Related papers: Analysis of Pivot Sampling in Dual-Pivot Quicksort
We investigate the implementation of an oracle for the Subset Sum problem for quantum search using Grover's algorithm. Our work concerns reducing the number of qubits, gates, and multi-controlled gates required by the oracle. We describe…
The number of comparisons X_n used by Quicksort to sort an array of n distinct numbers has mean mu_n of order n log n and standard deviation of order n. Using different methods, Regnier and Roesler each showed that the normalized variate…
Sequential algorithms for the Stable Matching Problem are often too slow in the context of some large scale applications like switch scheduling. Parallel architectures can offer a notable decrease in runtime complexity. We propose a stable…
Smoothed analysis is a framework for analyzing the complexity of an algorithm, acting as a bridge between average and worst-case behaviour. For example, Quicksort and the Simplex algorithm are widely used in practical applications, despite…
In many operations management problems, we need to make decisions sequentially to minimize the cost while satisfying certain constraints. One modeling approach to study such problems is constrained Markov decision process (CMDP). When…
The impracticality of posterior sampling has prevented the widespread adoption of spike-and-slab priors in high-dimensional applications. To alleviate the computational burden, optimization strategies have been proposed that quickly find…
Database query processing requires algorithms for duplicate removal, grouping, and aggregation. Three algorithms exist: in-stream aggregation is most efficient by far but requires sorted input; sort-based aggregation relies on external…
We consider learning problems over training sets in which both, the number of training examples and the dimension of the feature vectors, are large. To solve these problems we propose the random parallel stochastic algorithm (RAPSA). We…
Sorting is at the core of many database operations, such as index creation, sort-merge joins, and user-requested output sorting. As GPUs are emerging as a promising platform to accelerate various operations, sorting on GPUs becomes a viable…
Memory bloat is an important source of inefficiency in complex production software, especially in software written in managed languages such as Java. Prior approaches to this problem have focused on identifying objects that outlive their…
Sorting is a fundamental and well studied problem that has been studied extensively. Sorting plays an important role in the area of databases, as many queries can be served much faster if the relations are first sorted. One of the most…
We study very simple sorting algorithms based on a probabilistic comparator model. In our model, errors in comparing two elements are due to (1) the energy or effort put in the comparison and (2) the difference between the compared…
We consider energy-efficient scheduling on multiprocessors, where the speed of each processor can be individually scaled, and a processor consumes power $s^{\alpha}$ when running at speed $s$, for $\alpha>1$. A scheduling algorithm needs to…
We study a multi-objective scheduling problem on two dedicated processors. The aim is to minimize simultaneously the makespan, the total tardiness and the total completion time. This NP-hard problem requires the use of well-adapted methods.…
We present a deterministic sorting algorithm, SPMS (Sample, Partition, and Merge Sort), that interleaves the partitioning of a sample sort with merging. Sequentially, it sorts $n$ elements in $O(n \log n)$ time cache-obliviously with an…
We provide a probabilistic analysis of the output of Quicksort when comparisons can err.
This paper provides a block coordinate descent algorithm to solve unconstrained optimization problems. In our algorithm, computation of function values or gradients is not required. Instead, pairwise comparison of function values is used.…
Higher-order ODE solvers have become a standard tool for accelerating diffusion probabilistic model (DPM) sampling, motivating the widespread view that first-order methods are inherently slower and that increasing discretization order is…
Optimizing smooth convex functions in stochastic settings, where only noisy estimates of gradients and Hessians are available, is a fundamental problem in optimization. While first-order methods possess a low per-iteration cost, their…
Stochastic compositional optimization arises in many important machine learning tasks such as value function evaluation in reinforcement learning and portfolio management. The objective function is the composition of two expectations of…