Fully Dynamic Connectivity in O(log⁡n(log⁡log⁡n)2)O(\log n(\log\log n)^2) Amortized Expected Time

Dynamic connectivity is one of the most fundamental problems in dynamic graph algorithms. We present a randomized Las Vegas dynamic connectivity data structure with $O(\log n(\log\log n)^2)$ amortized expected update time and $O(\log n/\log\log\log n)$ worst case query time, which comes very close to the cell probe lower bounds of Patrascu and Demaine (2006) and Patrascu and Thorup (2011)

An Investigation into Animating Plant Structures within Real-time Constraints

This paper is an analysis of current developments in rendering botanical structures for scientic and entertainment purposes with a focus on visualising growth. The choices of practical investigations produce a novel approach for parallel parsing of difficult bracketed L-Systems, based upon the work of Lipp, Wonka and Wimmer (2010). Alongside this is a general overview of the issues involved when looking at growing systems, technical details involving programming for the Graphics Processing Unit (GPU) and other possible solutions for further work that also could achieve the project's goals

Cross-validated Bagged Prediction of Survival

In this article, we show how to apply our previously proposed Deletion/Substitution/Addition algorithm in the context of right-censoring for the prediction of survival. Furthermore, we introduce how to incorporate bagging into the algorithm to obtain a cross-validated bagged estimator. The method is used for predicting the survival time of patients with diffuse large B-cell lymphoma based on gene expression variables

Maintaining Discrete Probability Distributions in Practice

A classical problem in random number generation is the sampling of elements from a given discrete distribution. Formally, given a set of indices $S = \{1, \dots, n\}$ and sequence of weights $w_1, \dots, w_n \in \mathbb{R}^+$, the task is to provide samples from $S$ with distribution $p(i) = w_i / W$ where $W = \sum_j w_j$. A commonly accepted solution is Walker's Alias Table, which allows for each sample to be drawn in constant time. However, some applications correspond to a dynamic setting, where elements are inserted or removed, or weights change over time. Here, the Alias Table is not efficient, as it needs to be re-built whenever the underlying distribution changes. In this paper, we engineer a simple data structure for maintaining discrete probability distributions in the dynamic setting. Construction of the data structure is possible in time $O(n)$, sampling is possible in expected time $O(1)$, and an update of size $\Delta$ can be processed in time $O(\Delta n / W)$. As a special case, we maintain an urn containing $W$ marbles of $n$ colors where with each update $O(W / n)$ marbles can be added or removed in $O(1)$ time per update. To evaluate the efficiency of the data structure in practice we conduct an empirical study. The results suggest that the dynamic sampling performance is competitive with the static Alias Table. Compared to existing more complex dynamic solutions we obtain a sampling speed-up of up to half an order of magnitude.Comment: ALENEX 202

Make flows small again: revisiting the flow framework

We present a new flow framework for separation logic reasoning about programs that manipulate general graphs. The framework overcomes problems in earlier developments: it is based on standard fixed point theory, guarantees least flows, rules out vanishing flows, and has an easy to understand notion of footprint as needed for soundness of the frame rule. In addition, we present algorithms for automating the frame rule, which we evaluate on graph updates extracted from linearizability proofs for concurrent data structures. The evaluation demonstrates that our algorithms help to automate key aspects of these proofs that have previously relied on user guidance or heuristics

Fast Computation of Special Resultants

We propose fast algorithms for computing composed products and composed sums, as well as diamond products of univariate polynomials. These operations correspond to special multivariate resultants, that we compute using power sums of roots of polynomials, by means of their generating series

ORTHOGONAL RANGE SKYLINE QUERIES

Given a set of points P, we often need to report the ones that lie within a certain query range Q. This is referred to as orthogonal range reporting. We can also go further, reporting only the dominant points within that query. In 2 dimensions, a point p1 = (x1, y1) dominates a point p2 = (x2, y2) iff x1 ≥ x2 and y1 \u3e y2 or x1 \u3e x2 and y1 ≥ y2. The set of all dominant points within a query range is called the skyline of that query. There are several different variants of skyline queries. For example, we can consider each point in P to be colored. Given a query range Q, can we efficiently count the number of points of each color in the skyline? In this thesis, we will present a new O( log n log log n + D log log n) method for doing so. The method is possible thanks to a new reduction from skyline queries to orthogonal range queries. We will also explore novel algorithms for answering skyline query variants in the I/O model of computation, making use of techniques such as Ganguly et al.’s [2] double-chaining method and Alstrup et al.’s [14] grid approach. By applying these existing techniques in new ways, we can not only derive our own efficient algorithms for skyline queries, but also explore potential avenues for future researc

Dynamic Trees with Almost-Optimal Access Cost

An optimal binary search tree for an access sequence on elements is a static tree that minimizes the total search cost. Constructing perfectly optimal binary search trees is expensive so the most efficient algorithms construct almost optimal search trees. There exists a long literature of constructing almost optimal search trees dynamically, i.e., when the access pattern is not known in advance. All of these trees, e.g., splay trees and treaps, provide a multiplicative approximation to the optimal search cost. In this paper we show how to maintain an almost optimal weighted binary search tree under access operations and insertions of new elements where the approximation is an additive constant. More technically, we maintain a tree in which the depth of the leaf holding an element e_i does not exceed min(log(W/w_i),log n)+O(1) where w_i is the number of times e_i was accessed and W is the total length of the access sequence. Our techniques can also be used to encode a sequence of m symbols with a dynamic alphabetic code in O(m) time so that the encoding length is bounded by m(H+O(1)), where H is the entropy of the sequence. This is the first efficient algorithm for adaptive alphabetic coding that runs in constant time per symbol

Time-sensitive autonomous architectures

Autonomous and software-defined vehicles (ASDVs) feature highly complex systems, coupling safety-critical and non-critical components such as infotainment. These systems require the highest connectivity, both inside the vehicle and with the outside world. An effective solution for network communication lies in Time-Sensitive Networking (TSN) which enables high-bandwidth and low-latency communications in a mixed-criticality environment. In this work, we present Time-Sensitive Autonomous Architectures (TSAA) to enable TSN in ASDVs. The software architecture is based on a hypervisor providing strong isolation and virtual access to TSN for virtual machines (VMs). TSAA latest iteration includes an autonomous car controlled by two Xilinx accelerators and a multiport TSN switch. We discuss the engineering challenges and the performance evaluation of the project demonstrator. In addition, we propose a Proof-of-Concept design of virtualized TSN to enable multiple VMs executing on a single board taking advantage of the inherent guarantees offered by TSN