Gossip Problem Research Articles

A lightweight epistemic logic and its application to planning

We study multiagent epistemic planning with a simple epistemic logic whose language is a restriction of that of standard epistemic logic. Its formulas are boolean combinations of observability atoms: sequences of ‘knowing whether’ operators followed by propositional variables. This compares favourably with other restricted languages where formulas are boolean combinations of epistemic literals: sequences of ‘knowing that’ epistemic operators and negations followed by propositional variables; or in other terms: epistemic formulas without conjunctions or disjunctions. The reason is that our language enables a richer theory of mind: we can express statements such as “I don't know whether p, but I know that you know whether p” which are important in communication and more generally in interaction and which cannot be expressed with epistemic literals. Going beyond previous work, we also introduce a ‘common knowledge whether’ operator. We show that satisfiability is nevertheless NP-complete. We then define simple epistemic planning tasks as generalisations of classical planning tasks: action descriptions have sets of observability atoms as add- and delete-lists, initial states are sets of observability atoms, and goals are boolean combinations of observability atoms. We show that simple epistemic planning tasks can be polynomially translated into classical planning tasks. It follows that checking solvability of simple epistemic planning tasks is PSpace-complete. We present some application examples such as the gossip problem and some experimental results and clarify the relationship with Dynamic Epistemic Logic-based planning.

Solving Gossip Problems using Answer Set Programming: An Epistemic Planning Approach

We investigate the use of Answer Set Programming to solve variations of gossip problems, by modeling them as epistemic planning problems.

The logic of gossiping

The so-called gossip problem is a formal model of peer-to-peer communication. In order to perform such communication efficiently, it is important to keep track of what agents know about who holds what information at a given point in time. The knowledge that the agents possess depends strongly on the particular type of communication that is used.Here, we formally define a large number of different variants of the gossip problem, that differ in the extent to which communication is private (observable, synchronous or asynchronous), the direction of the flow of information (caller to callee, callee to caller or both) and whether the agents become aware of the exact set of information possessed by their communication partner.We consider a number of formulas that represent interesting properties that a gossip situation may or may not enjoy, and show for which variants they are valid. Additionally, we show that the model checking and validity checking problems for each variant are decidable, and we introduce sound and complete proof systems for them.

Accelerated Gossip in Networks of Given Dimension Using Jacobi Polynomial Iterations

Consider a network of agents connected by communication links, where each agent holds a real value. The gossip problem consists in estimating the average of the values diffused in the network in a distributed manner. We develop a method for solving the gossip problem that depends only on the spectral dimension of the network, that is, in the communication network set-up, the dimension of the space in which the agents live. This contrasts with previous work that required the spectral gap of the network as a parameter, or suffered from slow mixing. Our method shows an important improvement over existing algorithms in the nonasymptotic regime, i.e., when the values are far from being fully mixed in the network. Our approach stems from a polynomial-based point of view on gossip algorithms, as well as an approximation of the spectral measure of the graphs with a Jacobi measure. We show the power of the approach with simulations on various graphs, and with performance guarantees on graphs of known spectral dimension, such as grids and random percolation bonds. An extension of this work to distributed Laplacian solvers is discussed. As a side result, we also use the polynomial-based point of view to show the convergence of the message passing algorithm for gossip of Moallemi and Van Roy on regular graphs. The explicit computation of the rate of the convergence shows that message passing has a slow rate of convergence on graphs with small spectral gap.

FAKES, GOSSIP AND RUMORS AS A MEANS OF SOCIAL MISINFORMATION AND WEAKENING OF THE SAFETY COMPONENTS OF THE GOVERNMENT OF THE STATE

The purpose. The article is devoted to solving the problem of spreading gossip, rumor and fake as one of the tools of instilling the premonitions of a great anti-Ukrainian conspiracy in a hybrid war. Method. To solve this scientific problem the following methods were applied: the structural method; the method of comparative analysis of empirical data; the method of abstract-logical generalization. Results. Based on the analysis of literary sources and the existing experience of security work, problems with their prevention have been identified. The directions of strengthening and the development of national security in the conditions of social misinformation have been determined. Scientific novelty. The ways of increasing the effectiveness of security measures and preventing the negative influence of misinformation through the state ideological and educational and innovation-management factors have been proposed. Practical significance. The main provisions of the scientific article will provide an opportunity due to these factors, to ensure peace in society and the stable functioning of the national economy of Ukraine, which, in fact, can make them competitive in the conditions of the EU, since the research was carried out in the transformational post-totalitarian society.

FAKES, GOSSIP AND RUMORS AS A MEANS OF SOCIAL MISINFORMATION AND WEAKENING OF THE SAFETY COMPONENTS OF THE GOVERNMENT OF THE STATE

The purpose. The article is devoted to solving the problem of spreading gossip, rumor and fake as one of the tools of instilling the premonitions of a great anti-Ukrainian conspiracy in a hybrid war. Method. To solve this scientific problem the following methods were applied: the structural method; the method of comparative analysis of empirical data; the method of abstract-logical generalization. Results. Based on the analysis of literary sources and the existing experience of security work, problems with their prevention have been identified. The directions of strengthening and the development of national security in the conditions of social misinformation have been determined. Scientific novelty. The ways of increasing the effectiveness of security measures and preventing the negative influence of misinformation through the state ideological and educational and innovation-management factors have been proposed. Practical significance. The main provisions of the scientific article will provide an opportunity due to these factors, to ensure peace in society and the stable functioning of the national economy of Ukraine, which, in fact, can make them competitive in the conditions of the EU, since the research was carried out in the transformational post-totalitarian society.

The epistemic gossip problem

In the gossip problem information (‘secrets’) must be shared among a certain number of agents using the minimum number of calls. We extend the gossip problem to arbitrary epistemic depths. For example, we may require not only that all agents know all secrets but also that all agents know that all agents know all secrets. We give optimal protocols for various versions of this epistemic gossip problem, depending on the graph of communication links, in the case of two-way communication, one-way communication and parallel communication. We show, among other things, that increasing epistemic depth from 1 (all agents know all secrets) to 2 (so that all agents know that all agents know all secrets) does not double the required number of calls but increases this number by 3∕2 (for a complete graph). We also show that the following counter-intuitive result generalises to the epistemic gossip problem: asymptotically the same number of calls are required whether calls are two-way or one-way.

How to share knowledge by gossiping

Given n agents each of which has a secret (a fact not known to anybody else), the classical version of the gossip problem is to achieve shared knowledge of all secrets in a minimal number of phone calls. There exist protocols achieving shared knowledge in \(2(n{-}2)\) calls: when the protocol terminates everybody knows all the secrets. We generalize that problem and focus on higher-order shared knowledge: how many calls does it take to obtain that everybody knows that everybody knows all secrets? More generally, how many calls does it take to obtain shared knowledge of order k? This requires not only the communication of secrets, but also the communication of knowledge about secrets. We give a protocol that works in \((k{+}1)(n{-}2)\) steps and prove that it is correct: it achieves shared knowledge of level k. The proof is presented in a dynamic epistemic logic that is based on the observability of propositional variables by agents.

Epistemic protocols for dynamic gossip

A gossip protocol is a procedure for spreading secrets among a group of agents, using a connection graph. In each call between a pair of connected agents, the two agents share all the secrets they have learnt. In dynamic gossip problems, dynamic connection graphs are enabled by permitting agents to spread as well the telephone numbers of other agents they know. This paper characterizes different distributed epistemic protocols in terms of the (largest) class of graphs where each protocol is successful, i.e. where the protocol necessarily ends up with all agents knowing all secrets.

Security for Wireless Sensor Network withSpin Protocol

In the recent past, Wireless Sensor Networks have been introduced to use in many application. Wireless Sensor Networks provides a way of information sensing, processing, communicating and transfer of information. To designs the networks, the factors needed to be considered are the coverage area, mobility, power consumptions, communication capabilities, etc. Wireless Sensor Networks have limited energy has hence efficient of protocol has a significant impact on network’s lifetime. Security is a main concern everything, whether it is for Wired based networks or wireless based networks. Security is a fundamental requirement of Wireless Sensor Networks. Security in Wireless Sensor Network plays an important role in node communication. For Wireless Sensor Networks has lots of security protocol available but some have limitations. SPIN (Sensor Protocol for Information via Negotiation) has contained three messages which have given security and energy efficiency to Wireless Sensor Network. SPIN protocol is based on data centric approach which efficiently propagates information between sensor nodes in energy constrained mode. SPIN protocol solves the problem of flooding and gossiping. In this documentation we had implement SPIN protocol in NS2 and energy efficient for nodes. We have implement SPIN protocol in Network Simulator. After implementation of SPIN protocol, we had optimized SPIN-I which has given sufficient energy of three stages

In the Bedroom of the King: Affective Politics in the Restoration Secret History

In 1709, Sarah Churchill, Duchess of Marlborough, wrote a letter warning Queen Anne of rumors being spread about the queen's relationship with Abigail Masham, her current favorite, insinuating the Queen being a subject of gossip for her subjects, either orally or in print, was in itself a problem. What is interesting about Churchill's letter, which was prompted by the publication of Delarivier Manley's popular secret history, The New Atalantis, is how she links the problem of gossip about the Queen to the genre of the secret history itself, gesturing toward the low nature of Manley's text, which is not well written (Private Correspondence 1: 244). Churchill writes, that looks so much the worse, for it shews the notion is extensively spread among all sorts of people (1: 244, emphasis added).1 The idea subjects may be judging the queen and her counselors is clearly a notion troubles the Duchess, whose letter acknowledges the political potential of the community of brought together by the secret history text.Churchill's recognition of the potential problems inherent in this type of early novel has been noted by critics of early eighteenth-century secret histories: Nicola Parsons emphasizes Churchill's concern, arguing gossip, and its reiteration in the mediated form of the secret history could have serious material effects (Reading Gossip 56). Increased scholarly recognition of the political power of secret histories and their role in shaping reading practices in the early eighteenth century has renewed interest in a genre was too-often denigrated and overshadowed by a certain teleology of the history of the novel.2 What has been overlooked by critics interested in post-1688 secret histories is the political potential of the genre was being actively exploited in the name of factional politics well before Manley's text caused such concern at court. In the early 1680s, in the height of the Exclusion Crisis and its immediate aftermath, many texts-from John Dryden's well-known poem Absalom and Achitophel (1681) and Aphra Behn's novel Love Letters Between a Nobleman and his Sister (1684-87) to more obscure, anonymous works like The Perplex'd Prince ( 1682) and The Fugitive Statesman 1683)-intervened in the propaganda war surrounding the question of the succession.Although many of these texts operate solely on the level of factional propaganda, the secret histories use romance modes as their generic cover provide a more subtle, ideological slant to their propagandistic purposes.3 In contrast to post-1688 secret histories, which Rebecca Bullard forcefully argues encourage readers to believe their rulers are in league against them and encourage suspicion of Courts in general ( 4), the secret histories operate under the cover of romance narratives affectively lessen the distance between the reader and the monarch/hero. By bringing into their monarch's bedroom and by couching their political factionalism under the cover of a romance tale, these texts created an affective intimacy between Restoration subjects and their monarch. This affinity, I argue, temporarily enabled an illusory sense of power on the part of the subject, which acted as a perceived entitlement to sit in judgment over the behavior of the monarch. The illusory sense of power was intensified through communities in London's public spaces where socially oriented gathered to share their interpretations and to gossip over these popular texts. The interactions among secret histories and the communities of coalesced around them contributed to the contemporary ideological shifts concerning notions of who had the right to speak and to judge in political society.Focusing on two secret histories about Charles II-The Perplex'd Prince and Sebastien Bremond's Hattige: or the Amours of the King of Tatuaran ( originally published in French in 1676 and first translated into English in 1680)-I will demonstrate how these texts contributed to political shifts in England from 1660 through the 1688 revolution and after, and to the rise of party politics and parliamentary power in the eighteenth century. …

Information dissemination in unknown radio networks with large labels

We consider the problems of deterministic broadcasting and gossiping in completely unknown ad-hoc radio networks. It is assumed that nothing is known to the nodes of the network about the topology of the network, that is even the size of the network is not known, except that n>1. This lack of knowledge, about the value of n, is what distinguishes this setting from the vanilla model.For this setting, protocols for the vanilla model, may be executed with multiplicatively large estimates, say 2i in the ith phase, on the upper bound on the size of the network n. When the respective protocol with estimate 2i⩾n on the size of the network is run, it will accomplish the task successfully. However, the problem that still remains is to determine when this process should terminate. Thus, to apply this design paradigm successful completion or incompletion of the process should be detected and this knowledge circulated in the network after appropriate number of rounds/phases of the protocol. In radio networks literature, this setting is known as the Acknowledged setting and broadcasting and gossiping problems for it are referred to as Acknowledged broadcasting and gossiping. An important feature of dynamic radio networks is that radio nodes can be dynamically introduced in the network from time to time and can be assigned labels in a much larger range, say polynomial in the size of the network, e.g. [1,…,nc] for some constant c.It is easy to see that protocols can be designed for the acknowledged setting only when the underlying communication network is strongly connected. We present the following results for these networks: (a) A deterministic protocol for Acknowledged broadcasting which takes NRG(n,nc) rounds, where NRG(n,nc) is the round complexity of deterministic gossiping for vanilla model. (b) A deterministic protocol for acknowledged gossiping, which takes O(n2lgn) rounds when collision detection mechanism is available. The schedule of the transmissions of nodes in the network, to enable them to infer collisions and discover existence of unknown in-neighborhood as a result, is abstracted as a family of sets of natural numbers which we call the Selecting-Colliding family. We prove the existence of Selecting-Colliding families using the probabilistic method and employ them to design protocol for acknowledged gossiping when no collision detection mechanism is available. Finally, we present a deterministic protocol for Acknowledged broadcasting for bidirectional networks, with a round complexity of O(nlgn) rounds.

Random Walks, Bisections and Gossiping in Circulant Graphs

Circulant graphs are regular graphs based on Cayley graphs defined on the Abelian group $\mathbb{Z}_{n}$ . They are popular network topologies that arise in distributed computing. Using number theoretical tools, we first prove two main results for random directed k-regular circulant graphs with n vertices, when n is sufficiently large and k is fixed. First, for any fixed ?>0, n=p prime and L?p 1/k (logp)1+1/k+? , walks of length at most L terminate at every vertex with asymptotically the same probability. Second, for any n, there is a polynomial time algorithm that for almost all undirected 2r-regular circulant graphs finds a vertex bisector and an edge bisector, both of size less than n 1?1/r+o(1). We then prove that the latter result also holds for all (rather than for almost all) 2r-regular circulant graphs with n=p, prime, vertices, while, in general, it does not hold for composite n. Using the bisection results, we provide lower bounds on the number of rounds required by any gossiping algorithms for any n. We introduce generic distributed algorithms to solve the gossip problem in any circulant graphs. We illustrate the efficiency of these algorithms by giving nearly matching upper bounds of the number of rounds required by these algorithms in the vertex-disjoint and the edge-disjoint paths communication models in particular circulant graphs.

Round complexity of leader election and gossiping in bidirectional radio networks

We consider the setting of ad hoc radio networks when the underlying network is bidirectional, the number of nodes in the network n is known and nodes can be assigned labels which are polynomially large in n. For this setting we present a protocol for deterministic gossiping which takes O(nlg2nlglgn) rounds improving upon the previous best result by [L. Gasieniec, A. Pagourtizis, I. Potapov, Deterministic gossiping in radio networks with large labels, Algorithmica 47 (2007) 97–117], who give a complex protocol with the round complexity of O(nlg3nlglgn), resolving an open problem posed by Gasieniec in the survey article [L. Gasieniec, On efficient gossiping in radio networks, in: Proceedings of Sixteenth International Colloquium on Structural Information and Communication Complexity, SIROCCO 2009, Sirince, Turkey, in: LNCS, vol. 5869, 2010, pp. 2–14].The relationship between the asymptotic round complexity of deterministic Leader Election and Gossiping problem has not been known even for bidirectional networks. The gossiping protocol given by Gasieniec et al. invokes the leader election protocol O(lgn) times. Our gossiping protocol achieves this by a single invocation to the leader election protocol. We then use a known fact about the lower bound for leader election for bidirectional radio networks to conclude that the asymptotic round complexity of deterministic Leader Election and Gossiping is the same for bidirectional networks.

Optimal memory-aware Sensor Network Gossiping (or how to break the Broadcast lower bound)

Gossiping is a well-studied problem in Radio Networks. However, due to the strong resource limitations of sensor nodes, previous solutions are frequently not feasible in Sensor Networks. In this paper, we study the Gossiping problem in the restrictive context of Sensor Networks. We present a distributed algorithm that completes Gossiping with high probability in a Sensor Network of unknown topology and adversarial start-up. This algorithm exploits the geometry of sensor node distributions to achieve an optimal running time of Θ(D+Δ), where D is the diameter and Δ the maximum degree of the network. Given that any algorithm for Gossiping also solves the Broadcast problem, this result shows that the classical Broadcast lower bound of Kushilevitz and Mansour does not hold if nodes are allowed to do preprocessing. The proposed algorithm requires that a linear number of messages be stored and transmitted per unit time. We also show an optimal distributed algorithm that solves the problem in linear time for the case where only a constant number of messages can be stored.

Meeting the deadline: on the complexity of fault-tolerant continuous gossip

In this paper we introduce the problem of Continuous Gossip in which rumors are continually and dynamically injected throughout the network. Each rumor has a deadline, and the goal of a continuous gossip protocol is to ensure good “Quality of Delivery,” i.e., to deliver every rumor to every process before the deadline expires. Thus, a trivial solution to the problem of Continuous Gossip is simply for every process to broadcast every rumor as soon as it is injected. Unfortunately, this solution has high per-round message complexity. Complicating matters, we focus our attention on a highly dynamic network in which processes may continually crash and recover. In order to achieve good per-round message complexity in a dynamic network, processes need to continually form and re-form coalitions that cooperate to spread their rumors throughout the network. The key challenge for a Continuous Gossip protocol is the ongoing adaptation to the ever-changing set of active rumors and non-crashed process. In this work we show how to address this challenge; we develop randomized and deterministic protocols for Continuous Gossip and prove lower bounds on the per-round message-complexity, indicating that our protocols are close to optimal.

A Novel Energy Efficient Routing Protocol in Wireless Sensor Networks

Wireless sensor networks are employed in several applications, including military, medical, environmental and household. In all these applications, energy usage is the determining factor in the performance of wireless sensor networks. Consequently, methods of data routing and transferring to the base station are very important because the sensor nodes run on battery power and the energy available for sensors is limited. In this paper we intend to propose a new protocol called Fair Efficient Location-based Gossiping (FELGossiping) to address the problems of Gossiping and its extensions. We show how our approach increases the network energy and as a result maximizes the network life time in comparison with its counterparts. In addition, we show that the energy is balanced (fairly) between nodes. Saving the nodes energy leads to an increase in the node life in the network, in comparison with the other protocols. Furthermore, the protocol reduces propagation delay and loss of packets.

Minimum Latency Gossiping in Radio Networks

We studied the minimum latency gossiping (all-to-all broadcast) problem in multihop radio networks defined as follows: Each node in the network is preloaded with a message and the objective is to distribute each node's message to the entire network with minimum latency. We studied this problem in the unit-size message model and the unit disk graph model. The unit-size model means different messages cannot be combined as one message, and the unit disk graph model means a link exists between two nodes if and only if their euclidean distance is less than 1. The minimum latency gossiping problem is known to be NP-hard in these two models. In this work, we designed a gossiping scheme that significantly improved all current gossiping algorithms in terms of the approximation ratio. Our work has approximation ratio 27, a great improvement of the current state-of-the-art algorithm (which has ratio 1,947). We also discussed the single point of failure problem and its impact on our approximation ratio. We designed an amended gossiping algorithm with ratio 27 in case of a nonsource node failure. We also designed an amended gossiping algorithm with ratio 29 in case of source failure.

Quiescence of self-stabilizing gossiping among mobile agents in graphs

This paper considers gossiping among mobile agents in graphs: agents move on the graph and have to disseminate their initial information to every other agent. We focus on self-stabilizing solutions for the gossip problem, where agents may start from arbitrary locations in arbitrary states. Self-stabilization requires (some of the) participating agents to keep moving forever, hinting at maximizing the number of agents that could be allowed to stop moving eventually. This paper formalizes the self-stabilizing agent gossip problem, introduces the quiescence number (i.e., the maximum number of eventually stopping agents) of self-stabilizing solutions and investigates the quiescence number with respect to several assumptions related to agent anonymity, synchrony, link duplex capacity, and whiteboard capacity.

Gossiping by processors prone to omission failures

We consider the gossip problem in a synchronous message-passing system. Participating processors are prone to omission failures, that is, a faulty processor may fail to send or receive a message. The gossip problem in the fault-tolerant setting is defined as follows: every correct processor must learn the initial value of any other processor, unless the other one is faulty; in the latter case either the initial value or the information about the fault must be learned. We develop two efficient algorithms that solve the gossip problem in time O ( log n ) , where n is the number of processors in the system. The first one is an explicit algorithm (i.e., constructed in polynomial time) sending O ( n log n + f 2 ) messages, and the second one reduces the message complexity to O ( n + f 2 ) , where f is the upper bound on the number of faulty processors.