Fibonacci Heap Research Articles

An Efficient Approach for Shortest Path Planning in Automotive Navigation System

Emerging automotive engineering solutions extensively rely on navigation tools. Shortest path evaluation is core competency of optimal path planning, one of the most critical component of any navigation application. Fibonacci heap variant of state-of-the-art Dijkstra’s algorithm solve single source shortest path problems in asymptotic O(E + V log V) worst-case time. In spite Fibonacci heap is theoretically dominant in time efficiency, it might not work much better empirically with real-world data, because although large and intricate, the real-world road network graphs are sparse and the graph topology greatly affects the performance of the algorithms. SGO algorithm, a more efficient approch to address single source shortest path problem, is applied to solve optimal path planning problem in automotive navigation applications. Each road segment of the road graph leads to a particular location thus will hold unique distance values all the time. The SGO calculates the total distance from start location to the end of the each road segment and evaluates shortest path based on these calculations. The SGO algorithm and the Fibonacci and Binary heap variants of Dijkstra’s algorithm were tested on real-world intercity and intra-city road network graphs to evaluate running time efficiency of the algorithms in automotive navigation systems. The experimental results show that the SGO algorithm outperformed both the variants. The empirical superiority of the SGO algorithm suggests its usefulness in automotive navigation systems.

Linear-algebraic implementation of Fibonacci heap

Linear-algebraic implementation of Fibonacci heap

Shielding Graph for eXact Analytics With SGX

Graphs nicely capture data from various domains, allowing the computations of many analytic tasks via graph queries. Graphs of real-world data are often large, albeit useful, and the involved computation can be too heavyweight for commodity computers. For secure outsourcing, we propose (SGX) <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$^{2}$</tex-math></inline-formula> , a forward-secure structured encryption scheme for graph data, which uses lightweight cryptographic techniques with a trusted execution environment such as SGX. To process million-scale graphs by the limited memory of SGX, we load data on-demand using Dijkstra's algorithm and Fibonacci heap. Compared with most prior graph encryption schemes, (SGX) <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$^{2}$</tex-math></inline-formula> supports exact shortest-distance queries instead of approximation and can be easily extended to other graph-based analytics. Finally, we discuss some generic enhancements addressing active adversaries trying to exploit leakages originating from SGX.

Task Scheduling in Cloud Computing: A Priority-Based Heuristic Approach

In this paper, a task scheduling problem for a cloud computing environment is formulated by using the M/M/n queuing model. A priority assignment algorithm is designed to employ a new data structure named the waiting time matrix to assign priority to individual tasks upon arrival. In addition to this, the waiting queue implements a unique concept based on the principle of the Fibonacci heap for extracting the task with the highest priority. This work introduces a parallel algorithm for task scheduling in which the priority assignment to task and building of heap is executed in parallel with respect to the non-preemptive and preemptive nature of tasks. The proposed work is illustrated in a step-by-step manner with an appropriate number of tasks. The performance of the proposed model is compared in terms of overall waiting time and CPU time against some existing techniques like BATS, IDEA, and BATS+BAR to determine the efficacy of our proposed algorithms. Additionally, three distinct scenarios have been considered to demonstrate the competency of the task scheduling method in handling tasks with different priorities. Furthermore, the task scheduling algorithm is also applied in a dynamic cloud computing environment.

Application of Fibonacci heap to fast marching method

Abstract The fast marching method (FMM) is an efficient, stable and adaptable travel time calculation method. In the realization of this method, it is necessary to select the minimum travel time node from the narrow band many times. The selection method has an important influence on the calculation efficiency of FMM. Traditional FMM adopts the binary tree heap sorting method to achieve this step. Fibonacci heap sort method to FMM will be applied in this study. Compared with the binary tree heap sorting method, the Fibonacci heap sort method can realize the minimum travel time node selection in the narrow band in a more efficient way when the number of the narrow-band nodes is huge. The new method will be verified through error analysis and two numerical model calculations.

Proposal of Fibonacci Heap in the Dijkstra Algorithm for Low-power Ad-hoc Mobile Transmissions

Mobile devices have become indispensable to communication over the last decade. In a hypothetical scenario in which conventional forms of connection such as antennas and satellites are not available, other forms of information propagation must be used. Ad-hoc broadcasts are strategies for maintaining communication between devices in these situations, however, they require high transmission power. This article proposes the use of priority queues, such as the Fibonacci heap and the binary heap in the Dijkstra algorithm, in order to reduce its computational cost in the search for the smallest network route. From the limitation of the signal strength to reach the nearest device, our results obtained lower transmission power compared to the standard device settings. Simulations show that a fibonacci heap has higher performance than binary heap in networks with higher number of connections. This way, the implementation of the fibonacci heap brings improvements in the computational cost of the algorithm. In addition, we show that the calculation of the smallest route is directly connected to the choice of the path with the lowest transmission power.

An effective scheduling strategy based on hypergraph partition in geographically distributed datacenters

As the complexity of workflow applications increase, the scheduling and execution of workflow incur more waste of resources. In order to achieve load balancing and reduce the task execution time in the cloud system, an effective scheduling strategy based on hypergraph partition for workflow application in the geographically distributed datacenters is proposed. Firstly, a workflow job scheduling algorithm is proposed, which aims to reduce the response time and considers the cloud state. Besides, the task scheduling algorithm based on the hypergraph partition is designed with the goal of reducing the completion time and energy consumption for the tasks. In addition, the optimal task scheduling strategy can be obtained according to the Dijkstra shortest path algorithm based on Fibonacci heap. Finally, in the experiment, the workflow task scheduling algorithm can optimize the task execution performance and maintain the load balance of the computing nodes in each cloud, so that the average execution time of the tasks and the total energy consumption of the system are minimized.

A Fibonacci Heap Based Ensemble Model for Stock Price Prediction

The prediction of stock price with high accuracy and consistency is a major challenge. A lot of research has been done to predict the stock price. However, there is a scope of improvement in accuracy and consistency of the prediction. This article proposes a Fibonacci heap based ensemble model that predicts the closing price of a stock for the next trading day. The proposed model is a combination of different (time series and regression) models. The model computes the median of significant prediction models that are organized in a Fibonacci heap data structure. The performance of this model is tested with the datasets of well-known eleven stocks. The results prove the effectiveness of the proposed model over other traditional prediction models with respect to consistency and accuracy

Fast Methods for Eikonal Equations: An Experimental Survey

Fast methods are very popular algorithms to compute time-of-arrival maps (distance maps measured in time units) solving the Eikonal equation. Since fast marching was proposed in 1995, it has been applied to many different applications, such as robotics, medical computer vision, fluid simulation, and so on. From then on, many alternatives to the original method have been proposed with two main objectives: reducing its computational time and improving its accuracy. In this paper, we collect the main single-threaded approaches, which improve the computational time of the standard fast marching method and study them within a common mathematical framework. Then, they are evaluated using isotropic environments, which are representative of their possible applications. The studied methods are the fast marching method with the binary heap, the fast marching method with Fibonacci heap, the simplified fast marching method, the untidy fast marching method, the fast iterative method, the group marching method, the fast sweeping method, the locking sweeping method, and the double dynamic queue method.

Dynamically Reconstructing Minimum Spanning Trees After Swapping Pairwise Vertices

The minimum spanning tree (MST) problem is a fundamental problem in computer science and operations research, which has many real-life network design applications. Given a graph $G$ with $n$ vertices and $m$ edges, starting from an MST (denoted by $T$ ) covering a subgraph of $G$ , it is usually needed to reconstruct a new MST after swapping two vertices $v\in T$ and $v' \notin T$ . For this purpose, the most popular choice is to reconstruct an MST from scratch, for which the current fastest algorithm (Kruskal’s algorithm based on Fibonacci heap) requires a time complexity of $O(m+n\cdot \log n)$ , implying that a high time complexity of $O(n^{2})\cdot O(m+n\cdot \log n)$ is needed to evaluate all the $O(n^{2})$ possible swapping-based moves. In order to evaluate these moves more efficiently, we integrate a series of dynamic techniques to develop a fast dynamic swap-vertex move operator, which significantly reduces the overall time complexity from $O(n^{2})\cdot O(m+n\cdot \log n)$ to $O(n)\cdot O(m\cdot \log n)$ . We also strictly prove the correctness of the introduced method. Finally, we choose three well-studied Steiner/spanning tree problems as our test bed and carry out extensive experiments on 140 representative instances to show the effectiveness and efficiency of the proposed method. More importantly, as a general-purpose method, the dynamic swap-vertex move operator could be easily adapted to many other tree-related problems.

Quantum Algorithm for Shortest Path Search in Directed Acyclic Graph

In this work, we consider a well-known “Single Source Shortest Path Search” problems for weighted directed acyclic graphs (DAGs). We suggest a quantum algorithm with time complexity $O(\sqrt {nm} \,\log \;n)$ and O(1/n) error probability, where n is a number of Vertexes, m is the number of edges. We use quantum dynamic programming approach (Khadiev, 2018) and Durr and Hoyer minimum search algorithm to speed up our search. Our algorithm is better than C. Durr and coauthors’ quantum algorithm for an undirected graph. The time complexity of C. Durr’s algorithm is $O(\sqrt {nm} \,{(\log \;n)^2})$ . The best known deterministic algorithm for the problem is based on a dynamic programming approach and its time complexity is O (n + m). At the same time, if we use algorithms for general graphs, then we do not get better results. The time complexity of best implementations of Dijkstra’s algorithm with Fibonacci heap is O (m + n log n).

A Fibonacci Heap Based Ensemble Model for Stock Price Prediction

A Fibonacci Heap Based Ensemble Model for Stock Price Prediction

Hollow Heaps

We introduce the hollow heap , a very simple data structure with the same amortized efficiency as the classical Fibonacci heap. All heap operations except delete and delete - min take O (1) time, worst case as well as amortized; delete and delete - min take O (log n ) amortized time on a heap of n items. Hollow heaps are the simplest structure to achieve these bounds. Hollow heaps combine two novel ideas: the use of lazy deletion and re-insertion to do decrease - key operations and the use of a dag (directed acyclic graph) instead of a tree or set of trees to represent a heap. Lazy deletion produces hollow nodes (nodes without items), giving the data structure its name.

An improved Isomap method for manifold learning

PurposeIsometric feature mapping (Isomap) is a very popular manifold learning method and is widely used in dimensionality reduction and data visualization. The most time-consuming step in Isomap is to compute the shortest paths between all pairs of data points based on a neighbourhood graph. The classical Isomap (C-Isomap) is very slow, due to the use of Floyd’s algorithm to compute the shortest paths. The purpose of this paper is to speed up Isomap.Design/methodology/approachThrough theoretical analysis, it is found that the neighbourhood graph in Isomap is sparse. In this case, the Dijkstra’s algorithm with Fibonacci heap (Fib-Dij) is faster than Floyd’s algorithm. In this paper, an improved Isomap method based on Fib-Dij is proposed. By using Fib-Dij to replace Floyd’s algorithm, an improved Isomap method is presented in this paper.FindingsUsing the S-curve, the Swiss-roll, the Frey face database, the mixed national institute of standards and technology database of handwritten digits and a face image database, the performance of the proposed method is compared with C-Isomap, showing the consistency with C-Isomap and marked improvements in terms of the high speed. Simulations also demonstrate that Fib-Dij reduces the computation time of the shortest paths from O(N3) to O(N2lgN).Research limitations/implicationsDue to the limitations of the computer, the sizes of the data sets in this paper are all smaller than 3,000. Therefore, researchers are encouraged to test the proposed algorithm on larger data sets.Originality/valueThe new method based on Fib-Dij can greatly improve the speed of Isomap.

An evolutionary local search for the capacitated vehicle routing problem minimizing fuel consumption under three-dimensional loading constraints

This study introduces a new practical variant of the combined routing and loading problem called the capacitated vehicle routing problem minimizing fuel consumption under three-dimensional loading constraints (3L-FCVRP). It presents a meta-heuristic algorithm for solving the problem. The aim is to design routes for a fleet of homogeneous vehicles that will serve all customers, whose demands are formed by a set of three-dimensional, rectangular, weighted items. Unlike the well-studied capacitated vehicle routing problem with 3D loading constraints (3L-CVRP), the objective of the 3L-FCVRP is to minimize total fuel consumption rather than travel distance. The fuel consumption rate is assumed to be proportionate to the total weight of the vehicle. A route is feasible only if a feasible loading plan to load the demanded items into the vehicle exists and the loading plan must satisfy a set of practical constraints.To solve this problem, the evolutionary local search (ELS) framework incorporating the recombination method is used to explore the solution space, and a new heuristic based on open space is used to examine the feasibility of the solutions. In addition, two special data structures, Trie and Fibonacci heap, are adopted to speed up the procedure. To verify the effectiveness of our approach, we first test the ELS on the 3L-CVRP, which can be seen as a special case of the 3L-FCVRP. The results demonstrate that on average ELS outperforms all of the existing approaches and improves the best-known solutions for most instances. Then, we generate data for 3L-FCVRP and report the detailed results of the ELS for future comparisons.

An Adaptive Variable Neighborhood Search for a Heterogeneous Fleet Vehicle Routing Problem with Three-Dimensional Loading Constraints

The paper addresses the heterogeneous fleet vehicle routing problem with three-dimensional (3D) loading constraints (3L-HFVRP), a new practical variant of the combined routing and loading problem. In this problem, the loads consist of a set of three-dimensional, rectangular shaped items. The fleet is composed of heterogeneous vehicles with different weight and space capacities. The objective is to serve all customers by selecting a set of vehicles such that the total transportation cost is minimized. The cost consists of the fixed cost of the selected vehicles and their travel cost. In addition, loading sequence related constraints frequently encountered in realistic applications are respected when loading and unloading the items. To solve this challenging problem, we develop an adaptive variable neighborhood search (AVNS) which utilizes an extreme point based first fit heuristic to find a feasible loading pattern for each route. We design two strategies to accelerate the loading and routing processes. The Trie data structure is used to record the loading information of routes already visited and to control the computational effort spent for each route. The Fibonacci heap data structure is used to maintain all of the possible moves and vehicle type assignments, which avoids the duplicated evaluation of some moves and unnecessary loading check of unpromising solutions. The robustness and effectiveness of the proposed algorithm is validated by computational tests performed both on some newly generated 3L-HFVRP instances and well-known benchmark instances from the literature for two simplified VRP variants: the capacitated vehicle routing problem with 3D loading constraints (3L-CVRP) and the pure heterogeneous fleet vehicle routing problem (HFVRP). The numerical experiments show that the proposed AVNS outperforms other algorithms in 3L-CVRP and improves several best known solutions reported in the literature. The results obtained for the pure HFVRP are very close to the best known solutions.

Teknologi Location Based Service (Global Positioning System) Pada Perangkat Mobile

Article presents analysis and design of software using Location Based Service (LBS) that is part of communication technology based on geographic position. The goal of the research is designing LBS application to be implemented on mobile device that has GPS (Global Positioning System) technology and uses GPRS (General Packet Radio Service) to connect to server for generating shortest path by Dijkstra algorithm method Fibonacci Heap. Software development method used is LBS application implemented on mobile device. Conclusion of the research has shown that shortest path generated using Dijkstra algorithm method Fibonacci Heap as single source shortest path is faster than Dijkstra algorithm and Bellman Ford.

Thin heaps, thick heaps

The Fibonacci heap was devised to provide an especially efficient implementation of Dijkstra's shortest path algorithm. Although asyptotically efficient, it is not as fast in practice as other heap implementations. Expanding on ideas of Høyer [1995], we describe three heap implementations (two versions of thin heaps and one of thick heaps ) that have the same amortized efficiency as Fibonacci heaps, but need less space and promise better practical performance. As part of our development, we fill in a gap in Høyer's analysis.

An improved Dijkstra’s shortest path algorithm for sparse network

On a network with nonnegative-length edges, Dijkstra’s shortest path algorithm computes single-source shortest path in O( m + n log n) time. The time bound assumes that a Fibonacci heap is used during the implementation of Dijkstra’s algorithm. As the process of building heaps needs a little complex work, it makes the algorithm not easy to be used. In this paper, we make some very simple, but useful, changes in the original Dijkstra algorithm and obtain a new improved Dijkstra’s shortest path algorithm that avoids the process of building heap and runs in O( m + D max log( n!)) time. Here m, n and D max are the number of edges, vertices and the maximal number of edges incident with vertex, respectively. Thus, the new algorithm is very competitive for those sparse networks especially in road traffic networks in which D max is often a small number.

배열 표현을 이용한 M-힙에서 삽입/삭제 알고리즘

스케줄링, 정렬, 및 최단 거리 계산 네트워크 문제 등과 같은 응용에 이용될 수 있는 우선 순위 큐 중, 피보나치 힙, 페어링 힙, 및 M-힙은 포인터를 이용하는 자료 구조이다. 본 논문에서는 [1]에서 문제점으로 남겨두었던 M-힙을 배열을 이용하여 표현한 MA-힙(M-heap with an array representation)를 제안한다. MA-힙은 M-힙과 동일한 시간 복잡도인 O(1) 삽입 전이 시간과 O(logn) 삭제 시간 복잡도를 가지며, 단순한 전통적인 힙에 근거하고 있기 때문에 [5]에서 제안된 힙보다 구현이 매우 용이하다. Priority queues can be used in applications such as scheduling, sorting, and shortest path network problem. Fibonacci heap, pairing heap, and M-heap are priority queues based on pointers. This paper proposes a modified M-heap with an way representation, called MA-heap, that resolves the problem mentioned in [1]. The MA-heap takes O(1) amortized time and O(logn) time to insert an element and delete the max/min element, respectively. These time complexities are the same as those of the M-heap. In addition, it is much easier to implement an MA-heap than a heap proposed in [5] since it is based on the simple traditional heap.