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Optimal Algorithms for Broadcast and Gossip in the EdgeDisjoint Path Modes (Extended Abstract)
 INFORMATION AND COMPUTATION
, 1994
"... The communication power of the oneway and twoway edgedisjoint path modes for broadcast and gossip is investigated. The complexity of communication algorithms is measured by the number of communication steps (rounds). The main results achieved are the following: 1. For each connected graph Gn of ..."
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The communication power of the oneway and twoway edgedisjoint path modes for broadcast and gossip is investigated. The complexity of communication algorithms is measured by the number of communication steps (rounds). The main results achieved are the following: 1. For each connected graph Gn of n nodes, the complexity of broadcast in Gn , Bmin(Gn ), satisfies dlog 2 ne Bmin(Gn) dlog 2 ne + 1. The complete binary trees meet the upper bound, and all graphs containing a Hamiltonian path meet the lower bound. 2. For each connected graph Gn of n nodes, the oneway (twoway) gossip complexity R(Gn ) (R 2 (Gn)) satisfies dlog 2 ne R 2 (Gn) 2 \Delta dlog 2 ne + 1, 1:44 : : : log 2 n R(Gn) 2 \Delta dlog 2 ne + 2. All these lower and upper bounds a...
Optimized Broadcasting and Multicasting Protocols in Cutthrough Routed Networks
"... This paper addresses the onetoall broadcasting problem, and the onetomany broadcasting problem, usually simply called broadcasting and multicasting, respectively. Broadcasting is the information dissemination problem in which a node of a network sends the same piece of information to all the ..."
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This paper addresses the onetoall broadcasting problem, and the onetomany broadcasting problem, usually simply called broadcasting and multicasting, respectively. Broadcasting is the information dissemination problem in which a node of a network sends the same piece of information to all the other nodes. Multicasting is a partial broadcasting in the sense that only a subset of nodes forms the destination set. Both operations have many applications in parallel and distributed computing. In this paper, we study these problems in both line model, and cutthrough model. The former assumes long distance calls between nonneighboring processors. The latter strengthens the line model by taking into account the use of a routing function. Long distance calls are possible in circuitswitched and wormhole routed networks, and also in many networks supporting optical facilities. In the line model, it is wellknown that one can compute in polynomial time a dlog 2 neround broadcast o...
The Relationship Between Gossiping in VertexDisjoint Paths Mode and Bisection Width (Extended Abstract)
 In Proc. 19th Int. Symp. on Mathematical Foundations of Computer Science
, 1994
"... ) Ralf Klasing Department of Mathematics and Computer Science University of Paderborn 33095 Paderborn, Germany Abstract. The twoway communication mode used for sending messages to processors of interconnection networks via vertexdisjoint paths in one communication step is investigated. The comple ..."
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) Ralf Klasing Department of Mathematics and Computer Science University of Paderborn 33095 Paderborn, Germany Abstract. The twoway communication mode used for sending messages to processors of interconnection networks via vertexdisjoint paths in one communication step is investigated. The complexity of communication algorithms is measured by the number of communication steps (rounds). This paper establishes a direct relationship between the gossip complexity and the vertex bisection width. More precisely, the main results are the following: 1. The lower bound 2 log 2 n \Gamma log 2 k \Gamma log 2 log 2 k \Gamma 2 is proved on the number of rounds of every twoway gossip algorithm working on any graph Gn;k of n nodes and vertex bisection k. 2. A graph Gn;k of n nodes and vertex bisection k, and a twoway gossip algorithm for Gn;k is constructed working in 2 log 2 n \Gamma log 2 k \Gamma log 2 log 2 k + 2 rounds. The first result improves the lower bound of 2 log 2 n\Gammalog 2 k \...
Approximation algorithms for minimumtime broadcast under the vertexdisjoint paths mode
 In 9th Annual European Symposium on Algorithms (ESA '01), volume 2161 of LNCS
, 2001
"... We give a polynomialtime O( log n log OPT)approximation algorithm for minimumtime broadcast and minimumtime multicast in nnode networks under the singleport vertexdisjoint paths mode. This improves a previous approximation algorithm by Kortsarz and Peleg. In contrast, we give an (log n) lower ..."
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We give a polynomialtime O( log n log OPT)approximation algorithm for minimumtime broadcast and minimumtime multicast in nnode networks under the singleport vertexdisjoint paths mode. This improves a previous approximation algorithm by Kortsarz and Peleg. In contrast, we give an (log n) lower bound for the approximation ratio of the minimumtime multicast problem in directed networks. This lower bound holds unless NP Dtime(n log log n). An important consequence of this latter result is that the Steiner version of the Minimum Degree Spanning Tree (MDST) problem in digraphs cannot be approximated within a constant ratio, as opposed to the undirected version. Finally, we give a polynomialtime O(1)approximation algorithm for minimumtime gossip (i.e., alltoall broadcast).
On the Robustness of Interconnections in Random Graphs: A Symbolic Approach
, 2000
"... Graphs are models of communication networks. This paper applies symbolic combinatorial techniques in order to characterize the interplay between two parameters of a random graph, namely its density (the number of edges in the graph) and its robustness to link failures. Here, robustness means mul ..."
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Graphs are models of communication networks. This paper applies symbolic combinatorial techniques in order to characterize the interplay between two parameters of a random graph, namely its density (the number of edges in the graph) and its robustness to link failures. Here, robustness means multiple connectivity by short disjoint paths. We determine the expected number of ways to get from a source to a destination via two edgedisjoint paths of length ` in the classical random graph model G n;p . We then derive bounds on related threshold probabilities.
Polynomial Time Algorithms for MinimumTime Broadcast in Trees
 Theory of Computing Systems
"... This paper addresses the minimumtime broadcast problem under several modes of the line model, i.e., when longdistance calls can be placed along paths in the network. ..."
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This paper addresses the minimumtime broadcast problem under several modes of the line model, i.e., when longdistance calls can be placed along paths in the network.
Gossiping in chordal rings under the line model
 UNGER (EDS.), PROCEEDINGS OF THE MFCS’98 WORKSHOP ON COMMUNICATION
, 1998
"... This paper is devoted to the gossip (or alltoall) problem in the chordal ring under the oneport line model. The line model assumes long distance calls between non neighboring processors. In this sense, the line model is strongly related to circuitswitched networks, wormhole routing, optical netw ..."
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This paper is devoted to the gossip (or alltoall) problem in the chordal ring under the oneport line model. The line model assumes long distance calls between non neighboring processors. In this sense, the line model is strongly related to circuitswitched networks, wormhole routing, optical networks supporting wavelength division multiplexing, ATM switching, and networks supporting connected mode routing protocols. Since the chordal rings are competitors of networks as meshes or tori because of theirs short diameter and bounded degree, it is of interest to ask whether they can support intensive communications (typically alltoall) as e ciently as these networks. We propose polynomial algorithms to derive optimal or near optimal gossip protocols in the chordal ring.