Jrl Syst Sci & Complexity (2009) 22: 88–108 A PROBABILISTIC CHARACTERIZATION OF A FAULT-TOLERANT GOSSIPING ALGORITHM ∗† Xiaohu LI · Paul PARKER · Shouhuai XU Received: 17 September 2007 c 2009 Springer Science + Business Media, LLC Abstract Gossiping is a popular technique for probabilistic reliable multicast (or broadcast). However, it is often difficult to understand the behavior of gossiping algorithms in an analytic fashion. Indeed, existing analyses of gossip algorithms are either based on simulation or based on ideas borrowed from epidemic models while inheriting some features that do not seem to be appropriate for the setting of gossiping. On one hand, in epidemic spreading, an infected node typically intends to spread the infection an unbounded number of times (or rounds); whereas in gossiping, an infected node (i.e., a node having received the message in question) may prefer to gossip the message a bounded number of times. On the other hand, the often assumed homogeneity in epidemic spreading models (especially that every node has equal contact to everyone else in the population) has been silently inherited in the gossiping literature, meaning that an expensive membership protocol is often needed for maintaining nodes’ views. Motivated by these observations, the authors present a characterization of a popular class of fault-tolerant gossip schemes (known as “push-based gossiping”) based on a novel probabilistic model, while taking the afore-mentioned factors into consideration. Key words Fault-tolerance, gossip, probabilistic broadcast, reliable multicast. 1 Introduction Reliable multicast (or broadcast) is an important problem. Ideal solutions to this prob- lem would offer atomicity guarantees, but such solutions turn out to scale poorly [1] . At the other end of the spectrum are the reliable multicast protocols that offer best effort reliabil- ity, while still suffering from the scalability problem (e.g., the Reliable Multicast Transport Protocol [2] generates a flood of positive acknowledgements from receivers). A popular approach to reliable multicast has thus been to trade a certain probabilistic reliability assurance for scal- ability, known as probabilistic multicast protocols, gossip-based protocols, or rumor mongering protocols [3] . In this paradigm, a process (or node) sends the message to a randomly selected subset of other processes (called “gossip partners”); each process that receives the message also sends the message to a randomly selected subset of the processes, and so forth. In early gossip algorithms, gossip partners were chosen uniformly at random from the entire process popula- tion, meaning that every node has to maintain information about all the other processes (i.e., Xiaohu LI · Paul PARKER · Shouhuai XU Department of Computer Science, University of Texas at San Antonio, One UTSA Circle, San Antonio, TX 78249, USA. Email: {xli, tparker, shxu}@cs.utsa.edu. * This work is supported in part by the US National Science Foundation. † The views and conclusions contained in the paper are those of the authors and should not be interpreted as, in any sense, the official policies or endorsements of the government or the agencies.