On the Quantum Query Complexity of All-Pairs Shortest Paths

Nongmeikapam Brajabidhu Singh, Joseph L. Pachuau, Anish Kumar Saha

Aniket Bembale, Nagendra Singh, P. Vinayaka +1 more

Aija Bērziņa, Andrej Dubrovsky, Rūsiņš Freivalds +2 more

Fuwei Cai, Satoshi Tayu, Shuichi Ueno

We show lower bounds for the quantum query complex-ity of the all-pairs shortest paths problem (APSP) for non-negatively weighted directed graphs (digraphs), both in the adjacency matrix model and in an adja-

Christoph Dürr, Mark Heiligman, Peter Høyer +1 more

Christoph Dürr, Mark Heiligman, Peter Høyer +1 more

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.