Random Walk Search Algorithm Research Articles

Semi-empirical method for evaluating the robustness of QRWS algorithm for different coin sizes and functional dependence between coin phases

In this work we study the quantum random walk search algorithm when the walk coin is constructed by generalized Householder reflection and a phase multiplier. We focus on the algorithm’s robustness against errors in the phases – how the probability to find solution decreases with increasing the errors in those phases. The robustness depends on the functional dependence between the reflection phase φ and the phase multiplier ζ. Here we use interpolations by non-linear logistic regression functions to study a particular functional dependence between angles ζ = -2φ + 3π + α sin(2φ) for different coin sizes and parameters alpha. The obtained results in this work are discussed, together with their limitations.

Optimizing the walk coin in the quantum random walk search algorithm

This paper examines quantum random walk search algorithm with walk coin constructed by generalized Householder reflection and additional phase shift factor. The results from numerical simulations with neural network show that, with such a construction of the walk coin, the algorithm is more robust to inaccuracies in the specific values of its parameters, as long as it is possible to control the phase difference between the phase shift factor and the phase involved in the Householder reflection. This paper explicitly shows how achieving a properly designed phase difference would make quantum random walk search on a hypercube more robust for coin register consisting of one, two and three qubits.

A Machine Learning Study of High Robustness Quantum Walk Search Algorithm with Qudit Householder Coins

In this work, the quantum random walk search algorithm with a walk coin constructed by generalized Householder reflection and phase multiplier has been studied. The coin register is one qudit with an arbitrary dimension. Monte Carlo simulations, in combination with supervised machine learning, are used to find walk coins that make the quantum algorithm more robust to deviations in the coin’s parameters. This is achieved by introducing functional dependence between these parameters. The functions that give the best performance of the algorithm are studied in detail by numerical statistical methods. A thorough comparison between our modification and an algorithm, with coins made using only Householder reflection, shows significant advantages of the former. By applying a deep neural network, we make a prediction for the parameters of an optimal coin with an arbitrary size and estimate the algorithm’s stability for such a coin.

Reducing number of gates in quantum random walk search algorithm via modification of coin operators

This paper examines a way to simplify the circuit of quantum random walk search algorithm, when the traversing coin is constructed by both generalized Householder reflection and an additional phase multiplier. If an appropriate relation between corresponding parameters is realized, our algorithm becomes more robust to deviations in the phases. In this modification marking coin is not needed, and all advantages from above mentioned optimization to the stability, are preserved. It is shown explicitly how to construct such walk coin in order to obtain more robust quantum algorithm.

A Theoretical Framework for Studying Random Walk Planning

Random walks are a relatively new component used in several state of the art satisficing planners. Empirical results have been mixed: while the approach clearly outperforms more systematic search methods such as weighted A* on many planning domains, it fails in many others. So far, the explanations for these empirical results have been somewhat ad hoc. This paper proposes a formal framework for comparing the performance of random walk and systematic search methods. Fair homogenous graphs are proposed as a graph class that represents characteristics of the state space of prototypical planning domains, and is simple enough to allow a theoretical analysis of the performance of both random walk and systematic search algorithms. This gives well-founded insights into the relative strength and weaknesses of these approaches. The close relation of the models to some well-known planning domains is shown through simplified but semi-realistic planning domains that fulfill the constraints of the models. One main result is that in contrast to systematic search methods, for which the branching factor plays a decisive role, the performance of random walk methods is determined to a large degree by the Regress Factor, the ratio between the probabilities of progressing towards and regressing away from a goal with an action. The performance of random walk and systematic search methods can be compared by considering both branching and regress factors of a state space.

Mean Shift Cluster Recognition Method Implementation in the Nested Sampling Algorithm.

Nested sampling is an efficient algorithm for the calculation of the Bayesian evidence and posterior parameter probability distributions. It is based on the step-by-step exploration of the parameter space by Monte Carlo sampling with a series of values sets called live points that evolve towards the region of interest, i.e., where the likelihood function is maximal. In presence of several local likelihood maxima, the algorithm converges with difficulty. Some systematic errors can also be introduced by unexplored parameter volume regions. In order to avoid this, different methods are proposed in the literature for an efficient search of new live points, even in presence of local maxima. Here we present a new solution based on the mean shift cluster recognition method implemented in a random walk search algorithm. The clustering recognition is integrated within the Bayesian analysis program NestedFit. It is tested with the analysis of some difficult cases. Compared to the analysis results without cluster recognition, the computation time is considerably reduced. At the same time, the entire parameter space is efficiently explored, which translates into a smaller uncertainty of the extracted value of the Bayesian evidence.

Sustainability Assessment of Constructive Solutions for Urban Spain: A Multi-Objective Combinatorial Optimization Problem

Industrial areas are set up on plots of roads and associated infrastructure. These use materials and machinery that have environmental impacts, and thus require constructive solutions throughout their lifecycles. In turn, these solutions and their components cause environmental impacts that can be measured by sustainability indicators. The concept of sustainability is closely tied to sustainable development, which is defined as “development that meets the needs of the present, without compromising the ability of future generations to meet their own needs”. The large number of possible and available solutions means that identifying the best one for a given road section must employ a set of heuristic techniques, which conceptualize the issue as a combinatorial optimization problem that is purely discrete and non-differential. The system chosen can be based on a genetic algorithm method that differentiates individuals based on three sustainability indicators: CO2 emissions, embedded energy (also known as embodied energy, defined as the energy expended to manufacture a product), and economic cost. In this paper, we supplement traditional cost analyses using a three-objective multi-objective genetic algorithm that considers the aforementioned criteria, thus addressing sustainability in aggregate planning. The procedure is applied to three objective functions—CO2 emissions, economic cost and embedded energy—for each possible solution. We used the non-dominated sorting genetic algorithm (NSGA-II) to implement multi-objective optimization in MATLAB. Additional results for a random walk and multi-objective search algorithm are shown. This study involved 26 design variables, with different ranks of variation, and the application of the algorithm generates results for the defined Pareto fronts. Our method shows that the optimal approach effectively solves a real-world multi-objective project planning problem, as our solution is one of the Pareto-optimal solutions generated by the NSGA-II.

Development of Unstructured Architecture for Voice and Data Services in Mobile Communication

The huge popularity of voice and data services in mobile communication facilitates ubiquitous infrastructure that has been mainly driven by the scalability of their architectures and the flexibility of their search facilities. Such systems are usually designed as unstructured point-to-point networks and support highly versatile search algorithms.Developing search algorithms is difficult in unstructured peer-to-peer networks. Flooding and Random Walk are two typical search algorithms. Flooding covers most of the nodes by searching randomly. In the unstructured network peers are interconnected randomly, they rely on Flooding query messages to discover objects of interest. It generates a large amount of query messages which produces network traffic. Random walk search algorithms are used in mobile networks because of their dynamic nature. But it only generates a fixed amount of query messages at each peer but would take longer search time. Thus we propose development of unstructured architecture for voice and data services in mobile communication. In this architecture we are focusing on interconnection of various mobile devices. One way is to improve the algorithm for selecting path, second way to modify the routing algorithm by considering new characteristics for less signaling overhead.

Optimized quantum random-walk search algorithm for multi-solution search**Project supported by the National Basic Research Program of China (Grant No. 2013CB338002).

This study investigates the multi-solution search of the optimized quantum random-walk search algorithm on the hypercube. Through generalizing the abstract search algorithm which is a general tool for analyzing the search on the graph to the multi-solution case, it can be applied to analyze the multi-solution case of quantum random-walk search on the graph directly. Thus, the computational complexity of the optimized quantum random-walk search algorithm for the multi-solution search is obtained. Through numerical simulations and analysis, we obtain a critical value of the proportion of solutions q. For a given q, we derive the relationship between the success rate of the algorithm and the number of iterations when q is no longer than the critical value.

Decoherence in optimized quantum random-walk search algorithm**Project supported by the National Basic Research Program of China (Grant No. 2013CB338002).

This paper investigates the effects of decoherence generated by broken-link-type noise in the hypercube on an optimized quantum random-walk search algorithm. When the hypercube occurs with random broken links, the optimized quantum random-walk search algorithm with decoherence is depicted through defining the shift operator which includes the possibility of broken links. For a given database size, we obtain the maximum success rate of the algorithm and the required number of iterations through numerical simulations and analysis when the algorithm is in the presence of decoherence. Then the computational complexity of the algorithm with decoherence is obtained. The results show that the ultimate effect of broken-link-type decoherence on the optimized quantum random-walk search algorithm is negative.

Effects of systematic phase errors on optimized quantum random-walk search algorithm**Project supported by the National Basic Research Program of China (Grant No. 2013CB338002).

This study investigates the effects of systematic errors in phase inversions on the success rate and number of iterations in the optimized quantum random-walk search algorithm. Using the geometric description of this algorithm, a model of the algorithm with phase errors is established, and the relationship between the success rate of the algorithm, the database size, the number of iterations, and the phase error is determined. For a given database size, we obtain both the maximum success rate of the algorithm and the required number of iterations when phase errors are present in the algorithm. Analyses and numerical simulations show that the optimized quantum random-walk search algorithm is more robust against phase errors than Grover’s algorithm.

Alternative Coins for Quantum Random Walk Search Optimized for a Hypercube

The present paper is focused on non-uniform quantum coins for the quantum random walk search algorithm. This is an alternative to the modification of the shift operator, which divides the search space into two parts. This method changes the quantum coins, while the shift operator remains unchanged and sustains the hypercube topology. The results discussed in this paper are obtained by both theoretical calculations and numerical simulations.

Towards a theory of random walk planning: Regress factors, fair homogeneous graphs and extensions

Random walks are a relatively new component used in several state of the art satisficing planners. Empirical results have been mixed: while the approach clearly outperforms more systematic search methods such as weighted A* on many planning domains, it fails in many others. So far, the explanations for these empirical results have been somewhat ad hoc. This paper proposes a formal framework for comparing the performance of random walk and systematic search methods. Fair homogenous and Infinitely Regressable homogenous graphs are proposed as graph classes that represents characteristics of the state space of prototypical planning domains, and is simple enough to allow a theoretical analysis of the performance of both random walk and systematic search algorithms. This gives well-founded insights into the relative strength and weaknesses of these approaches. The close relation of the models to some well-known planning domains is shown through simplified but semi-realistic planning domains that fulfill the constraints of the models. One main result is that in contrast to systematic search methods, for which the branching factor plays a decisive role, the performance of random walk methods is determined to a large degree by the Regress Factor, the ratio between the probabilities of progressing towards and regressing away from a goal with an action. The performance of random walk and systematic search methods can be compared by considering both branching and regress factors of a state space.

An efficient and distributed file search in unstructured peer-to-peer networks

Peer-to-peer (P2P) networks are gaining increased attention from both the scientific community and the larger Internet user community. Data retrieval algorithms lie at the center of P2P networks, and this paper addresses the problem of efficiently searching for files in unstructured P2P systems. We propose an Improved Adaptive Probabilistic Search (IAPS) algorithm that is fully distributed and bandwidth efficient. IAPS uses ant-colony optimization and takes file types into consideration in order to search for file container nodes with a high probability of success. We have performed extensive simulations to study the performance of IAPS, and we compare it with the Random Walk and Adaptive Probabilistic Search algorithms. Our experimental results show that IAPS achieves high success rates, high response rates, and significant message reduction.

Autotuning a Random Walk Boolean Satisfiability Solver

Abstract In this paper we present a performance optimization case study for a kernel with dynamic data structures, few instructions on boolean variables per node, and data-dependent control flow. This kernel serves as model for wide class of important algorithms operating on dynamic data structures. Our example is a simple random walk search algorithm to solve boolean satisfiability (SAT) and our goal is to gain better understanding on how such a kernel must be optimized, not to build a better SAT solver. We start from a very compact, reasonable C++ implementation using the STL vector class, and arrive at a fully optimized, parallelized, vectorized C implementation in which we use algorithm-level optimization, data structure and layout optimization, and program generation and autotuning. We evaluate our example on a 2.66 GHz quad-core Core2 Extreme in 32-bit mode and a 3 GHz dual-core Xeon 5160 in 64-bit mode. On the Core2 Extreme quad-core processor for L1 resident synthetic benchmarks, the final version achieves up to 47% of machine peak (240 useful logical operations per cycle) and the realistic benchmarks 60–230 operations/cycle. The baseline C++ STL implementation requires between 7 and 50 cycles per useful logical operation for the synthetic benchmark; this translates into about 1,700–12,000x performance gain.

Reliable Resource Search in Scale Free Peer-to-Peer Network

The resource distribution and peer links in P2P network have an obvious scale free character follows power law distribution . Using this inherent character of P2P network to design resource search strategy is great significant for improving the search efficiency and reducing the costs. We analyze the scale free character in P2P network, and propose the reliable random walk search algorithm which can achieve high and reliable resource search through transferring query messages based on P2P power law distribution. We design simulation experiments to evaluate the performance of our reliable random walk. The simulation experimental results show that the reliable random walk based on power law distribution is a scalable resource search algorithm with high and reliable search efficiency and low search costs.

Limited Scale-Free Overlay Topologies for Unstructured Peer-to-Peer Networks

In unstructured peer-to-peer (P2P) networks, the overlay topology (or connectivity graph) among peers is a crucial component in addition to the peer/data organization and search. Topological characteristics have profound impact on the efficiency of a search on such unstructured P2P networks, as well as other networks. A key limitation of scale-free (power-law) topologies is the high load (i.e., high degree) on a very few number of hub nodes. In a typical unstructured P2P network, peers are not willing to maintain high degrees/loads as they may not want to store a large number of entries for construction of the overlay topology. Therefore, to achieve fairness and practicality among all peers, hard cutoffs on the number of entries are imposed by the individual peers, which limits scale-freeness of the overall topology, hence limited scale-free networks. Thus, it is expected that the efficiency of the flooding search reduces as the size of the hard cutoff does. We investigate the construction of scale-free topologies with hard cutoffs (i.e., there are not any major hubs) and the effect of these hard cutoffs on the search efficiency. Interestingly, we observe that the efficiency of normalized flooding and random walk search algorithms increases as the hard cutoff decreases.

Optimized quantum random-walk search algorithms on the hypercube

Shenvi, Kempe, and Whaley's quantum random-walk search (SKW) algorithm [Phys. Rev. A 67, 052307 (2003)] is known to require $O(\sqrt{N})$ number of oracle queries to find the marked element, where $N$ is the size of the search space. The overall time complexity of the SKW algorithm differs from the best achievable on a quantum computer only by a constant factor. We present improvements to the SKW algorithm which yield a significant increase in success probability, and an improvement on query complexity such that the theoretical limit of a search algorithm succeeding with probability close to one is reached. We point out which improvement can be applied if there is more than one marked element to find.

Energy-efficient search for finite-lifetime resources in sensor networks with time-constrained queries

We examine the performance of a random-walk search algorithm for wireless sensor networks when resources are subject to limited lifetimes and queries are constrained by application-specific deadlines. Specifically, via the time-to-live and transmission range parameters, we estimate the appropriate number of resource copies that must be created within the network to minimize the total node arrival rate (the energy-centric approach) or to ensure the total proportion of queries failures does not exceed a specified threshold (the failure-centric approach). The effect of node transmission range on network performance is also investigated. We compare the results of our network simulations to our queueing-based analytic node model and find that there is an inverse relationship between transmission range and the time-to-live value required to minimize the total node arrival rate.

Optimizing random walk search algorithms in P2P networks

In this paper we develop a model for random walk-based search mechanisms in unstructured P2P networks. This model is used to obtain analytical expressions for the performance metrics of random walk search in terms of the popularity of the resource being searched for and the random walk parameters. We propose an equation-based adaptive search mechanism that uses an estimate of the popularity of a resource in order to choose the parameters of random walk such that a targeted performance level is achieved by the search. We also propose a low-overhead method for maintaining an estimate of popularity that utilizes feedback (or lack there-off) obtained from previous searches. Simulation results show that the performance of the equation-based adaptive search is significantly better than the non-adaptive random walk and other straight-forward adaptive mechanisms.