On the Complexity of Information Spreading in Dynamic Networks

We study the design of small cost temporally connected graphs, under various constraints. We mainly consider undirected graphs of n vertices, where each edge has an associated set of discrete availability instances (labels). A journey from vertex u to vertex v is a path from u to v where successive path edges have strictly increasing labels. A graph is temporally connected iff there is a (u, v)-journey for any pair of vertices u, v, u = v. We first give a simple polynomial-time algorithm to check whether a given temporal graph is temporally connected. We then consider the case in which a designer of temporal graphs can freely choose availability instances for all edges and aims for temporal connectivity with very small cost; the cost is the total number of availability instances used. We achieve this via a simple polynomialtime procedure which derives designs of cost linear in n. We also show that the above procedure is (almost) optimal when the underlying graph is a tree, by proving a lower bound on the cost for any tree. However, there are pragmatic cases where one is not free to design a temporally connected graph anew, but is instead given a temporal graph design with the claim that it is temporally connected, and wishes to make it more cost-efficient by removing labels without destroying temporal connectivity (redundant labels). Our main technical result is that computing the maximum number of redundant labels is APX-hard, i.e., there is no PTAS unless P = NP . On the positive side, we show that in dense graphs with random edge availabilities, there is asymptotically almost surely a very large number of redundant labels. A temporal design may, however, be minimal, i.e., no redundant labels exist. We show the existence of minimal temporal designs with at least n log n labels.

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“…In recent years, there is a growing interest in distributed computing systems that are inherently dynamic [5,6,10,12,13,22,26,27,30,32].…”

Section: Dynamic Distributed Networkmentioning

confidence: 99%

The Complexity of Optimal Design of Temporally Connected Graphs

et al. 2017

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“…When proving a lower bound result, we will typically show that there exists a dynamic network contained within the relevant type for which the result holds. In this paper, we will define and analyze two existing dynamic network types: (1-interval) connected networks [10,11,8,6], in which the graph in each round is connected and C describes reliable broadcast to neighbors in the graph, and pairing networks [4], in which the graph in each round is a matching and C describes reliable message passing with each node's neighbor (if any).…”

Section: Dynamic Graphs Network and Typesmentioning

confidence: 99%

“…This section defines the two dynamic network types studied in this paper: the connected network type [10,11,8,6], and the pairing network type [4]. We study random walks (Section 6) and flooding (Section 5) in the context of the connected network type, whereas we study token aggregation (Section 7) in the context of the pairing type.…”

Section: Connected and Pairing Dynamic Network Typesmentioning

confidence: 99%

“…Recent interest in studying distributed algorithms in dynamic networks was sparked by Kuhn et al [10]. Many different problems and dynamic network models have since been proposed; e.g., [11,8,6,3,1,5,13,7] (see [9] for a survey). The dynamic random walk lower bound we study was first proposed by Avin et al [2], while the dynamic aggregation lower bound we study was first proposed by Cornejo et al [4].…”

Section: Introductionmentioning

confidence: 99%

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Smoothed analysis of dynamic networks

et al. 2017

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We generalize the technique of smoothed analysis to distributed algorithms in dynamic network models. Whereas standard smoothed analysis studies the impact of small random perturbations of input values on algorithm performance metrics, dynamic graph smoothed analysis studies the impact of random perturbations of the underlying changing network graph topologies. Similar to the original application of smoothed analysis, our goal is to study whether known strong lower bounds in dynamic network models are robust or fragile: do they withstand small (random) perturbations, or do such deviations push the graphs far enough from a precise pathological instance to enable much better performance? Fragile lower bounds are likely not relevant for real-world deployment, while robust lower bounds represent a true difficulty caused by dynamic behavior. We apply this technique to three standard dynamic network problems with known strong worst-case lower bounds: random walks, flooding, and aggregation. We prove that these bounds provide a spectrum of robustness when subjected to smoothing-some are extremely fragile (random walks), some are moderately fragile / robust (flooding), and some are extremely robust (aggregation).

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“…Dynamic Distributed Networks. In recent years, there is a growing interest in distributed computing systems that are inherently dynamic [2,3,5,7,8,9,11,23,25,26,27,29,31]. Distance labelling.…”

Section: Other Related Workmentioning

confidence: 99%

Ephemeral networks with random availability of links: The case of fast networks

Akrida

Gąsieniec

Mertzios

et al. 2016

Journal of Parallel and Distributed Computing

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Use policyThe full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-pro t purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. This is a PDF file of an unedited manuscript that has been accepted for publication. As a service to our customers we are providing this early version of the manuscript. The manuscript will undergo copyediting, typesetting, and review of the resulting proof before it is published in its final form. Please note that during the production process errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal pertain. Highlights• We define the Temporal Diameter (TD) and the expected TD of temporal networks with random availabilities of links• We define fast and slow random temporal networks, according to their expected TD• Random temporal networks on instances of dense (directed) random graphs G n,p are fast• We introduce the critical availability as a measure of periodic availability of links• We give a lower and an upper bound on the critical availability AbstractWe consider here a model of temporal networks, the links of which are available only at certain moments in time, chosen randomly from a subset of the positive integers. We define the notion of the Temporal Diameter of such networks. We also define fast and slow such temporal networks with respect to the expected value of their temporal diameter. We then provide a partial characterisation of fast random temporal networks. We also define the critical availability as a measure of periodic random availability of the links of a network, required to make the network fast. We finally give a lower bound as well as an upper bound on the (critical) availability.

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On the Complexity of Information Spreading in Dynamic Networks

Cited by 55 publications

References 22 publications

The Complexity of Optimal Design of Temporally Connected Graphs

The Complexity of Optimal Design of Temporally Connected Graphs

Smoothed analysis of dynamic networks

Ephemeral networks with random availability of links: The case of fast networks

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