Year: 2006
Type: article
Abstract: Quantum algorithms for graph problems are considered, both in the adjacency matrix model and in an adjacency list-like array model. We give almost tight lower and upper bounds for the bounded error quantum query complexity of Connectivity, Strong Connectivity, Minimum Spanning Tree, and Single Source Shortest Paths. For example, we show that the query complexity of Minimum Spanning Tree is in $\Theta(n^{3/2})$ in the matrix model and in $\Theta(\sqrt{nm})$ in the array model, while the complexity of Connectivity is also in $\Theta(n^{3/2})$ in the matrix model but in $\Theta(n)$ in the array model. The upper bounds utilize search procedures for finding minima of functions under various conditions.
Source: SIAM Journal on Computing
DOI: 10.1137/050644719
Authors: Christoph Dürr, Mark Heiligman, Peter HOyer, Mehdi Mhalla
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2008231303