The Worst Case Behavior of Randomized Gossip
نویسندگان
چکیده
This paper considers the quasi-random rumor spreading model introduced by Doerr, Friedrich, and Sauerwald in [SODA 2008], hereafter referred to as the list-based model. Each node is provided with a cyclic list of all its neighbors, chooses a random position in its list, and from then on calls its neighbors in the order of the list. This model is known to perform asymptotically at least as well as the random phone-call model, for many network classes. Motivated by potential applications of the list-based model to live streaming, we are interested in its worst case behavior. Our first main result is the design of an O(m + n logn)-time algorithm that, given any n-node m-edge network G, and any source-target pair s, t ∈ V (G), computes the maximum number of rounds it may take for a rumor to be broadcast from s to t in G, in the list-based model. This algorithm yields an O(n(m + n logn))-time algorithm that, given any network G, computes the maximum number of rounds it may take for a rumor to be broadcast from any source to any target, in the list-based model. Hence, the list-based model is computationally easy to tackle in its basic version. The situation is radically different when one is considering variants of the model in which nodes are aware of the status of their neighbors, i.e., are aware of whether or not they have already received the rumor, at any point in time. Indeed, our second main result states that, unless P = NP, the worst case behavior of the list-based model with the additional feature that every node is perpetually aware of which of its neighbors have already received the rumor cannot be approximated in polynomial time within a ( 1 n ) 1 2 − multiplicative factor, for any > 0. As a byproduct of this latter result, we can show that, unless P = NP, there are no PTAS enabling to approximate the worst case behavior of the list-based model, whenever every node perpetually keeps track of the subset of its neighbors which have sent the rumor to it so far.
منابع مشابه
Information Spreading in Dynamic Networks
We study the fundamental problem of information spreading (also known as gossip) in dynamic networks. In gossip, or more generally, k-gossip, there are k pieces of information (or tokens) that are initially present in some nodes and the problem is to disseminate the k tokens to all nodes. The goal is to accomplish the task in as few rounds of distributed computation as possible. The problem is ...
متن کاملGGRA: a grouped gossip-based reputation aggregation algorithm
An important issue in P2P networks is the existence of malicious nodes that decreases the performance of such networks. Reputation system in which nodes are ranked based on their behavior, is one of the proposed solutions to detect and isolate malicious (low ranked) nodes. Gossip Trust is an interesting previously proposed algorithm for reputation aggregation in P2P networks based on t...
متن کاملStochastic and Deterministic Byzantine Fault Detection for Randomized Gossip Algorithms
This paper addresses the problem of detecting Byzantine faults in linear randomized gossip algorithms, where the selection of the dynamics matrix is stochastic. A Byzantine fault is a disturbance signal injected by an attacker to corrupt the states of the nodes. We propose the use of Set-Valued Observers (SVOs) to detect if the state observations are compatible with the system dynamics for the ...
متن کاملDisTriB: Distributed Trust Management Model Based on Gossip Learning and Bayesian Networks in Collaborative Computing Systems
The interactions among peers in Peer-to-Peer systems as a distributed collaborative system are based on asynchronous and unreliable communications. Trust is an essential and facilitating component in these interactions specially in such uncertain environments. Various attacks are possible due to large-scale nature and openness of these systems that affects the trust. Peers has not enough inform...
متن کاملConvergence analysis of the global FOM and GMRES methods for solving matrix equations $AXB=C$ with SPD coefficients
In this paper, we study convergence behavior of the global FOM (Gl-FOM) and global GMRES (Gl-GMRES) methods for solving the matrix equation $AXB=C$ where $A$ and $B$ are symmetric positive definite (SPD). We present some new theoretical results of these methods such as computable exact expressions and upper bounds for the norm of the error and residual. In particular, the obtained upper...
متن کامل