Related papers: Replacing Mark Bits with Randomness in Fibonacci H…
We present results of extensive statistical and bit level tests on three implementations of a pseudorandom number generator algorithm using the lagged Fibonacci method with an occasional addition of an extra bit. First implementation is the…
Makespan scheduling on identical machines is one of the most basic and fundamental packing problems studied in the discrete optimization literature. It asks for an assignment of $n$ jobs to a set of $m$ identical machines that minimizes the…
Recent advances in the binary classification setting by Hanneke [2016b] and Larsen [2023] have resulted in optimal PAC learners. These learners leverage, respectively, a clever deterministic subsampling scheme and the classic heuristic of…
Motivated by an application in computational topology, we consider a novel variant of the problem of efficiently maintaining dynamic rooted trees. This variant requires merging two paths in a single operation. In contrast to the standard…
Kernel herding belongs to a family of deterministic quadratures that seek to minimize the worst-case integration error over a reproducing kernel Hilbert space (RKHS). These quadrature rules come with strong experimental evidence that this…
Bin Packing with $k$ bins is a fundamental optimisation problem in which we are given a set of $n$ integers and a capacity $T$ and the goal is to partition the set into $k$ subsets, each of total sum at most $T$. Bin Packing is NP-hard…
We study the problem of minimizing an ordered norm of a load vector (indexed by a set of $d$ resources), where a finite number $n$ of customers $c$ contribute to the load of each resource by choosing a solution $x_c$ in a convex set $X_c…
We present a randomized algorithm for dynamic graph connectivity. With failure probability less than $1/n^c$ (for any constant $c$ we choose), our solution has worst case running time $O(\log^3 n)$ per edge insertion, $O(\log^4 n)$ per edge…
We introduce the subset assignment problem in which items of varying sizes are placed in a set of bins with limited capacity. Items can be replicated and placed in any subset of the bins. Each (item, subset) pair has an associated cost. Not…
We assume the permutation $\pi$ is given by an $n$-element array in which the $i$-th element denotes the value $\pi(i)$. Constructing its inverse in-place (i.e. using $O(\log{n})$ bits of additional memory) can be achieved in linear time…
We extend the work of Narasimhan and Bilmes [30] for minimizing set functions representable as a dierence between submodular functions. Similar to [30], our new algorithms are guaranteed to monotonically reduce the objective function at…
Feature Selection is a crucial procedure in Data Science tasks such as Classification, since it identifies the relevant variables, making thus the classification procedures more interpretable, cheaper in terms of measurement and more…
We investigate iterative methods with randomized preconditioners for solving overdetermined least-squares problems, where the preconditioners are based on a random embedding of the data matrix. We consider two distinct approaches: the…
Data compression has been widely applied in many data processing areas. Compression methods use variable-size codes with the shorter codes assigned to symbols or groups of symbols that appear in the data frequently. Fibonacci coding, as a…
This paper aims to put forward the concept that learning to take safe actions in unknown environments, even with probability one guarantees, can be achieved without the need for an unbounded number of exploratory trials, provided that one…
Perfect hash functions can potentially be used to compress data in connection with a variety of data management tasks. Though there has been considerable work on how to construct good perfect hash functions, there is a gap between theory…
This paper describes the shortest path problem in weighted graphs and examines the differences in efficiency that occur when using Dijkstra's algorithm with a Fibonacci heap, binary heap, and self-balancing binary tree. Using C++…
We show that any randomized first-order algorithm which minimizes a $d$-dimensional, $1$-Lipschitz convex function over the unit ball must either use $\Omega(d^{2-\delta})$ bits of memory or make $\Omega(d^{1+\delta/6-o(1)})$ queries, for…
The traditional framework for feature selection treats all features as costing the same amount. However, in reality, a scientist often has considerable discretion regarding which variables to measure, and the decision involves a tradeoff…
Network design problems involve constructing edges in a transportation or supply chain network to minimize construction and daily operational costs. We study a stochastic version where operational costs are uncertain due to fluctuating…