Timeline Cover in Temporal Graphs: Exact and Approximation Algorithms

In this paper we study a variant of vertex cover on temporal graphs that has been recently introduced for timeline activities summarization in social networks. The problem has been proved to be NP-hard, even in restricted cases. In this paper, we present algorithmic contributions for the problem. First, we present an approximation algorithm of factor O(T log n), on a temporal graph of T timestamps and n vertices.
Then, we consider the restriction where at most one temporal edge is defined in each timestamp. For this restriction, which has been recently shown to be NP-hard, we present a 4(T − 1) approximation algorithm
and a parameterized algorithm when the parameter is the cost (called span) of the solution.