On computing the length of longest increasing subsequences

On longest increasing subsequences in random permutations

The expected value of L n , the length of the longest increasing subsequence of a random permutation of f1; : : : ; ng, has been studied extensively. This paper presents the results of both Monte Carlo and exact computations that explore the ner structure of the distribution of L n. The results suggested that several of the conjectures that had been made about L n were incorrect, and led to new...

Computing Longest Increasing Subsequences over Sequential Data Streams

In this paper, we propose a unified index, an orthogonal list-based index, to support real time queries of all longest increasingsubsequence (LIS) and LIS with constraints over sequential datastreams. The index built by our algorithm requires O(w) space,where w is the time window size. The running time for building theinitial index takes O(wlogw) time. Applying the index, de...

Faster Algorithms for Computing Longest Common Increasing Subsequences

We present algorithms for finding a longest common increasing subsequence of two or more input sequences. For two sequences of lengths n and m, where m ≥ n, we present an algorithm with an output-dependent expected running time of O((m + nl) log log σ + Sort) and O(m) space, where l is the length of an LCIS, σ is the size of the alphabet, and Sort is the time to sort each input sequence. For k ...

The Surprising Mathematics of Longest Increasing Subsequences

Longest Increasing Subsequences : From PatienceSorting to the

We describe a simple one-person card game, patience sorting. Its analysis leads to a broad circle of ideas linking Young tableaux with the longest increasing subsequence of a random permutation via the Schensted correspondence. A recent highlight of this area is the work of Baik-Deift-Johansson which yields limiting probability laws via hard analysis of Toeplitz determinants.