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27
Computing on an Anonymous Ring
 Journal of the ACM
, 1988
"... Abstract. The computational capabilities of a system of n indistinguishable (anonymous) processors arranged on a ring in the synchronous and asynchronous models of distributed computation are analyzed. A precise characterization of the functions that can be computed in this setting is given. It is s ..."
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Cited by 99 (2 self)
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Abstract. The computational capabilities of a system of n indistinguishable (anonymous) processors arranged on a ring in the synchronous and asynchronous models of distributed computation are analyzed. A precise characterization of the functions that can be computed in this setting is given. It is shown that any of these functions can be computed in O(r?) messages in the asynchronous model. This is also proved to be a lower bound for such elementary functions as AND, SUM, and Orientation. In the synchronous model any computable function can be computed in O(n log n) messages. A ring can be oriented and start synchronized within the same bounds. The main contribution of this paper is a new technique for proving lower bounds in the synchronous model. With this technique tight lower bounds of O(nlogn) (for particular n) are proved for XOR, SUM, Orientation, and Start Synchronization. The technique is based on a stringproducing mechanism from formal language theory, first introduced by Thue to study squarefree words. Two methods for generalizing the synchronous lower bounds to arbitrary ring sizes are presented.
Computing on anonymous networks, part I: characterizing the solvable cases
 IEEE TRANSACTION ON PARALLEL AND DISTRIBUTED COMPUTING
, 1996
"... In anonymous networks, the processors do not have identity numbers. We investigate the following representative problems on anonymous networks: (a) the leader election problem, (b) the edge election problem, (c) the spanning tree construction problem, and (d) the topology recognition problem. On a g ..."
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Cited by 81 (3 self)
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In anonymous networks, the processors do not have identity numbers. We investigate the following representative problems on anonymous networks: (a) the leader election problem, (b) the edge election problem, (c) the spanning tree construction problem, and (d) the topology recognition problem. On a given network, the above problems may or may not be solvable, depending on the amount of information about the attributes of the network made available to the processors. Some possibilities are: (1) no network attribute information at all is available, (2) an upper bound on the number of processors in the network is available, (3) the exact number of processors in the network is available, and (4) the topology of the network is available. In terms of a new graph property called “symmetricity, ” in each of the four cases (1)–(4) above, we characterize the class of networks on which each of the four problems (a)–(d) is solvable. We then relate the symmetricity of a network to its 1 and 2factors.
Hundreds of Impossibility Results for Distributed Computing
 Distributed Computing
, 2003
"... We survey results from distributed computing that show tasks to be impossible, either outright or within given resource bounds, in various models. The parameters of the models considered include synchrony, faulttolerance, different communication media, and randomization. The resource bounds refe ..."
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Cited by 52 (5 self)
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We survey results from distributed computing that show tasks to be impossible, either outright or within given resource bounds, in various models. The parameters of the models considered include synchrony, faulttolerance, different communication media, and randomization. The resource bounds refer to time, space and message complexity. These results are useful in understanding the inherent difficulty of individual problems and in studying the power of different models of distributed computing.
MemoryEfficient and SelfStabilizing Network RESET (Extended Abstract)
 In PODC94 Proceedings of the Thirteenth Annual ACM Symposium on Principles of Distributed Computing
, 1994
"... ) Baruch Awerbuch Rafail Ostrovsky y August 15, 1994 Abstract In this paper we consider the question of faulttolerant distributed network protocols with extremely small memory requirements per processor. In particular, we show that even in the case of worstcase transient faults (i.e., in a ..."
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Cited by 28 (3 self)
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) Baruch Awerbuch Rafail Ostrovsky y August 15, 1994 Abstract In this paper we consider the question of faulttolerant distributed network protocols with extremely small memory requirements per processor. In particular, we show that even in the case of worstcase transient faults (i.e., in a selfstabilizing setting), many fundamental network protocols can be achieved using only O(log n) bits of memory per incident network edge. In the heart of our construction is a selfstabilizing asynchronous network reset protocol with the same small memory requirements. Johns Hopkins University, Baltimore, MD 21218, and MIT Lab. for Computer Science. Email: baruch@blaze.cs.jhu.edu. Supported by Air Force Contract TNDGAFOSR860078, ARPA/Army contract DABT6393C0038, ARO contract DAAL0386K0171, NSF contract 9114440CCR, DARPA contract N00014J921799. y U.C. Berkeley and ICSI. Supported by NSF postdoctoral fellowship and ICSI. Email: rafail@cs.berkeley.edu. 1 1 Introduction...
A Tradeoff Between Information and Communication in Broadcast Protocols
 Journal of the ACM
, 1990
"... This paper concerns the message complexity of broadcast in arbitrary pointtopoint communication networks. Broadcast is a task initiated by a single processor that wishes to convey a message to all processors in the network. We assume the widely accepted model of communication networks, in which eac ..."
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Cited by 25 (3 self)
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This paper concerns the message complexity of broadcast in arbitrary pointtopoint communication networks. Broadcast is a task initiated by a single processor that wishes to convey a message to all processors in the network. We assume the widely accepted model of communication networks, in which each processor initially knows the identity of its neighbors, but does not know the entire network topology. Although it seems obvious that the number of messages required for broadcast in this model equals the number of links, no proof of this basic fact has been given before. We show that the message complexity of broadcast depends on the exact complexity measure. If messages of unbounded length are counted at unit cost, then broadcast requires \Theta(jV j) messages, where V is the set of processors in the network. We prove that if one counts messages of bounded length then broadcast requires \Theta(jEj) messages, where E is the set of edges in the network. Assuming an intermediate model in w...
Symmetry and Computability in Anonymous Networks: A Brief Survey
 Proc. 3rd Int. Conf. on Structural Information and Communication Complexity (SIROCCO'96), Carleton
, 1996
"... . Processors in anonymous networks are as identical to each other as possible and possess "little" knowledge about the network. Anonymous networks are very useful in theoretical studies for testing "true distributivity". In this paper we give a brief survey of results illuminatin ..."
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Cited by 23 (4 self)
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. Processors in anonymous networks are as identical to each other as possible and possess "little" knowledge about the network. Anonymous networks are very useful in theoretical studies for testing "true distributivity". In this paper we give a brief survey of results illuminating how symmetry influences computability in anonymous networks. Problems and issues considered include leader election, spanning tree construction, orientations, randomization, processor views, and computability problems on arbitrary as well as symmetric functions. Results mentioned are applicable to several topologies ranging from the rings, tori, hypercubes, and Cayley networks to arbitrary networks. We also propose several related open problems. 1980 Mathematics Subject Classification: 68Q99 CR Categories: C.2.1 Key Words and Phrases: Anonymous network, boolean function, cayley graphs, computability, gap theorem, hypercube, leader election, ring, symmetry. SCS Technical report: TR9618 1 Introduction Id...
Distributed Anonymous Discrete Function Computation
"... Abstract—We propose a model for deterministic distributed function computation by a network of identical and anonymous nodes. In this model, each node has bounded computation and storage capabilities that do not grow with the network size. Furthermore, each node only knows its neighbors, not the ent ..."
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Cited by 19 (2 self)
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Abstract—We propose a model for deterministic distributed function computation by a network of identical and anonymous nodes. In this model, each node has bounded computation and storage capabilities that do not grow with the network size. Furthermore, each node only knows its neighbors, not the entire graph. Our goal is to characterize the class of functions that can be computed within this model. In our main result, we provide a necessary condition for computability which we show to be nearly sufficient, in the sense that every function that violates this condition can at least be approximated. The problem of computing (suitably rounded) averages in a distributed manner plays a central role in our development; we provide an algorithm that solves it in time that grows quadratically with the size of the network. Index Terms—Averaging algorithms, distributed computing, distributed control. I.
Computing on Anonymous Networks with Sense of Direction
 in Proc. of 3rd Colloquium on Structural Information and Communication Complexity
, 1996
"... Sense of direction refers to a set of global consistency constraints of the local labeling of the edges of a network. Sense of direction has a large impact on the communication complexity of many distributed problems. In this paper, we study the impact that sense of direction has on computability an ..."
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Cited by 18 (9 self)
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Sense of direction refers to a set of global consistency constraints of the local labeling of the edges of a network. Sense of direction has a large impact on the communication complexity of many distributed problems. In this paper, we study the impact that sense of direction has on computability and we focus on anonymous networks. We establish several results. In particular, we prove that with weak sense of direction, the intuitive knowledgecomputability hierarchy between levels of a priori structural knowledge collapses. A powerful implication is the formal proof that shortest path routing is possible in anonymous networks with sense of direction. We prove that weak sense of direction is computationally stronger than topological awareness. We also consider several fundamental problems; for each, we provide a complete characterization of the anonymous networks on which it is computable with sense of direction. 1 Introduction A distributed system is a collection of autonomous entitie...
New lower bound techniques for distributed leader finding and other problems on rings of processors
 COMPUTER SCIENCE DEPT., INDIANA UNIVERSITY, BLOOMINGTON
, 1991
"... Several new lower bounds are derived for deterministic and randomized extrema finding and some other problems on asynchronous, nonanonymous rings of processors, where the ring size n is known in advance to the processors. With a new technique, using results from extremal graph theory, an f2(n log n ..."
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Cited by 17 (1 self)
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Several new lower bounds are derived for deterministic and randomized extrema finding and some other problems on asynchronous, nonanonymous rings of processors, where the ring size n is known in advance to the processors. With a new technique, using results from extremal graph theory, an f2(n log n) lower bound is obtained for the average number of messages for distributed leader finding, on rings where the processors know the ring size n, and processors take identities from a set I with size as small as en, for any constant e> 1. Formerly, this bound was only known for special values of n, and exponential size of I. Also, improvements are made on the constant factor of the f2(n log n) bound. An elementary, but powerful result shows that the same bounds hold for randomized algorithms. It is shown that f2(n log n) lower bounds can be derived for the expected message complexity for computing AND on an input 1 ', OR on an input 0 ' or XOR over all inputs, even when processors have unique identities. This confirms a conjecture of Abrahamson et. al. [2].
Backward Consistency and Sense of Direction in Advanced Distributed Systems (Extended Abstract)
 IN PROC. OF THE 18TH A.C.M. SYMPOSIUM ON PRINCIPLES OF DISTRIBUTED COMPUTING
, 1999
"... The studies on the relationship between label consistency, computability and complexity assume the existence of local orientation; this assumption is in fact at the basis of the pointtopoint model and is realistic for systems where a communication link can connect only two entities. However, in ..."
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Cited by 8 (5 self)
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The studies on the relationship between label consistency, computability and complexity assume the existence of local orientation; this assumption is in fact at the basis of the pointtopoint model and is realistic for systems where a communication link can connect only two entities. However, in systems which use more advanced communication and interconnection technology such as buses, optical networks, wireless communication media, etc., and more importantly, heterogeneous systems (such as internet) which include any combination of the above, local orientation can not be assumed. In this paper we consider a new type of consistency which we shall call backward consistency and which, unlike sense of direction, can exist even without local orientation. Thus...