851 research outputs found
The Traveling Salesman Problem
This paper presents a self-contained introduction into algorithmic and computational aspects of the traveling salesman problem and of related problems, along with their theoretical prerequisites as seen from the point of view of an operations researcher who wants to solve practical problem instances. Extensive computational results are reported on most of the algorithms described. Optimal solutions are reported for instances with sizes up to several thousand nodes as well as heuristic solutions with provably very high quality for larger instances
Multilevel Combinatorial Optimization Across Quantum Architectures
Emerging quantum processors provide an opportunity to explore new approaches
for solving traditional problems in the post Moore's law supercomputing era.
However, the limited number of qubits makes it infeasible to tackle massive
real-world datasets directly in the near future, leading to new challenges in
utilizing these quantum processors for practical purposes. Hybrid
quantum-classical algorithms that leverage both quantum and classical types of
devices are considered as one of the main strategies to apply quantum computing
to large-scale problems. In this paper, we advocate the use of multilevel
frameworks for combinatorial optimization as a promising general paradigm for
designing hybrid quantum-classical algorithms. In order to demonstrate this
approach, we apply this method to two well-known combinatorial optimization
problems, namely, the Graph Partitioning Problem, and the Community Detection
Problem. We develop hybrid multilevel solvers with quantum local search on
D-Wave's quantum annealer and IBM's gate-model based quantum processor. We
carry out experiments on graphs that are orders of magnitudes larger than the
current quantum hardware size, and we observe results comparable to
state-of-the-art solvers in terms of quality of the solution
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