proposed learning automata‐based sampling method decreases the number of samples that need to be taken from the graph by reducing the rate of unnecessary samples. Experimental results show the superiority of the proposed algorithm over the well‐known existing methods both in terms of the number of samples and the running time of algorithm.