Given a string S = a1a2a3 · · · an, the longest increasing subsequence (LIS) problem is to find a subsequence of S such that the subsequence is increasing and its length is maximal. In this paper, we propose and solve two variants of the LIS problem. The first one is the minimal height LIS where the height means the difference between the greatest and smallest elements. We propose an algorithm ...

We present a number of results relating partial Cauchy-Littlewood sums, integrals over the compact classical groups, and increasing subsequences of permutations. These include: integral formulae for the distribution of the longest increasing subsequence of a random involution with constrained number of fixed points; new formulae for partial Cauchy-Littlewood sums, as well as new proofs of old f...

In this paper, we present algorithms and lower bounds for the Longest Increasing Subsequence (LIS) and Longest Common Subsequence (LCS) problems in the data streaming model. For the problem of deciding whether the LIS of a given stream of integers drawn from {1, . . . ,m} has length at least k, we discuss a one-pass streaming algorithm using O(k log m) space, with update time either O(log k) or...

A rollercoaster is a sequence of real numbers for which every maximal contiguous subsequence, that is increasing or decreasing, has length at least three. By translating this sequence to a set of points in the plane, a rollercoaster can be defined as a polygonal path for which every maximal sub-path, with positiveor negative-slope edges, has at least three points. Given a sequence of distinct r...

The longest increasing subsequence of a random walk with mean zero and finite variance is known to be n1/2+o(1). We show that this is not universal for symmetric random walks. In particular, the symmetric fat-tailed random walk has a longest increasing subsequence that is asymptotically at least n0.690 and at most n0.815. An exponent strictly greater than 1/2 is also shown for the symmetric sta...

In the study, we were investigated effect of bioactive coating composed of quince seed mucilage (QSM) incorporating green tea extract(GTE) on oil and water content, lipid oxidation, texture, color and sensory evolution of shrimp after deep-fat frying. For this purpose, different concentration of GTE (0-20%) was blended to obtain five coating solutions (QG 0-4). We observed a significant effect ...