Content Delivery Networks have become commonly used by content providers such as Netflix to deliver TV programmes to a large number of customers. This solution however breaks down when intensive processing is required and when content cannot be stored ahead of time, as is the case with live (real time) content. We study here resource management issues when a cloud infrastructure is used to deliver live content. More specifically, we look at the allocation of machines to host servers and how to keep that number as small as possible while meeting user demand. We express the problem as an online bin packing model and show how, by exploiting a simple property of the media, we can derive an efficient solution.

A contract algorithm is an algorithm which is given, as part of the input, a specified amount of allowable computation time. The algorithm must then complete its execution within the allotted time. An interruptible algorithm, in contrast, can be interrupted at an arbitrary point in time, at which point it must report its currently best solution. It is known that contract algorithms can simulate interruptible algorithms using iterative deepening techniques. This simulation is done at a penalty in the performance of the solution, as measured by the so-called acceleration ratio. In this paper we give matching (i.e., optimal) upper and lower bounds for the acceleration ratio under such a simulation. We assume the most general setting in which n problem instances must be solved by means of scheduling executions of contract algorithms in $m$ identical parallel processors. This resolves an open conjecture of Bernstein, Filkenstein, and Zilberstein who gave an optimal schedule under the restricted setting of round robin and length-increasing schedules, but whose optimality in the general unrestricted case remained open. Lastly, we show how to evaluate the average acceleration ratio of the class of exponential strategies in the setting of n problem instances and m parallel processors. This is a broad class of schedules that tend to be either optimal or near-optimal, for several variants of the basic problem.

We provide a combinatorial proof of a symplectic character identity relating the sum of a product of symplectic Schur functions to the product [Formula: see text]. This formula owes its origin to the existence of a dual pair of symplectic groups acting on spinors, as pointed out by Hasegawa. The first combinatorial proof, based on symplectic tableaux and a variation of the Robinson–Schensted–Knuth correspondence, was due to Terada. Here we use Schützenberger’s jeu de taquin, augmented by two simple zero weight transformations. The identity itself generalizes a well-known identity expressing [Formula: see text] as a sum of products of Schur functions that was due to Littlewood and proved combinatorially by Remmel. We offer an alternative combinatorial proof of this identity by means of the jeu de taquin, as a precursor to the proof of the symplectic identity.

MOTIVATION: A major challenge in gene expression analysis is effective data organization and visualization. One of the most popular tools for this task is hierarchical clustering. Hierarchical clustering allows a user to view relationships in scales ranging from single genes to large sets of genes, while at the same time providing a global view of the expression data. However, hierarchical clustering is very sensitive to noise, it usually lacks of a method to actually identify distinct clusters, and produces a large number of possible leaf orderings of the hierarchical clustering tree. In this paper we propose a new hierarchical clustering algorithm which reduces susceptibility to noise, permits up to k siblings to be directly related, and provides a single optimal order for the resulting tree. RESULTS: We present an algorithm that efficiently constructs a k-ary tree, where each node can have up to k children, and then optimally orders the leaves of that tree. By combining k clusters at each step our algorithm becomes more robust against noise and missing values. By optimally ordering the leaves of the resulting tree we maintain the pairwise relationships that appear in the original method, without sacrificing the robustness. Our k-ary construction algorithm runs in O(n(3)) regardless of k and our ordering algorithm runs in O(4(k)n(3)). We present several examples that show that our k-ary clustering algorithm achieves results that are superior to the binary tree results in both global presentation and cluster identification. AVAILABILITY: We have implemented the above algorithms in C++ on the Linux operating system.

An assignment of colors to objects induces a natural integer weight on each tree that has these objects as leaves. This weight is called "parsimony length" in biostatistics and is the basis of the "maximum parsimony" technique for reconstructing evolutionary trees. Equations for the average value (over all binary trees) of the parsimony length of both fixed and random colorations are derived using generating function techniques. This leads to asymptotic results that extend earlier results confined to just two colors. A potential application to DNA sequence analysis is outlined briefly.