An improved competitive algorithm for reordering buffer management

We design and analyze an online reordering buffer management algorithm with improved O(logk/loglogk) competitive ratio for nonuniform costs, where k is the buffer size. This improves on the best previous result (even for uniform costs) of Englert and Westermann (2005) giving O(log k) competitive ratio, which was also the best (offline) polynomial time approximation guarantee for this problem. Our analysis is based on an intricate dual fitting argument using a linear programming relaxation for the problem that we introduce in this article.