Gossip-based Search in Multipeer Communication Networks

We study a gossip-based algorithm for searching data objects in a multipeer communication network. All of the nodes in the network are able to communicate with each other. There exists an initiator node that starts a round of searches by randomly querying one or more of its neighbors for a desired object. The queried nodes can also be activated and look for the object. We examine several behavioural patterns of nodes with respect to their willingness to cooperate in the search. We derive mathematical models for the search process based on the balls and bins model, as well as known approximations for the rumour-spreading problem. All models are validated with simulations. We also evaluate the performance of the algorithm and examine the impact of search parameters.

💡 Research Summary

This paper investigates a gossip‑based algorithm for locating data objects in a fully connected multipeer communication network. The network consists of N nodes, and a target file f is replicated on m of them (m ≤ N‑1). An initiator node I starts a search round by randomly querying k of its neighbors (k ≤ N‑1). Queried nodes may become “active” and forward the query in subsequent rounds, but only with cooperation probability c (0 ≤ c ≤ 1). Nodes that do not cooperate (non‑cooperative) simply ignore the query, while “stifler” nodes may stop participating after a certain time, representing a special case of cooperation loss.

Two search strategies are defined:

1. Blind search – each active node selects k neighbors uniformly at random in every round, possibly re‑querying nodes that have already been contacted. This model captures devices with limited memory or situations where node identities are unknown (e.g., random encounters in mobile networks). The time until a node is queried follows a geometric distribution, the discrete analogue of an exponential waiting time.

2. Smart search – each active node avoids previously queried nodes, requiring global knowledge of which nodes have already been contacted. This incurs additional overhead (e.g., exchanging peer‑lists) but yields the fastest possible search.

Blind‑search analytical model

The probability that a single query of k random neighbors discovers the file is
(p_s = 1 - \frac{\binom{N-1-m}{k}}{\binom{N-1}{k}}),
the complement of selecting only non‑file nodes. If at round r there are (\hat A(r)) active nodes, the probability that at least one discovers the file is
(S(r) = 1 - (1-p_s)^{\hat A(r)}).

To estimate (\hat A(r)) the authors adapt the classic rumor‑spreading model