arXiv subjects

Joseph Peters

Publications and source records attributed to Joseph Peters.

4 recordsLinked to original sources

arXiv2018

Time-Bounded Influence Diffusion with Incentives

A widely studied model of influence diffusion in social networks represents the network as a graph $G=(V,E)$ with an influence threshold $t(v)$ for each node. Initially the members of an initial set $S\subseteq V$ are influenced. During each subsequent round, the set of influenced nodes is augmented by including every node $v$ that has at least $t(v)$ previously influenced neighbours. The general problem is to find a small initial set that influences the whole network. In this paper we extend this model by using \emph{incentives} to reduce the thresholds of some nodes. The goal is to minimize the total of the incentives required to ensure that the process completes within a given number of rounds. The problem is hard to approximate in general networks. We present polynomial-time algorithms for paths, trees, and complete networks.

cs.DS↗

arXiv2015

Spread of Influence in Weighted Networks under Time and Budget Constraints

Given a network represented by a weighted directed graph G, we consider the problem of finding a bounded cost set of nodes S such that the influence spreading from S in G, within a given time bound, is as large as possible. The dynamic that governs the spread of influence is the following: initially only elements in S are influenced; subsequently at each round, the set of influenced elements is augmented by all nodes in the network that have a sufficiently large number of already influenced neighbors. We prove that the problem is NP-hard, even in simple networks like complete graphs and trees. We also derive a series of positive results. We present exact pseudo-polynomial time algorithms for general trees, that become polynomial time in case the trees are unweighted. This last result improves on previously published results. We also design polynomial time algorithms for general weighted paths and cycles, and for unweighted complete graphs.

cs.SI↗

arXiv2015

How to go Viral: Cheaply and Quickly

Given a social network represented by a graph $G$, we consider the problem of finding a bounded cardinality set of nodes $S$ with the property that the influence spreading from $S$ in $G$ is as large as possible. The dynamics that govern the spread of influence is the following: initially only elements in $S$ are influenced; subsequently at each round, the set of influenced elements is augmented by all nodes in the network that have a sufficiently large number of already influenced neighbors. While it is known that the general problem is hard to solve --- even in the approximate sense --- we present exact polynomial time algorithms for trees, paths, cycles, and complete graphs.

cs.SI↗

arXiv2012

Consensus vs Broadcast in Communication Networks with Arbitrary Mobile Omission Faults

We compare the solvability of the Consensus and Broadcast problems in synchronous communication networks in which the delivery of messages is not reliable. The failure model is the mobile omission faults model. During each round, some messages can be lost and the set of possible simultaneous losses is the same for each round. We investigate these problems for the first time for arbitrary sets of possible failures. Previously, these sets were defined by bounding the numbers of failures. In this setting, we present a new necessary condition for the solvability of Consensus that unifies previous impossibility results in this area. This condition is expressed using Broadcastability properties. As a very important application, we show that when the sets of omissions that can occur are defined by bounding the numbers of failures, counted in any way (locally, globally, etc.), then the Consensus problem is actually equivalent to the Broadcast problem.

cs.DC↗