Deterministic Resource Discovery in Distributed Networks

The resource discovery problem was introduced by Harchol-Balter, Leighton, and Lewin. They developed a number of algorithms for the problem in the weakly connected directed graph model. This model is a directed logical graph that represents the vertices' knowledge about the topology of the underlying communication network. The current paper proposes a deterministic algorithm for the problem in the same model, with improved time, message, and communication complexities. Each previous algorithm had a complexity that was higher at least in one of the measures. Specifically, previous deterministic solutions required either time linear in the diameter of the initial network, or communication complexity O(n³) (with message complexity O(n²)), or message complexity O(|E₀| log n) (where E₀ is the arc set of the initial graph G₀). Compared with the main randomized algorithm of Harchol-Balter, Leighton, and Lewin, the time complexity is reduced from O(log² n) to O(log n), the message complexity from O(n log² n) to O (n log n), and the communication complexity from O(n² log³ n) to O(|E₂| log² n). Our work significantly extends the connectivity algorithm of Shiloach and Vishkin which was originally given for a parallel model of computation. Our result also confirms a conjecture of Harchol-Balter, Leighton, and Lewin, and addresses an open question due to Lipton.