Related papers: Decomposition algorithms for solving NP-hard probl…
Quantum Error Correction (QEC) is required in quantum computers to mitigate the effect of errors on physical qubits. When adopting a QEC scheme based on surface codes, error decoding is the most computationally expensive task in the…
Variational quantum algorithms, such as the Recursive Quantum Approximate Optimization Algorithm (RQAOA), have become increasingly popular, offering promising avenues for employing Noisy Intermediate-Scale Quantum devices to address…
Graph partitioning is a fundamental combinatorial optimization problem that attracts a lot of attention from theoreticians and practitioners due to its broad applications. From multilevel graph partitioning to more general-purpose…
The matching problem between two adjacency matrices can be formulated as the NP-hard quadratic assignment problem (QAP). Previous work on semidefinite programming (SDP) relaxations to the QAP have produced solutions that are often tight in…
The problem of identifying the maximum edge biclique in bipartite graphs has attracted considerable attention in bipartite graph analysis, with numerous real-world applications such as fraud detection, community detection, and online…
Nucleus decompositions have been shown to be a useful tool for finding dense subgraphs. The coreness value of a clique represents its density based on the number of other cliques it is adjacent to. One useful output of nucleus decomposition…
We tackle the problem of graph partitioning for image segmentation using correlation clustering (CC), which we treat as an integer linear program (ILP). We reformulate optimization in the ILP so as to admit efficient optimization via…
A range of quantum algorithms, especially those leveraging variational parameterization and circuit-based optimization, are being studied as alternatives for solving classically intractable combinatorial optimization problems (COPs).…
Many practical problems in almost all scientific and technological disciplines have been classified as computationally hard (NP-hard or even NP-complete). In life sciences, combinatorial optimization problems frequently arise in molecular…
In our paper, we consider the following general problems: check feasibility, count the number of feasible solutions, find an optimal solution, and count the number of optimal solutions in $P \cap Z^n$, assuming that $P$ is a polyhedron,…
In this paper, we apply the Rank-Sparsity Matrix Decomposition to the planted Maximum Quasi-Clique Problem (MQCP). This problem has the planted Maximum Clique Problem (MCP) as a special case. The maximum clique problem is NP-hard. A…
Realizing quantum speedup for practically relevant, computationally hard problems is a central challenge in quantum information science. Using Rydberg atom arrays with up to 289 qubits in two spatial dimensions, we experimentally…
With the aim of establishing a framework to efficiently perform the practical application of quantum chemistry simulation on near-term quantum devices, we envision a hybrid quantum--classical framework for leveraging problem decomposition…
An abundance of real-world problems manifest as covering edges and/or vertices of a graph with cliques that are optimized for some objectives. We consider different structural parameters of graph, and design fixed-parameter tractable…
We suggest a hybrid quantum-classical routine for the NP-hard Electric Vehicle Fleet Charging and Allocation Problem. The original formulation is a Mixed Integer Linear Program with continuous variables and inequality constraints. To…
While Annealing Machines (AM) have shown increasing capabilities in solving complex combinatorial problems, positioning themselves as a more immediate alternative to the expected advances of future fully quantum solutions, there are still…
Many resource allocation problems in the cloud can be described as a basic Virtual Network Embedding Problem (VNEP): finding mappings of request graphs (describing the workloads) onto a substrate graph (describing the physical…
In this work, we attempt to solve the integer-weight knapsack problem using the D-Wave 2000Q adiabatic quantum computer. The knapsack problem is a well-known NP-complete problem in computer science, with applications in economics, business,…
We consider the problem of identifying the densest k-node subgraph in a given graph. We write this problem as an instance of rank-constrained cardinality minimization and then relax using the nuclear and 11 norms. Although the original…
Core decomposition is a fundamental operator in network analysis. In this paper, we study the problem of computing distance-generalized core decomposition on a network. A distance-generalized core, also termed $(k, h)$-core, is a maximal…