Greedy–Merge Degrading has Optimal Power-Law

Near Optimal Adjacency Labeling Schemes for Power-Law Graphs

An adjacency labeling scheme labels the n nodes of a graph with bit strings in a way that allows, given the labels of two nodes, to determine adjacency based only on those bit strings. Though many graph families have been meticulously studied for this problem, a non-trivial labeling scheme for the important family of power-law graphs has yet to be obtained. This family is particularly useful fo...

Near-optimal adjacency labeling scheme for power-law graphs

An adjacency labeling scheme is a method that assigns labels to the vertices of a graph such that adjacency between vertices can be inferred directly from the assigned label, without using a centralized data structure. We devise adjacency labeling schemes for the family of power-law graphs. This family that has been used to model many types of networks, e.g. the Internet AS-level graph. Further...

Optimal Specifications for Degrading Characteristics

In this article, we show that the manufacturing target for a product characteristic affected by degradation is not the value that maximizes the quality of the product. By sacrificing some quality at the manufacturing stage it is possible to increase the product’s lifetime and thus reduce the quality loss over a long period. We propose a procedure for finding the optimal manufacturing target tha...

Optimal Renewal Policy for Slowly Degrading Systems

In the paper we address the problem of determining the optimal time to renew a system when it experiences so called soft failures because of aging. It is assumed that crash failures, which reduce the service rate to 0 immediately, do not occur. However, the service rate of the examined system gradually decreases with time and settles to a very low value. Since the performance in this state is v...

Law and Power