A Randomized Algorithm for Online Scheduling with Interval Conflicts

In the contiguous variant of the Scheduling with Interval Conflicts problem, there is a universe U consisting of elements being consecutive positive integers. An input is a sequence of conflicts in the form of intervals of length at most σ. For each conflict, an algorithm has to choose at most one surviving element, with the ultimate goal of maximizing the number of elements that survived all conflicts. We present an O(log σ/ log log σ)-competitive randomized algorithm for this problem, beating known lower bound of Ω(log σ) that holds for deterministic algorithms.