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Symmetry Breaking In Distributed Networks
 Information and Computation
, 1981
"... Given a ring of n processors it is required to design the processors such that they will be able to choose a leader (a uniquely designated processor) by sending messages along the ring. If the processors are indistinguishable then there exists no deterministic algorithm to solve the problem. To over ..."
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Cited by 70 (0 self)
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Given a ring of n processors it is required to design the processors such that they will be able to choose a leader (a uniquely designated processor) by sending messages along the ring. If the processors are indistinguishable then there exists no deterministic algorithm to solve the problem. To overcome this difficulty, probabilistic algorithms are proposed. The algorithms may run forever but they terminate within finite time on the average. For the synchronous case several algorithms are presented: The simplest requires, on the average, the transmission of no more than 2.442n bits and O (n) time. More sophisticated algorithms trade time for communication complexity. If the processors work asynchronously then on the average O (nlogn) bits are transmitted. In the above cases the size of the ring was assumed to be known to all the processors. If the size is not known then finding it may be done only with high probability: any algorithm may yield incorrect results (with nonzero probabilit...
The MultiTree Approach to Reliability in Distributed Networks
 Information and Computation
, 1984
"... Consider a network of asynchronous processors communicating by sending messages over unreliable lines. There are many advantages to restricting all communications to a spanning tree. To overcome the possible failure of k
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Cited by 60 (1 self)
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Consider a network of asynchronous processors communicating by sending messages over unreliable lines. There are many advantages to restricting all communications to a spanning tree. To overcome the possible failure of k <k edges, we describe a communication protocol which uses k rooted spanning trees having the property that for every vertex v the paths from v to the root are edgedisjoint. An algorithm to find two such trees in a 2 edgeconnected graph is described that runs in time proportional to the number of edges in the graph. This algorithm has a distributed version which finds the two trees even when a single edge fails during their construction. The two trees them may be used to transform certain centralized algorithms to distributed, reliable and efficient ones.  1  1. INTRODUCTION Consider a network G=(V ,E ) of n = V asynchronous processors (or vertices) connected by e = E edges. The network may be used to conduct a computation which cannot be done in a single pr...
ErrorResilient Optimal Data Compression
 SIAM J. Computing
, 1997
"... . The problem of communication and computation in the presence of errors is di#cult, and general solutions can be time consuming and inflexible (particularly when implemented with a prescribed error detection/correction). A reasonable approach is to investigate reliable communication in ..."
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Cited by 7 (1 self)
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.<F4.039e+05> The problem of communication and computation in the presence of errors is di#cult, and general solutions can be time consuming and inflexible (particularly when implemented with a prescribed error detection/correction). A reasonable approach is to investigate reliable communication in carefully selected areas of fundamental interest where specific solutions may be more practical than general purpose techniques. In this paper, we study the problem of errorresilient communication and computation in a particularly challenging area,<F4.112e+05> adaptive lossless data<F4.039e+05> compression, where the devastating e#ect of error propagation is a longstanding open problem that was posed in the papers of Lempel and Ziv in the late 1970s. In fact, the nonerror resilience of adaptive data compression has been a practical drawback of its use in many applications. Protocols that require the receiver to request retransmission from the sender when an error is detected can be imprac...