Combined TTL-based search algorithm

Expanding ring search and blocking expanding ring search are two prominent time-to-live value based search techniques for routes and resources in networks. Each uses a different technique to extend the search, with advantages in cost reduction that depend on the setting. In this paper, we introduce the Combined Expanding Ring Search which uses both techniques for extending the search in a way that guarantees expected costs at least as low as the lowest of the two. We show how to derive the search strategy with minimum expected costs in polynomial time, and in so doing introduce an important optimization to blocking expanding ring search. We further show how to derive the optimal sequence under delay constraints in polynomial time. In numerical evaluations of synthetic settings, we show that our optimization to blocking expanding ring search makes it far more efficient than previously considered, and consequently the combined search to be much more efficient than either technique.