Related papers: Spatial Search Algorithms on Hanoi Networks
We establish a lower bound concerning the computational complexity of Grover's algorithms on fractal networks. This bound provides general predictions for the quantum advantage gained for searching unstructured lists. It yields a…
Sparse optimization is a central problem in machine learning and computer vision. However, this problem is inherently NP-hard and thus difficult to solve in general. Combinatorial search methods find the global optimal solution but are…
Continuing the recent trend, in this article we design several space-efficient algorithms for two well-known graph search methods. Both these search methods share the same name {\it breadth-depth search} (henceforth {\sf BDS}), although…
Recent works put much effort into tensor network structure search (TN-SS), aiming to select suitable tensor network (TN) structures, involving the TN-ranks, formats, and so on, for the decomposition or learning tasks. In this paper, we…
Computing high-quality independent sets quickly is an important problem in combinatorial optimization. Several recent algorithms have shown that kernelization techniques can be used to find exact maximum independent sets in medium-sized…
Communities play a crucial role to describe and analyse modern networks. However, the size of those networks has grown tremendously with the increase of computational power and data storage. While various methods have been developed to…
We recast Grover's generalised search algorithm in a geometric language even when the states are not approximately orthogonal. We provide a possible search algorithm based on an arbitrary unitary transformation which can speed up the steps…
In this paper, we demonstrate our work on Gaussian Process Occupancy Mapping (GPOM). We concentrate on the inefficiency of the frame computation of the classical GPOM approaches. In robotics, most of the algorithms are required to run in…
Vertex hunting (VH) is the task of estimating a simplex from noisy data points and has many applications in areas such as network and text analysis. We introduce a new variant, semi-supervised vertex hunting (SSVH), in which partial…
This article presents a novel and succinct algorithmic framework via alternating quantum walks, unifying quantum spatial search, state transfer and uniform sampling on a large class of graphs. Using the framework, we can achieve exact…
One of the most important AI research questions is to trade off computation versus performance since ``perfect rationality" exists in theory but is impossible to achieve in practice. Recently, Monte-Carlo tree search (MCTS) has attracted…
This paper presents a parallel random-search method for reducing additive complexity in fast matrix multiplication algorithms with ternary coefficients $\{-1,0,1\}$. The approach replaces expensive exact evaluation with fast heuristic…
The quantum SearchRank algorithm is a promising tool for a future quantum search engine based on PageRank quantization. However, this algorithm loses its functionality when the $N/M$ ratio between the network size $N$ and the number of…
We present space-efficient parallel strategies for two fundamental combinatorial search problems, namely, backtrack search and branch-and-bound, both involving the visit of an $n$-node tree of height $h$ under the assumption that a node can…
The problem of finding a marked node in a graph can be solved by the spatial search algorithm based on continuous-time quantum walks (CTQW). However, this algorithm is known to run in optimal time only for a handful of graphs. In this work,…
Efficient Neural Architecture Search methods based on weight sharing have shown good promise in democratizing Neural Architecture Search for computer vision models. There is, however, an ongoing debate whether these efficient methods are…
In this paper we present a novel quantum algorithm, namely the quantum grid search algorithm, to solve a special search problem. Suppose $ k $ non-empty buckets are given, such that each bucket contains some marked and some unmarked items.…
We propose a new stochastic algorithm (generalized simulated annealing) for computationally finding the global minimum of a given (not necessarily convex) energy/cost function defined in a continuous D-dimensional space. This algorithm…
A decentralized search algorithm is a method of routing on a random graph that uses only limited, local, information about the realization of the graph. In some random graph models it is possible to define such algorithms which produce…
We analyze the performance of classical and quantum search algorithms from a thermodynamic perspective, focusing on resources such as time, energy, and memory size. We consider two examples that are relevant to post-quantum cryptography:…