We give a survey of some of the recent results on certain two-dimensional random growth models and their relation to random matrix theory, in particular to the Tracy-Widom distribution for the largest eigenvalue. The problems are related to that of finding the length of the longest increasing subsequence in a random permutation. We also give a new approach to certain results for the Schur measu...

The Longest Increasing Subsequence (LIS) and Common Longest Increasing Subsequence (CLIS) have their importance in many data mining applications. We propose algorithms to discover LIS and CLIS from varied databases. This work finds all increasing subsequences from the given database, find increasing subsequences in n sliding window, longest increasing sequences in one and more sequences, decrea...

Following the entropy method this paper presents general concentration inequalities, which can be applied to combinatorial optimization and empirical processes. The inequalities give improved concentration results for optimal travelling salesmen tours, Steiner trees and the eigenvalues of random symmetric matrices. 1 Introduction Since its appearance in 1995 Talagrand’s convex distance inequali...

Ulam (1961) apparently first posed the following question: what is the average (or distribution of) the length Ln of the longest increasing subsequence of a random permutation of the first n integers? Experimental (Monte-Carlo) evidence has played an important role in the study of Ln begining with Ulam (1961), and continuing with Baer and Brock (1969), and Odlyzko and Rains (2000). We present e...

In this paper, we study the problem of privately computing ordered statistics with the goal of monitoring sequential data streams. Despite the broad series of techniques for time-series monitoring, only few works provide provable privacy guarantees employing the formal notion of differential privacy. While these solutions are well established, their focus is mostly limited to count based statis...