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. §.

The interplay between two-dimensional percolation growth models and one-dimensional particle processes has always been a fruitful source of interesting mathematical phenomena. In this paper we develop a connection between the construction of Busemann functions in the Hammersley last-passage percolation model with i.i.d. random weights, and the existence, ergodicity and uniqueness of equilibrium...

Agriculture has to keep pace with the food requirements of increasing human populations. Also, with rising incomes, the consumption of meat and dairy products also rises. This has been very vividly reflected in several countries in South East Asia, including Malaysia. Meat consumption per capita is now well above 5% per year, and is likely to rise further. A major justification for improved ani...

petroleum and its subjected economic structurs play a significant role in iran's political social and economic develovement. iranian economy highly depends on oil exports and incomes. oil industry provides almost 50% of national budjet and 80 percent of exportation resources. oil's incomes have fluctuated during different decades and experienced the most increasing trend in (2007-2011...

We consider the concentration of measure for n iid, two-dimensional random variables, under the conditioning that they form a record. Under mild conditions, we show that all random variables tend to concentrate, as n ! 1, around limiting curves, which are the solutions of an appropriate variational problem. We also show that the same phenomenum occurs, without the records conditioning, for the ...

A longest increasing subsequence problem (LIS) is a well-known combinatorial problem with applications mainly in bioinformatics, where it is used in various projects on DNA sequences. Recently, a number of generalisations of this problem were proposed. One of them is to find an LIS among all fixed-size windows of the input sequence (LISW). We propose an algorithm for the LISW problem based on c...

ABSTRACT. We study the shape of the Young diagram λ associated via the Robinson–Schensted– Knuth algorithm to a random permutation in Sn such that the length of the longest decreasing subsequence is not bigger than a fixed number d; in other words we study the restriction of the Plancherel measure to Young diagrams with at most d rows. We prove that in the limit n → ∞ the rows of λ behave like ...

Given a sequence π1π2 . . . πn, a longest increasing subsequence (LIS) in a window π〈l, r〉= πlπl+1 . . . πr is a longest subsequence σ = πi1πi2 . . . πiT such that l ≤ i1 < i2 < · · · < iT ≤ r and πi1 < πi2 < · · · < πiT . We consider the Lisw problem, which is to find the longest increasing subsequences in a sliding window of fixed-size w over a sequence. Formally, it is to find a LIS for ever...