Analysis of hop limit in opportunistic networks by static and time-aggregated graphs

Hop count limitation helps controlling the spread of messages as well as the protocol complexity and overhead in a distributed network. For a mobile opportunistic network, we examine how the paths between any two nodes change with increasing number of hops a message can follow. Using the all hops optimal path (AHOP) problem, we represent the total delay of a route from a source node to a destination node as additive weight and use the number of encounters as a representation of bottleneck weight. First, we construct a static (contact) graph from the meetings recorded in a human contact trace and then analyze the change in these two weights with increasing hop count. Alternatively, we aggregate all the contact events in a time interval and construct several time-aggregated graphs over which we calculate the capacity metrics. Although, we observe differences in the properties of the static and the time-aggregated graphs (e.g., higher connectivity and average degree in static graph), our analysis shows that second hop brings most of the benefits of multi-hop routing for the studied networks. However, the optimal paths - path that provides the most desirable bottleneck/additive weight - are achieved at further hops, e.g, hop count ≈ 4. Our finding, which is also verified by simulations, is paramount as it puts an upper bound on the hop count for the hop-limited routing schemes by discovering the optimal hop count for both additive and bottleneck weights.