Related papers: No Infinite Tail Beats Optimal Spatial Search
Quantum walks have been useful for designing quantum algorithms that outperform their classical versions for a variety of search problems. Most of the papers, however, consider a search space containing a single marked element only. We show…
Recently the continuous time algorithm based on the generalized quantum search Hamiltonian was presented. In this letter, we consider the running time of the generalized quantum search Hamiltonian. We provide the surprising result that the…
We give a dimension independent formulation of the quantum search algorithm introduced in [L. K. Grover, Phys. Rev. Lett. {\bf 79}, 325 (1997)]. This algorithm provides a quadratic gain when compared to its classical counterpart by…
The "abstract search algorithm" is a well known quantum method to find a marked vertex in a graph. It has been applied with success to searching algorithms for the hypercube and the two-dimensional grid. In this work we provide an example…
The dynamic optimality conjecture, postulating the existence of an $O(1)$-competitive online algorithm for binary search trees (BSTs), is among the most fundamental open problems in dynamic data structures. Despite extensive work and some…
Previous studies of search in channel graphs has assumed that the search is global; that is, that the status of any link can be probed by the search algorithm at any time. We consider for the first time local search, for which only links to…
Grover's quantum search algorithm is considered as one of the milestone in the field of quantum computing. The algorithm can search for a single match in a database with $N$ records in $O(\sqrt{N})$ assuming that the item must exist in the…
Some of the quantum searching models have been given by perturbed quantum walks. Driving some perturbed quantum walks, we may quickly find one of the targets with high probability. In this paper, we construct a quantum searching model…
By a theorem of Volkov (2001) we know that on most graphs with positive probability the linearly vertex-reinforced random walk (VRRW) stays within a finite "trapping" subgraph at all large times. The question of whether this tail behavior…
This introduction to graphs and graph algebras provides the optimal bound for the number of all paths of length $k$ in a graph with $N\geq k$ edges and no loops. Our proof relies on a construction of a number of terminating algorithms that…
L. K. Grover's search algorithm in quantum computing gives an optimal, quadratic speedup in the search for a single object in a large unsorted database. In this paper, we generalize Grover's algorithm in a Hilbert-space framework for both…
We study the optimization of navigational graph queries, i.e., queries which combine recursive and pattern-matching fragments. Current approaches to their evaluation are not effective in practice. Towards addressing this, we present a…
We present several new results on one of the most extensively studied topics in computational geometry, orthogonal range searching. All our results are in the standard word RAM model for points in rank space: ** We present two data…
Path planning is an active area of research essential for many applications in robotics. Popular techniques include graph-based searches and sampling-based planners. These approaches are powerful but have limitations. This paper continues…
One of the significant breakthroughs in quantum computation is Grover's algorithm for unsorted database search. Recently, the applications of Grover's algorithm to solve global optimization problems have been demonstrated, where unknown…
Infinite graphs are finitary in the sense that their points are connected via finite paths. So what would an infinitary generalization of finite graphs look like? Usually this question is answered with the aid of topology, e.g. in the case…
We present a simple $O(n^4)$-time algorithm for computing optimal search trees with two-way comparisons. The only previous solution to this problem, by Anderson et al., has the same running time, but is significantly more complicated and is…
We investigate the behavior of coherence in scattering quantum walk search on complete graph under the condition that the total number of vertices of the graph is greatly larger than the marked number of vertices we are searching, $N \gg…
The classical linear search problem is studied from the view point of Hamiltonian dynamics. For the specific, yet representative case of exponentially distributed position of the hidden object, we show that the optimal plan follows an…
Moving an autonomous agent through an unknown environment is one of the crucial problems for robotics and network analysis. Therefore, it received a lot of attention in the last decades and was analyzed in many different settings. The graph…