arXiv subjects
Publications and source records attributed to A. S. Gupta.
Classical Floyd-Warshall algorithm is used to solve all-pairs shortest path problem on a directed graph. The classical algorithm runs in \mathcal{O} (V^{3}) time where V represents the number of nodes. Here we have modified the algorithm and proposed a quantum algorithm analogous to Floyd-Warshall algorithm which exploits the superposition principle and runs in \mathcal{O} (Vlog_{2}V) time.
The present letter proposes a modification in the well known Grover's search algorithm, which searches a database of $N$ unsorted items in $O(\sqrt{N/M})$ steps, where $M$ represents the number of solutions to the search problem. Concurrency control techniques and extra registers for marking and storing the solutions are used in the modified algorithm. This requires additional space but it is shown that the use of extra register and marking techniques can reduce the time complexity to $O(M+\log N)$.
Grover's search algorithm searches a database of $N$ unsorted items in $O(\sqrt{N/M})$ steps where $M$ represents the number of solutions to the search problem. This paper proposes a scheme for searching a database of $N$ unsorted items in $O(logN)$ steps, provided the value of $M$ is known. It is also shown that when $M$ is unknown but if we can estimate an upper bound of possible values of $M$, then an improvement in the time complexity of conventional Grover's algorithm is possible. In that case, the present scheme reduces the time complexity to $O(MlogN)$.