Related papers: Round-Competitive Algorithms for Uncertainty Probl…
In this work we investigate the min-max-min robust optimization problem and the k-adaptability robust optimization problem for binary problems with uncertain costs. The idea of the first approach is to calculate a set of k feasible…
Consider the classical Min-Sum Set Cover problem: We are given a universe $\mathcal{U}$ of $n$ elements and a collection $\mathcal{S}$ of $k$ subsets of $\mathcal{U}$. Moreover, a cost function is associated with each set. The goal is to…
An instance of a group testing problem is a set of objects $\cO$ and an unknown subset $P$ of $\cO$. The task is to determine $P$ by using queries of the type ``does $P$ intersect $Q$'', where $Q$ is a subset of $\cO$. This problem occurs…
Two widely-used computational paradigms for sublinear algorithms are using linear measurements to perform computations on a high dimensional input and using structured queries to access a massive input. Typically, algorithms in the former…
We consider the setting of online computation with advice, and study the bin packing problem and a number of scheduling problems. We show that it is possible, for any of these problems, to arbitrarily approach a competitive ratio of $1$…
Data integration is a notoriously difficult and heuristic-driven process, especially when ground-truth data are not readily available. This paper presents a measure of uncertainty by providing maximal and minimal ranges of a query outcome…
Given two sets A and B and two oracles O(A) and O(B) that can identify the elements of these sets respectively, the goal is to find an element common to both sets using minimum number of oracle queries. Each application of either O(A) or…
We present scalable parallel algorithms with sublinear per-processor communication volume and low latency for several fundamental problems related to finding the most relevant elements in a set, for various notions of relevance: We begin…
We are given n base elements and a finite collection of subsets of them. The size of any subset varies between p to k (p < k). In addition, we assume that the input contains all possible subsets of size p. Our objective is to find a…
We consider the problem of search of an unstructured list for a marked element, when one is given advice as to where this element might be located, in the form of a probability distribution. The goal is to minimise the expected number of…
Machine learning can significantly improve performance for decision-making under uncertainty across a wide range of domains. However, ensuring robustness guarantees requires well-calibrated uncertainty estimates, which can be difficult to…
We use a Bayesian approach to optimally solve problems in noisy binary search. We deal with two variants: 1. Each comparison can be erroneous with some probability $1 - p$. 2. At each stage $k$ comparisons can be performed in parallel and a…
Submodular maximization is a general optimization problem with a wide range of applications in machine learning (e.g., active learning, clustering, and feature selection). In large-scale optimization, the parallel running time of an…
Decision-making problems can be modeled as combinatorial optimization problems with Constraint Programming formalisms such as Constrained Optimization Problems. However, few Constraint Programming formalisms can deal with both optimization…
We present a massively parallel algorithm, with near-linear memory per machine, that computes a $(2+\varepsilon)$-approximation of minimum-weight vertex cover in $O(\log\log d)$ rounds, where $d$ is the average degree of the input graph.…
Several well-studied online resource allocation problems can be formulated in terms of infinite, increasing sequences of positive values, in which each element is associated with a corresponding allocation value. Examples include problems…
In this paper we present a deterministic parallel algorithm solving the multiple selection problem in congested clique model. In this problem for given set of elements S and a set of ranks $K = \{k_1 , k_2 , ..., k_r \}$ we are asking for…
Searching for collisions in random functions is a fundamental computational problem, with many applications in symmetric and asymmetric cryptanalysis. When one searches for a single collision, the known quantum algorithms match the query…
Given an implicit $n\times n$ matrix $A$ with oracle access $x^TA x$ for any $x\in \mathbb{R}^n$, we study the query complexity of randomized algorithms for estimating the trace of the matrix. This problem has many applications in quantum…
We consider the problem of learning uncertainty regions for parameter estimation problems. The regions are ellipsoids that minimize the average volumes subject to a prescribed coverage probability. As expected, under the assumption of…