Online Bottleneck Matching Problem with Two Heterogeneous Sensors in a Metric Space

In this paper, we consider the online matching problem with two heterogeneous sensors s1 and s2 in a metric space (X,d). If a request r is assigned to sensor s1, the service cost of r is the distance d(r,s1). Otherwise, r is assigned to sensor s2, and the service cost of r is d(r,s2)w, where w≥1 is the weight of sensor s2. The goal is to minimize the maximum matching cost, we design an optimal online algorithm with a competitive ratio of 1+w+1w for 1≤w≤1.839, and an optimal online algorithm with a competitive ratio of w+1+w2+6w+12 for w>1.839.