Online Deterministic Algorithms for Connected Dominating Set & Set Cover Leasing Problems

Connected Dominating Set (CDS) and Set Cover (SC) are classical optimization problems that have been widely studied in both theory and practice, as many variants and in different settings, motivated by applications in wireless and social networks. In this paper, we consider the online setting, in which the input sequence arrives in portions over time and the so-called online algorithm needs to react to each portion. Online algorithms are measured using the notion of competitive analysis. An online algorithm A is said to have competitive ratio r, where r is the worst-case ratio, over all possible instances of a given minimization problem, of the solution constructed by A to the solution constructed by an offline optimal algorithm that knows the entire input sequence in advance. Online Connected Dominating Set (OCDS) (Hamann et al., 2018) is an online variant of CDS that is currently solved by a randomized online algorithm with optimal competitive ratio. We present in this paper the first deterministic online algorithm for OCDS, with optimal competitive ratio. We further introduce generalizations of OCDS, in the leasing model (Meyerson, 2005) and in the multiple hop model (Coelho et al., 2017), and design deterministic online algorithms for each of these generalizations. We also propose the first deterministic online algorithm for the leasing variant of SC (Abshoff et al., 2016), that is currently solved by a randomized online algorithm.