FIFO anomaly is unbounded

Virtual memory of computers is usually implemented by demand paging. For some page replacement algorithms the number of page faults may increase as the number of page frames increases. Belady, Nelson and Shedler constructed reference strings for which page replacement algorithm FIFO produces near twice more page faults in a larger memory than in a smaller one. They formulated the conjecture that 2 is a general bound. We prove that this ratio can be arbitrarily large

Greedy D-Approximation Algorithm for Covering with Arbitrary Constraints and Submodular Cost

This paper describes a simple greedy D-approximation algorithm for any covering problem whose objective function is submodular and non-decreasing, and whose feasible region can be expressed as the intersection of arbitrary (closed upwards) covering constraints, each of which constrains at most D variables of the problem. (A simple example is Vertex Cover, with D = 2.) The algorithm generalizes previous approximation algorithms for fundamental covering problems and online paging and caching problems