List Update Problem by Béla Csaba

Note on the Work Function Algorithm

We prove that the work function algorithm is (n ? 1)-competitive for the k-server problem, where n is the number of points in the metric space. This gives improved upper bounds when k + 3 n 2k ?1; in particular, it shows that the work function algorithm is optimal for k = n ? 1.

Budapest University of Technology and Economics

A randomized on-line algorithm for the k-server problem on a line

We give a O(n 2 3 logn)–competitive randomized k–server algorithm when the underlying metric space is given by n equally spaced points on a line. For n = k+o(k 3 2/ log k), this algorithm is o(k)–competitive.

Regular Spanning Subgraphs of Bipartite Graphs of High Minimum Degree

Let G be a simple balanced bipartite graph on 2n vertices, δ = δ(G)/n, and ρ0 = δ+ √ 2δ−1 2 . If δ ≥ 1/2 then G has a ⌊ρ0n⌋-regular spanning subgraph. The statement is nearly tight.

Multimodality Imaging of Giant Right Coronary Aneurysm and Postsurgical Coronary Artery Inflammation.