Tight bounds for the advice complexity of the online minimum steiner tree problem

Abstract

In this work, we study the advice complexity of the online minimum Steiner tree problem (ST). Given a (known) graph G = (V,E) endowed with a weight function on the edges, a set of N terminals are revealed in a step-wise manner. The algorithm maintains a sub-graph of chosen edges, and at each stage, chooses more edges from G to its solution such that the terminals revealed so far are connected in it. In the standard online setting this problem was studied and a tight bound of O(log(N)) on its competitive ratio is known. Here, we study the power of non-uniform advice and fully characterize it. As a first result we show that using q ·log(|V|) advice bits, where 0 ≤ q ≤ N-1, it is possible to obtain an algorithm with a competitive ratio of O(log(N/q). We then show a matching lower bound for all values of q, and thus settle the question. © 2014 Springer International Publishing Switzerland.