Timeliness Through Telephones: Approximating Information Freshness in Vector Clock Models

Abstract

We consider an information dissemination problem where the root of an undirected graph constantly updates its information and we wish to keep everyone in the graph as freshly informed about the root as possible. Our synchronous information spreading model uses telephone calls at each time step, in which any node can call at most one neighbor, thus inducing a matching over which information is transmitted at each step. These matchings that define the schedule over time ad infinitum are specified in a centralized manner. We introduce two problems in minimizing two natural objectives (Maximum and Average) of the latency of the root's information at all nodes in the network.First we show that it suffices to consider periodic finite schedules with a loss of at most a factor of two in each of these objectives. Next, by relating the maximum rooted latency problem to minimizing the maximum broadcast-time, we derive new approximation algorithms for this version. For the average rooted latency objective, such an approach introduces a necessary logarithmic factor overhead. We overcome this and give a constant-factor approximation for trees by devising near-optimal schedules that are locally periodic at each node and where each node has the same offset value in hearing fresh information from its parent. The average latency version motivates the problem of finding a spanning tree that minimizes a new Average Broadcast Time objective in graphs, which is interesting in its own right for future study.