A Problem with Telephones

Bumby, Richard T.

doi:10.1137/0602002

Cited by 71 publications

(35 citation statements)

References 6 publications

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“…There is a large literature on gossiping and broadcasting algorithms in networks; see [11] for a survey. Two paradigmatic problems in this area are (i) the Telephone Problem [2,5,8,10,20], in which we seek a way for & individuals to each transmit a distinct piece of information to everyone else using the minimum number of person-to-person phone calls; and (ii) the Minimum Broadcast Time (see [3,17] and the references therein), in which we seek a way for a designated source node in a graph to transmit a piece of information to all other nodes in the minimum number of parallel rounds of node-to-node communication. Note the fundamental difference between this body of work and the types of problems we will be considering.…”

mentioning

confidence: 99%

Connectivity and inference problems for temporal networks

Kempe

Kleinberg

Kumar

2000

Proceedings of the Thirty-Second Annual ACM Symposium on Theory of Computing

177

115

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Many network problems are based on fundamental relationships involving time. Consider, for example, the problems of modeling the flow of information through a distributed network, studying the spread of a disease through a population, or analyzing the reachability properties of an airline timetable. In such settings, a natural model is that of a graph in which each edge is annotated with a time label specifying the time at which its endpoints "communicated." We will call such a graph a temporal network. To model the notion that information in such a network "flows" only on paths whose labels respect the ordering of time, we call a path time-respecting if the time labels on its edges are non-decreasing.The central motivation for our work is the following question: how do the basic combinatorial and algorithmic properties of graphs change when we impose this additional temporal condition? The notion of a path is intrinsic to many of the most fundamental algorithmic problems on graphs; spanning trees, connectivity, flows, and cuts are some examples. When we focus on time-respecting paths in place of arbitrary paths, many of these problems acquire a character that is different from the traditional setting, but very rich in its own right.We provide results on two types of problems for temporal networks. First, we consider connectivity problems, in which we seek disjoint time-respecting paths between pairs of nodes. The natural analogue of Menger's Theorem for node-disjoint paths fails in general for time-respecting paths; we give a non-trivial characterization of those graphs for which the theorem does hold in terms of an excluded subdivision theorem, and provide a polynomial-time algorithm for connectivity on this class of graphs. (The problem on general graphs is NP-complete.) We then define and study the class of inference problems, in which we seek to reconstruct a partially specified time labeling of a network in a manner consistent with an observed history of information flow.A preliminary version of this paper appears in Proc. 32nd ACM Symposium on Theory of Computing.¡

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mentioning

confidence: 99%

Connectivity and inference problems for temporal networks

Kempe

Kleinberg

Kumar

2000

Proceedings of the Thirty-Second Annual ACM Symposium on Theory of Computing

177

115

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“…In our case, since each item of gossip is a data item that might take considerable time to transfer between two disks, we cannot assume that an arbitrary number of data items can be exchanged in a single round. Several other papers use the same telephone call model [2,7,14,18,30]. Liben-Nowell [23] gives an exponential time exact algorithm for the problem.…”

Section: Related Workmentioning

confidence: 99%

On generalized gossiping and broadcasting

Khuller¹,

Kim²,

Wan³

2006

Journal of Algorithms

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Abstract. The problems of gossiping and broadcasting have been widely studied. The basic gossip problem is defined as follows: there are n individuals, with each individual having an item of gossip. The goal is to communicate each item of gossip to every other individual. Communication typically proceeds in rounds, with the objective of minimizing the number of rounds. One popular model, called the telephone call model, allows for communication to take place on any chosen matching between the individuals in each round. Each individual may send (receive) a single item of gossip in a round to (from) another individual. In the broadcasting problem, one individual wishes to broadcast an item of gossip to everyone else. In this paper, we study generalizations of gossiping and broadcasting. The basic extensions are: (a) each item of gossip needs to be broadcast to a specified subset of individuals and (b) several items of gossip may be known to a single individual. We study several problems in this framework that generalize gossiping and broadcasting. Our study of these generalizations was motivated by the problem of managing data on storage devices, typically a set of parallel disks. For initial data distribution, or for creating an initial data layout we may need to distribute data from a single server or from a collection of sources.

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“…The goal is to determine the minimum number of calls necessary for all of the participants to learn all of the initial information. A number of researchers have independently proven that 2n − 4 calls are necessary and sufficient to achieve this goal [3,6,17,21,35].…”

Section: Incomplete Gossipmentioning

confidence: 99%

Gossip is synteny: Incomplete gossip and the syntenic distance between genomes

Liben-Nowell

2002

Journal of Algorithms

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The syntenic distance between two genomes is given by the minimum number of fusions, fissions, and translocations required to transform one into the other, ignoring the order of genes within chromosomes. Computing this distance is NP-hard. In the present work, we give a tight connection between syntenic distance and the incomplete gossip problem, a novel generalization of the classical gossip problem. In this problem, there are n gossipers, each with a unique piece of initial information; they communicate by phone calls in which the two participants exchange all their information. The goal is to minimize the total number of phone calls necessary to inform each gossiper of his set of relevant gossip which he desires to learn.As an application of the connection between syntenic distance and incomplete gossip, we derive an O(2 O(n log n) ) algorithm to exactly compute the syntenic distance between two genomes with at most n chromosomes each. Our algorithm requires O(n 2 + 2 O(d log d) ) time when this distance is d, improving the O(n 2 + 2 O(d 2 ) ) running time of the best previous exact algorithm.

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A Problem with Telephones

Cited by 71 publications

References 6 publications

Connectivity and inference problems for temporal networks

Connectivity and inference problems for temporal networks

On generalized gossiping and broadcasting

Gossip is synteny: Incomplete gossip and the syntenic distance between genomes

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