In this paper, we construct a data structure using a forest of redblack trees to efficiently compute the longest increasing subsequence of a dynamically updated sequence. Our data structure supports a query for the longest increasing subsequence in O(r + logn) worst case time and supports inserts anywhere in the sequence in O (r logn/r) worst case time, where r is the length of the longest incr...

Given a random permutation of the numbers 1, 2, . . . . n, let L, be the length of the longest descending subsequence of this permutation. Let F, be the minimal header (first element) of the descending subsequences having maximal length. It is known that EL,/&,,,, c and that c=2. However, the proofs that r=2 are far from elementary and involve limit processes. Several relationships between thes...

BACKGROUND AND OBJECTIVES In this study we examined whether prestorage leucocyte reduction prevents the accumulation of bioreactive substances in red cell units. MATERIALS AND METHODS Measurements were performed in the supernatants of buffy-coat-depleted (standard red cells) and leucocyte-reduced (filtered red cells) red cell units. The effect of storage was evaluated by taking repetitive sam...

We investigate partitioning of integer sequences into heapable subsequences (previously defined and established by Mitzenmacher et al. [BHMZ11]). We show that an extension of patience sorting computes the decomposition into a minimal number of heapable subsequences (MHS). We connect this parameter to an interactive particle system, a multiset extension of Hammersley’s process, and investigate i...