Related papers: Quantum and Classical Algorithms for Approximate S…
Quantum $k$-minimum finding is a fundamental subroutine with numerous applications in combinatorial problems and machine learning. Previous approaches typically assume oracle access to exact function values, making it challenging to…
The emergence of huge-scale, data-intensive linear optimization (LO) problems in applications such as machine learning has driven the need for more computationally efficient interior point methods (IPMs). While conventional IPMs are…
In this paper, we obtain a number of new simple pseudo-polynomial time algorithms on the well-known knapsack problem, focusing on the running time dependency on the number of items $n$, the maximum item weight $w_\mathrm{max}$, and the…
Subset Sum is a classical optimization problem taught to undergraduates as an example of an NP-hard problem, which is amenable to dynamic programming, yielding polynomial running time if the input numbers are relatively small. Formally,…
Submodular continuous functions are a category of (generally) non-convex/non-concave functions with a wide spectrum of applications. We characterize these functions and demonstrate that they can be maximized efficiently with approximation…
We present new advances towards achieving exponential quantum speedups for solving optimization problems by low-depth quantum algorithms. Specifically, we focus on families of combinatorial optimization problems that exhibit symmetry and…
Quasi-2D Coulomb systems are of fundamental importance and have attracted much attention in many areas nowadays. Their reduced symmetry gives rise to interesting collective behaviors, but also brings great challenges for particle-based…
Recently, it has become evident that submodularity naturally captures widely occurring concepts in machine learning, signal processing and computer vision. Consequently, there is need for efficient optimization procedures for submodular…
We consider the problem of multi-objective maximization of monotone submodular functions subject to cardinality constraint, often formulated as $\max_{|A|=k}\min_{i\in\{1,\dots,m\}}f_i(A)$. While it is widely known that greedy methods work…
A $k$-submodular function is an extension of a submodular function in that its input is given by $k$ disjoint subsets instead of a single subset. For unconstrained nonnegative $k$-submodular maximization, Ward and \v{Z}ivn\'y proposed a…
Real continuous submodular functions, as a generalization of the corresponding discrete notion to the continuous domain, gained considerable attention recently. The analog notion for entropy functions requires additional properties: a real…
We present quantum algorithms, for Hamiltonians of linear combinations of local unitary operators, for Hamiltonian matrix-vector products and for preconditioning with the inverse of shifted reduced Hamiltonian operator that contributes to…
Variational quantum algorithms constitute one of the most widespread methods for using current noisy quantum computers. However, it is unknown if these heuristic algorithms provide any quantum-computational speedup, although we cannot…
Submodular optimization has numerous applications such as crowdsourcing and viral marketing. In this paper, we study the fundamental problem of non-negative submodular function maximization subject to a $k$-system constraint, which…
Evolutionary algorithms (EAs) are a kind of nature-inspired general-purpose optimization algorithm, and have shown empirically good performance in solving various real-word optimization problems. During the past two decades, promising…
We investigate two new optimization problems -- minimizing a submodular function subject to a submodular lower bound constraint (submodular cover) and maximizing a submodular function subject to a submodular upper bound constraint…
In submodular $k$-secretary problem, the goal is to select $k$ items in a randomly ordered input so as to maximize the expected value of a given monotone submodular function on the set of selected items. In this paper, we introduce a…
The closest pair problem is a fundamental problem of computational geometry: given a set of $n$ points in a $d$-dimensional space, find a pair with the smallest distance. A classical algorithm taught in introductory courses solves this…
Submodular maximization constitutes a prominent research topic in combinatorial optimization and theoretical computer science, with extensive applications across diverse domains. While substantial advancements have been achieved in…
Classical optimization is a cornerstone of the success of variational quantum algorithms, which often require determining the derivatives of the cost function relative to variational parameters. The computation of the cost function and its…