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Virtual Time and Global States of Distributed Systems
 PARALLEL AND DISTRIBUTED ALGORITHMS
, 1988
"... A distributed system can be characterized by the fact that the global state is distributed and that a common time base does not exist. However, the notion of time is an important concept in every day life of our decentralized "real world" and helps to solve problems like getting a consiste ..."
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Cited by 741 (6 self)
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A distributed system can be characterized by the fact that the global state is distributed and that a common time base does not exist. However, the notion of time is an important concept in every day life of our decentralized "real world" and helps to solve problems like getting a consistent population census or determining the potential causality between events. We argue that a linearly ordered structure of time is not (always) adequate for distributed systems and propose a generalized nonstandardmodel of time which consists of vectors of clocks. These clockvectors arepartially orderedand form a lattice. By using timestamps and a simple clock update mechanism the structure of causality is represented in an isomorphic way. The new model of time has a close analogy to Minkowski's relativistic spacetime and leads among others to an interesting characterization of the global state problem. Finally, we present a new algorithm to compute a consistent global snapshot of a distributed system where messages may bereceived out of order.
A new approach to the maximum flow problem
 JOURNAL OF THE ACM
, 1988
"... All previously known efficient maximumflow algorithms work by finding augmenting paths, either one path at a time (as in the original Ford and Fulkerson algorithm) or all shortestlength augmenting paths at once (using the layered network approach of Dinic). An alternative method based on the pre ..."
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Cited by 672 (34 self)
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All previously known efficient maximumflow algorithms work by finding augmenting paths, either one path at a time (as in the original Ford and Fulkerson algorithm) or all shortestlength augmenting paths at once (using the layered network approach of Dinic). An alternative method based on the preflow concept of Karzanov is introduced. A preflow is like a flow, except that the total amount flowing into a vertex is allowed to exceed the total amount flowing out. The method maintains a preflow in the original network and pushes local flow excess toward the sink along what are estimated to be shortest paths. The algorithm and its analysis are simple and intuitive, yet the algorithm runs as fast as any other known method on dense. graphs, achieving an O(n³) time bound on an nvertex graph. By incorporating the dynamic tree data structure of Sleator and Tarjan, we obtain a version of the algorithm running in O(nm log(n²/m)) time on an nvertex, medge graph. This is as fast as any known method for any graph density and faster on graphs of moderate density. The algorithm also admits efticient distributed and parallel implementations. A parallel implementation running in O(n²log n) time using n processors and O(m) space is obtained. This time bound matches that of the ShiloachVishkin algorithm, which also uses n processors but requires O(n²) space.
Concurrent Online Tracking of Mobile Users
 J. ACM
, 1991
"... This paper deals with the problem of maintaining a distributed directory server, that enables us to keep track of mobile users in a distributed network in the presence of concurrent requests. The paper uses the graphtheoretic concept of regional matching for implementing efficient tracking mechanis ..."
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Cited by 233 (7 self)
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This paper deals with the problem of maintaining a distributed directory server, that enables us to keep track of mobile users in a distributed network in the presence of concurrent requests. The paper uses the graphtheoretic concept of regional matching for implementing efficient tracking mechanisms. The communication overhead of our tracking mechanism is within a polylogarithmic factor of the lower bound. 1 Introduction Since the primary function of a communication network is to provide communication facilities between users and processes in the system, one of the key problems such a network faces is the need to be able to Department of Mathematics and Lab. for Computer Science, M.I.T., Cambridge, MA 02139, USA. Email: baruch@theory.lcs.mit.edu. Supported by Air Force Contract TNDGAFOSR860078, ARO contract DAAL0386K0171, NSF contract CCR8611442, DARPA contract N0001489J 1988, and a special grant from IBM. y Departmentof Applied Mathematicsand Computer Science, The Weizm...
A Tradeoff between Space and Efficiency for Routing Tables
, 1988
"... Abstract. Two conflicting goals play a crucial role in the design of routing schemes for communication networks. A routing scheme should use paths that are as short as possible for routing messages in the network, while keeping the routing information stored in the processors ’ local memory as succi ..."
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Cited by 164 (7 self)
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Abstract. Two conflicting goals play a crucial role in the design of routing schemes for communication networks. A routing scheme should use paths that are as short as possible for routing messages in the network, while keeping the routing information stored in the processors ’ local memory as succinct as possible. The efficiency of a routing scheme is measured in terms of its stretch factorthe maximum ratio between the length of a route computed by the scheme and that of a shortest path connecting the same pair of vertices. Most previous work has concentrated on finding good routing schemes (with a small fixed stretch factor) for special classes of network topologies. In this paper the problem for general networks is studied, and the entire range of possible stretch factors is examined. The results exhibit a tradeoff between the efficiency of a routing scheme and its space requirements. Almost tight upper and lower bounds for this tradeoff are presented. Specifically, it is proved that any routing scheme for general nvertex networks that achieves a stretch factor k 2 1 must use a total of Q(n ‘+“fzLcJ)) bits of routing information in the networks. This lower bound is complemented by a family Z(k) of hierarchic:al routing schemes (for every k z 1) for unitcost general networks, which guarantee a stretch factor of O(k), require storing a total of O(k. n ‘+(““logn) bits of routing information in the network, name the vertices with O(log’n)bit names and use O(logn)bit headers.
Consistent global states of distributed systems: Fundamental concepts and mechanisms
 DISTRIBUTED SYSTEMS
, 1993
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AdHoc Networks Beyond Unit Disk Graphs
, 2003
"... In this paper we study a model for adhoc networks close enough to reality as to represent existing networks, being at the same time concise enough to promote strong theoretical results. The Quasi Unit Disk Graph model contains all edges shorter than a parameter d between 0 and 1 and no edges longer ..."
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Cited by 142 (11 self)
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In this paper we study a model for adhoc networks close enough to reality as to represent existing networks, being at the same time concise enough to promote strong theoretical results. The Quasi Unit Disk Graph model contains all edges shorter than a parameter d between 0 and 1 and no edges longer than 1. We show that  in comparison to the cost known on Unit Disk Graphs  the complexity results in this model contain the additional factor 1/d&sup2;. We prove that in Quasi Unit Disk Graphs flooding is an asymptotically messageoptimal routing technique, provide a geometric routing algorithm being more efficient above all in dense networks, and show that classic geometric routing is possible with the same performance guarantees as for Unit Disk Graphs if d 1/ # 2.
A GraphTheoretic Game and its Application to the kServer Problem
 SIAM J. COMPUT
, 1995
"... This paper investigates a zerosum game played on a weighted connected graph G between two players, the tree player and the edge player. At each play, the tree player chooses a spanning tree T and the edge player chooses an edge e. The payoff to the edge player is cost(T; e), defined as follows: If ..."
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Cited by 141 (4 self)
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This paper investigates a zerosum game played on a weighted connected graph G between two players, the tree player and the edge player. At each play, the tree player chooses a spanning tree T and the edge player chooses an edge e. The payoff to the edge player is cost(T; e), defined as follows: If e lies in the tree T then cost(T; e) = 0; if e does not lie in the tree then cost(T; e) = cycle(T; e)=w(e), where w(e) is the weight of edge e and cycle(T; e) is the weight of the unique cycle formed when edge e is added to the tree T. Our main result is that the value of the game on any nvertex graph is bounded above by exp(O( p log n log log n)). The game arises in connection with the kserver problem on a road network; i.e., a metric space that can be represented as a multigraph G in which each edge e represents a road of length w(e). We show that, if the value of the game on G is V al(G; w), then there is a randomized strategy that achieves a competitive ratio of k(1 + V al(G; w)) against any oblivious adversary. Thus, on any nvertex road network, there is a randomized algorithm for the kserver problem that is k exp(O( p log n log log n))competitive against oblivious adversaries. At the heart of our analysis of the game is an algorithm that, for any nvertex weighted, connected multigraph, constructs a spanning tree T such
Compact Routing with Minimum Stretch
 Journal of Algorithms
"... We present the first universal compact routing algorithm with maximum stretch bounded by 3 that uses sublinear space at every vertex. The algorithm uses local routing tables of size O(n 2=3 log 4=3 n) and achieves paths that are most 3 times the length of the shortest path distances for all node ..."
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Cited by 121 (4 self)
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We present the first universal compact routing algorithm with maximum stretch bounded by 3 that uses sublinear space at every vertex. The algorithm uses local routing tables of size O(n 2=3 log 4=3 n) and achieves paths that are most 3 times the length of the shortest path distances for all nodes in an arbitrary weighted undirected network. This answers an open question of Gavoille and Gengler who showed that any universal compact routing algorithm with maximum stretch strictly less than 3 must use\Omega\Gamma n) local space at some vertex. 1 Introduction Let G = (V; E) with jV j = n be a labeled undirected network. Assuming that a positive cost, or distance is assigned with each edge, the stretch of path p(u; v) from node u to node v is defined as jp(u;v)j jd(u;v)j , where jd(u; v)j is the length of the shortest u \Gamma v path. The approximate allpairs shortest path problem involves a tradeoff of stretch against time short paths with stretch bounded by a constant are com...
Uniform dynamic selfstabilizing leader election
 IEEE Transactions on Parallel and Distributed Systems
, 1997
"... Abstract—A distributed system is selfstabilizing if it can be started in any possible global state. Once started the system regains its consistency by itself, without any kind of outside intervention. The selfstabilization property makes the system tolerant to faults in which processors exhibit a ..."
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Cited by 113 (10 self)
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Abstract—A distributed system is selfstabilizing if it can be started in any possible global state. Once started the system regains its consistency by itself, without any kind of outside intervention. The selfstabilization property makes the system tolerant to faults in which processors exhibit a faulty behavior for a while and then recover spontaneously in an arbitrary state. When the intermediate period in between one recovery and the next faulty period is long enough, the system stabilizes. A distributed system is uniform if all processors with the same number of neighbors are identical. A distributed system is dynamic if it can tolerate addition or deletion of processors and links without reinitialization. In this work, we study uniform dynamic selfstabilizing protocols for leader election under readwrite atomicity. Our protocols use randomization to break symmetry. The leader election protocol stabilizes in OaD'log nf time when the number of the processors is unknown and OaD'f, otherwise. Here D denotes the maximal degree of a node, ' denotes the diameter of the graph and n denotes the number of processors in the graph. We introduce selfstabilizing protocols for synchronization that are used as building blocks by the leaderelection algorithm. We conclude this work by presenting a simple, uniform, selfstabilizing ranking protocol. Index Terms—Selfstabilizing systems, leader election, distributed algorithms, randomized distributed algorithms, synchronization. 1