Related papers: Space-efficient classical and quantum algorithms f…
We investigate distributed classical and quantum approaches for the survivable network design problem (SNDP), sometimes called the generalized Steiner problem. These problems generalize many complex graph problems of interest, such as the…
In the lattice formulation of the Heavy Quark Effective Theory, the value of the classical velocity v, as defined through the separation of the 4-momentum of a heavy quark into a part proportional to the heavy quark mass and a residual part…
We introduce a novel quantum algorithm for the lattice Boltzmann method (LBM) based on the one-step simplified LBM. The structure of the algorithm allows for more flexibility in modelling different physics in contrast to earlier quantum…
Quantum annealing (QA) is proposed for vector perturbation precoding (VPP) in multiple input multiple output (MIMO) communications systems. The mathematical framework of VPP is presented, outlining the problem formulation and the benefits…
Given an undirected graph, the k-vertex cut problem (k-VCP) asks for a minimum-cost set of vertices whose removal yields at least k connected components in the resulting graph. The k-VCP is an important problem in network optimization, with…
Many claims of computational advantages have been made for quantum computing over classical, but they have not been demonstrated for practical problems. Here, we present algorithms for solving time-dependent PDEs, with particular reference…
It has been shown that the parallel Lattice Linear Predicate (LLP) algorithm solves many combinatorial optimization problems such as the shortest path problem, the stable marriage problem and the market clearing price problem. In this…
We study quantum algorithms for several fundamental string problems, including Longest Common Substring, Lexicographically Minimal String Rotation, and Longest Square Substring. These problems have been widely studied in the stringology…
The quadratic shortest path problem is the problem of finding a path in a directed graph such that the sum of interaction costs over all pairs of arcs on the path is minimized. We derive several semidefinite programming relaxations for the…
The Shortest-Path Problem in Graph of Convex Sets (SPP in GCS) is a recently developed optimization framework that blends discrete and continuous decision making. Many relevant problems in robotics, such as collision-free motion planning,…
The problem of finding the shortest path in a graph G(V, E) has been widely studied. However, in many applications it is necessary to compute an arbitrary number of them, k. Even though the problem has raised a lot of interest from…
We study space and time efficient quantum algorithms for two graph problems -- deciding whether an $n$-vertex graph is a forest, and whether it is bipartite. Via a reduction to the s-t connectivity problem, we describe quantum algorithms…
We consider an algorithmic problem inspired by the Battleship game. In the variant of the problem that we investigate, there is a unique ship of shape $S \subset Z^2$ which has been translated in the lattice $Z^2$. We assume that a player…
We consider online algorithms for the $k$-server problem on trees. Chrobak and Larmore proposed a $k$-competitive algorithm for this problem that has the optimal competitive ratio. However, a naive implementation of their algorithm has…
We prove new hardness results for fundamental lattice problems under the Exponential Time Hypothesis (ETH). Building on a recent breakthrough by Bitansky et al.\ \cite{BHIRW24}, who gave a polynomial-time reduction from $\mathsf{3SAT}$ to…
Support vector machine (SVM) is a particularly powerful and flexible supervised learning model that analyzes data for both classification and regression, whose usual algorithm complexity scales polynomially with the dimension of data space…
The problem of finding the sparsest vector (direction) in a low dimensional subspace can be considered as a homogeneous variant of the sparse recovery problem, which finds applications in robust subspace recovery, dictionary learning,…
In this paper, we present a deterministic algorithm for the closest vector problem for all l_p-norms, 1 < p < \infty, and all polyhedral norms, especially for the l_1-norm and the l_{\infty}-norm. We achieve our results by introducing a new…
Quantum optimization algorithms hold the promise of solving classically hard, discrete optimization problems in practice. The requirement of encoding such problems in a Hamiltonian realized with a finite -- and currently small -- number of…
Let G=(V,E)(|V|=n and |E|=m) be an undirected graph with positive edge weights. Let P_{G}(s, t) be a shortest s-t path in G. Let l be the number of edges in P_{G}(s, t). The \emph{Edge Replacement Path} problem is to compute a shortest s-t…