We study the uctuations, in the large deviations regime, of the longest increasing subsequence of a random i.i.d. sample on the unit square. In particular, our results yield the precise upper and lower exponential tails for the length of the longest increasing subsequence of a random permutation. i=1 denote a sequence of i.i.d. random variables with marginal law on the unit square Q = 0; 1] 2. ...

This diploma thesis deals with four big groups of random trees, namely Polya trees, simple generated trees, increasing trees and scale-free trees. Di erent characteristics, similarities and di erences of these varieties are discussed, e.g. the limiting distribution of node-degrees. Most results are obtained using generating functions and methods of singulary analysis and stochastics. In the rst...

ABSTRACT- To study the effect of tree roots on increasing water infiltration in soil and also to determine and assess the coefficients of different infiltration models, some infiltration tests were performed in three tree plantation areas in Badjgah, Fars province with different soil textures (clay loam for pear plantation, sandy loam for grape plantation, loamy sand for pine trees). In each pl...

poplar trees are becoming extremely important as fast growing species due to the increasing need for wood and decreasing productivity of some lands in iran. the present study aimed to find the effect of canopy of poplar clones as one of the most important effective factors on soil properties compared to the distances inter-row trees. five poplar clones and species included: populus euramericana...

Given a sequence of integers, we want to find a longest increasing subsequence of the sequence. It is known that this problem can be solved in O(n log n) time and space. Our goal in this paper is to reduce the space consumption while keeping the time complexity small. For √ n ≤ s ≤ n, we present algorithms that use O(s log n) bits and O( 1 s · n · log n) time for computing the length of a longe...

The deterministic space complexity of approximating the length of the longest increasing subsequence of a stream of N integers is known to be Θ̃( √ N). However, the randomized complexity is wide open. We show that the technique used in earlier work to establish the Ω( √ N) deterministic lower bound fails strongly under randomization: specifically, we show that the communication problems on which...

By reviewing Longest Increasing Subsequence (LIS) and Longest Common Subsequence (LCS), the Longest Common Increasing Subsequence (LCIS) problem is explored for two non-random input cases in details. Specifically, we designed two algorithms, one solving the input sequence scenario with the case that one sequence is ordered and duplicate elements are allowed in each of sequences, and the second ...

We consider the problem of :nding the longest increasing subsequence in a sliding window over a given sequence (LISW). We propose an output-sensitive data structure that solves this problem in time O(n log log n+OUTPUT) for a sequence of n elements. This data structure substantially improves over the na?@ve generalization of the longest increasing subsequence algorithm and in fact produces an o...

In this paper we give parallel solutions to the problem of finding the Longest Increasing Subsequence of a given sequence of n integers. First, we show the existence of a simple dynamic programming solution. Its running time is Θ(n) and its space requirement is Θ(n). Then, we continue by showing that it is possible to develop two parallel solutions based on optical bus system of n processors, o...

We study the fluctuations, in the large deviations regime, of the longest increasing subsequence of a random i.i.d. sample on the unit square. In particular, our results yield the precise upper and lower exponential tails for the length of the longest increasing subsequence of a random permutation. §.