Limit Theory for the Domination Number of Random Class Cover Catch Digraphs

摘要

We discuss the limiting behavior of the domination number of random class cover catch digraphs (CCCDs). The CCCD problem is motivated by its applications in pattern classification. For the special case of uniformly distributed data in one dimension, Priebe, Marchette and Devinney found the exact distribution of the domination number of the random data-induced CCCD, and Devinney and Wierman proved the Strong Law of Large Numbers (SLLN). We will present progress toward the SLLN and the Central Limit Theorem (CLT) for general data distributions in one dimension. The ultimate goal is to establish SLLN and CLT results for higher dimensional CCCDs.