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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 72 (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 <k edges, we describe a communication protocol which uses k rooted spanning ..."
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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 935 Fig. 1.1. Dynamic dictionary communication.
"... may cause the decoder’s dictionary to differ from that of the encoder. Note also that D contains a set of entries (so when we talk about adding a new entry to D, we always mean to add it if it is not already present). 1.2. Applications of dynamic dictionary communication. The major application of dy ..."
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may cause the decoder’s dictionary to differ from that of the encoder. Note also that D contains a set of entries (so when we talk about adding a new entry to D, we always mean to add it if it is not already present). 1.2. Applications of dynamic dictionary communication. The major application of dynamic dictionary communication that motivates this work is adaptive lossless data compression by textual substitution (Storer and Szymanski [1978]), where the dictionary stores a set of strings that have been seen in the past and data is compressed by sending only indices of strings over the channel; such compression algorithms are often called “LZ algorithms ” after the work of Lempel and Ziv [1976] and Ziv and Lempel [1977, 1978]. (See Storer [1988] for an introduction to the subject and references to the literature.) Other possible applications of dynamic dictionary communication include computational learning theory and robotics (e.g., reporting of data by an autonomous remote robot that is mapping unexplored terrain and transmitting coordinates as displacements from previous locations). 1.3. Error resilience. A potential drawback of dynamic dictionary communication
CONCATENATED CODES
, 1965
"... numerous academic departments conduct research. The research reported in this document was made possible in ..."
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numerous academic departments conduct research. The research reported in this document was made possible in