A Deterministic Algorithm for Online Steiner Tree Leasing

We study the Online Steiner Tree Leasing (OSTL) problem, defined in a weighted undirected graph with a distinguished root node r. There is a known set L of available lease types, where each type ` ∈ L is characterized by its duration D` and cost factor C`. As an input, an online algorithm is given a sequence of terminals and has to connect them to the root r using leased edges. An edge of length d can be leased using lease type ` for cost C` · d and remains valid for time D`. The OSTL problem contains the online Steiner tree and the single-source rent-or-buy problems as specific subcases. We present the first deterministic online algorithm for OSTL, whose competitive ratio is O(|L| · log k), where k is the number of different terminals in the input. The currently best randomized algorithm attains the ratio of O(log |L| · logn), where n ≥ k is the number of nodes in the graph.