## The Multi-Tree Approach to Reliability in Distributed Networks (1984)

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Venue: | Information and Computation |

Citations: | 59 - 1 self |

### BibTeX

@ARTICLE{Itai84themulti-tree,

author = {Alon Itai and Michael Rodeh},

title = {The Multi-Tree Approach to Reliability in Distributed Networks},

journal = {Information and Computation},

year = {1984},

volume = {79},

pages = {43--59}

}

### Years of Citing Articles

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### Abstract

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 edge-disjoint. An algorithm to find two such trees in a 2 edge-connected 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...

### Citations

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Citation Context ...ient to the failure of vertices since we were not able to overcome the following difficulties: (1) In our model the processors cannot come to an agreement which depends on the course of the algorithm =-=[FLP]-=-. (2) The algorithm might terminate prematurely because it started at a single vertex which failed before sending any messages. (3) When a vertex fails, all the information stored there is lost. (4) I... |

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Citation Context ... w such that g (u )sg (v )sg (w ). Thus if every edge is oriented from its low numbered end to its high numbered end then every vertex lies on a directed path from s to t . Lempel, Even and Cederbaum =-=[LEC]-=- have shown that every 2-vertex connected graph G has an s-t numbering and used it to test graph planarity. Even and Tarjan [ET] gave a linear algorithm based on DFS to find such a numbering. We follo... |

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Graph Algorithms. Computer Science
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Citation Context ...graph G has an s-t numbering and used it to test graph planarity. Even and Tarjan [ET] gave a linear algorithm based on DFS to find such a numbering. We follow the algorithm and proof as presented in =-=[Ev]-=-. To construct an s-t numbering we have to look more closely at the DFS algorithm. Let D be a DFS tree rooted at t whose first edge is (t ,s ). Let N (v ) be the number given to v by the DFS. Thus N (... |

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Nash-Williams, On orientations, connectivity and odd vertex pairings in finite graphs
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Citation Context ...is a k -edge-connected graph then G satisfies the k -Tree Condition. The converse, a counterpart of Lemma 1, is easy. We now show some weaker results for k 3. The orientation theorem of Nash-Williams =-=[NW]-=- and the branching theorem of Edmonds [Ed, T, Shi] show that every k -edge-connected graph has l f loork /2 rf loor edge-disjoint spanning trees. Thus k -edge connectivity implies the condition for l ... |

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private communication
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Citation Context ...s section we develop an algorithm to construct two such trees. 2.2. s-t Numbering To show that 2-edge connectivity implies the 2-tree condition for edges we follow a suggestion of Professor A. Lempel =-=[L]-=- (thus replacing a previous lengthier direct proof). Let G be a 2-vertex connected graph, and (s ,t ) an edge of G , then g : Vs{1,2, . . . ,n } is an s-t numbering if the following conditions are sat... |

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Tarjan, Computing an s-t numbering, Th
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(Show Context)
Citation Context ...ertex lies on a directed path from s to t . Lempel, Even and Cederbaum [LEC] have shown that every 2-vertex connected graph G has an s-t numbering and used it to test graph planarity. Even and Tarjan =-=[ET]-=- gave a linear algorithm based on DFS to find such a numbering. We follow the algorithm and proof as presented in [Ev]. To construct an s-t numbering we have to look more closely at the DFS algorithm.... |

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