Related papers: Quantum-Guided Cluster Algorithms for Combinatoria…
Motivated by near term quantum computing hardware limitations, combinatorial optimization problems that can be addressed by current quantum algorithms and noisy hardware with little or no overhead are used to probe capabilities of quantum…
Combinatorial optimization is a promising area for achieving quantum speedup. Quantum approximate optimization algorithm (QAOA) is designed to search for low-energy states of the Ising model, which correspond to near-optimal solutions of…
Motivated by the fact that distances between data points in many real-world clustering instances are often based on heuristic measures, Bilu and Linial~\cite{BL} proposed analyzing objective based clustering problems under the assumption…
Bipartite Correlation clustering is the problem of generating a set of disjoint bi-cliques on a set of nodes while minimizing the symmetric difference to a bipartite input graph. The number or size of the output clusters is not constrained…
Simulated annealing (SA) attracts more attention among classical heuristic algorithms because the solution of the combinatorial optimization problem can be naturally mapped to the ground state of the Ising Hamiltonian. However, in practical…
Although many efficient heuristics have been developed to solve binary optimization problems, these typically produce correlated solutions for degenerate problems. Most notably, transverse-field quantum annealing - the heuristic employed in…
Clustering is a long-standing research problem and a fundamental tool in AI and data analysis. The traditional k-center problem, a fundamental theoretical challenge in clustering, has a best possible approximation ratio of 2, and any…
The paper describes clustering problems from the combinatorial viewpoint. A brief systemic survey is presented including the following: (i) basic clustering problems (e.g., classification, clustering, sorting, clustering with an order over…
Combinatorial problems are formulated to find optimal designs within a fixed set of constraints. They are commonly found across diverse engineering and scientific domains. Understanding how to best use quantum computers for combinatorial…
In stochastic optimisation, the large number of scenarios required to faithfully represent the underlying uncertainty is often a barrier to finding efficient numerical solutions. This motivates the scenario reduction problem: by find a…
In many statistical linear inverse problems, one needs to recover classes of similar curves from their noisy images under an operator that does not have a bounded inverse. Problems of this kind appear in many areas of application.…
Combinatorial optimization problems are pervasive across science and industry. Modern deep learning tools are poised to solve these problems at unprecedented scales, but a unifying framework that incorporates insights from statistical…
We establish a general framework for developing approximation algorithms for a class of counting problems. Our framework is based on the cluster expansion of abstract polymer models formalism of Koteck\'y and Preiss. We apply our framework…
We present combinatorial approximation algorithms for the weighted correlation clustering problem. In this problem, we have a set of vertices and two weight values for each pair of vertices, denoting their difference and similarity. The…
Correlation clustering is a central topic in unsupervised learning, with many applications in ML and data mining. In correlation clustering, one receives as input a signed graph and the goal is to partition it to minimize the number of…
We study the spacial and temporal multiscale properties of complex systems. We present accelerated algorithms for dilute spin glasses and display explicitly their relation to the effective dynamics of specific collective degrees of freedom…
A promising paradigm of quantum computing for achieving practical quantum advantages is quantum annealing or quantum approximate optimization algorithm, where the classical problems are encoded in Ising interactions. However, it is…
Correlation clustering is a central problem in unsupervised learning, with applications spanning community detection, duplicate detection, automated labelling and many more. In the correlation clustering problem one receives as input a set…
Quantum annealing is a heuristic algorithm for searching the ground state of an Ising model. Heuristic algorithms aim to obtain near-optimal solutions with a reasonable computation time. Accordingly, many algorithms have so far been…
Clustering is a NP-hard problem. Thus, no optimal algorithm exists, heuristics are applied to cluster the data. Heuristics can be very resource-intensive, if not applied properly. For substantially large data sets computational efficiencies…