A. We give a fully polynomial-time randomized approximation scheme (FPRAS) for two terminal reliability in directed acyclic graphs.

No abstract

No abstract

We introduce the novel concept of knowledge states. The knowledge state approach can be used to construct competitive randomized online algorithms and study the trade-off between competitiveness and memory. Many well-known algorithms can be viewed as knowledge state algorithms. A knowledge state consists of a distribution of states for the algorithm, together with a work function which approximates the conditional obligations of the adversary. When a knowledge state algorithm receives a request, it then calculates one or more "subsequent" knowledge states, together with a probability of transition to each. The algorithm uses randomization to select one of those subsequents to be the new knowledge state. We apply this method to randomized k-paging. The optimal minimum competitiveness of any randomized online algorithm for the k-paging problem is the kth harmonic number, H k = k i=1 1 i . Existing algorithms which achieve that optimal competitiveness must keep bookmarks, i.e., memory of the names of pages not in the cache. An H kcompetitive randomized algorithm for that problem which uses O(k) bookmarks is Research of W.

No abstract