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The Maximum Matching problem has a quantum query complexity lower bound of $\Omega(n^{3/2})$ for graphs on $n$ vertices represented by an adjacency matrix. The current best quantum algorithm has the query complexity $O(n^{7/4})$, which is…
Quantum computing has the potential to speed up some optimization methods. One can use quantum computers to solve linear systems via Quantum Linear System Algorithms (QLSAs). QLSAs can be used as a subroutine for algorithms that require…
Local search is a fundamental optimization technique that is both widely used in practice and deeply studied in theory, yet its computational complexity remains poorly understood. The traditional frameworks, PLS and the standard algorithm…
This paper employs a powerful argument, called an algorithmic argument, to prove lower bounds of the quantum query complexity of a multiple-block ordered search problem in which, given a block number i, we are to find a location of a target…
Efficient global optimization is a widely used method for optimizing expensive black-box functions such as tuning hyperparameter, and designing new material, etc. Despite its popularity, less attention has been paid to analyzing the…
A local search algorithm solving an NP-complete optimisation problem can be viewed as a stochastic process moving in an 'energy landscape' towards eventually finding an optimal solution. For the random 3-satisfiability problem, the…
Exact algorithms for learning Bayesian networks guarantee to find provably optimal networks. However, they may fail in difficult learning tasks due to limited time or memory. In this research we adapt several anytime heuristic search-based…
The compact genetic algorithm (cGA) is an non-elitist estimation of distribution algorithm which has shown to be able to deal with difficult multimodal fitness landscapes that are hard to solve by elitist algorithms. In this paper, we…
Optimization is ubiquitous in our daily lives. In the past, (sub-)optimal solutions to any problem have been derived by trial and error, sheer luck, or the expertise of knowledgeable individuals. In our contemporary age, there thankfully…
Benchmark instances for the unbounded knapsack problem are typically generated according to specific criteria within a given constant range $R$, and these instances can be referred to as the unbounded knapsack problem with bounded…
In this paper, we build upon previous work on designing informative and efficient Exploratory Landscape Analysis features for characterizing problems' landscapes and show their effectiveness in automatically constructing algorithm selection…
We study the problem of estimating the number of defective items $d$ within a pile of $n$ elements up to a multiplicative factor of $\Delta>1$, using deterministic group testing algorithms. We bring lower and upper bounds on the number of…
We consider the problem of hypothesis testing for discrete distributions. In the standard model, where we have sample access to an underlying distribution $p$, extensive research has established optimal bounds for uniformity testing,…
Fair algorithm evaluation is conditioned on the existence of high-quality benchmark datasets that are non-redundant and are representative of typical optimization scenarios. In this paper, we evaluate three heuristics for selecting diverse…
One of the key difficulties in using estimation-of-distribution algorithms is choosing the population size(s) appropriately: Too small values lead to genetic drift, which can cause enormous difficulties. In the regime with no genetic drift,…
We describe approximation algorithms in Linial's classic LOCAL model of distributed computing to find maximum-weight matchings in a hypergraph of rank $r$. Our main result is a deterministic algorithm to generate a matching which is an…
The paper is devoted to upper bounds on the expected first hitting times of the sets of local or global optima for non-elitist genetic algorithms with very high selection pressure. The results of this paper extend the range of situations…
We study the online submodular maximization problem with free disposal under a matroid constraint. Elements from some ground set arrive one by one in rounds, and the algorithm maintains a feasible set that is independent in the underlying…
Consider the problem: we are given $n$ boxes, labeled $\{1,2,\ldots, n\}$ by an adversary, each containing a single number chosen from an unknown distribution; these $n$ distributions are not necessarily identical. We are also given an…
We attempt to better understand randomization in local distributed graph algorithms by exploring how randomness is used and what we can gain from it: - We first ask the question of how much randomness is needed to obtain efficient…