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Clifford algebra method for network expression, computation, and algorithm construction

MATHEMATICAL METHODS IN THE APPLIED SCIENCES 2014年第10期37卷 1428-1435页

作者： Yuan, Linwang Yu, Zhaoyuan Luo, Wen Zhang, Jiyi Hu, Yong Nanjing Normal Univ Minist Educ Key Lab Virtual Geog Environm Nanjing 210046 Jiangsu Peoples R China Nanjing Normal Univ Jiangsu Prov Key Lab Numer Simulat Large Scale Co Nanjing 210046 Jiangsu Peoples R China Nanjing Normal Univ Dept Comp Sci & Technol Nanjing 210046 Jiangsu Peoples R China

Clifford algebra is introduced as a theoretical foundation for network topology expression and algorithm construction. Network nodes are coded with basis vectors in a vector space Rn, and the edges and k-walk routes can be expressed by 2-blades and k-blades, respectively, in the Clifford algebra Cl(n,0). The topologies among nodes, edges, and routes of networks can be directly calculated, and the network routes can be extended and traversed with oriented join products. The network algorithm construction processes based on Clifford algebra are instantiated by the single source shortest path algorithm. The experimental results on different scale random networks suggest that Clifford algebra is suited for network expression and relation computation. The Clifford algebra-based shortest path algorithm is vivid and clear in geometric meaning and has great advantage on temporal and spatial complexity. Copyright (c) 2013 John Wiley & Sons, Ltd.

关键词： Clifford algebra algorithm construction network analysis shortest path algorithm

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Modeling costs of turns in route planning

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GEOINFORMATICA 2002年第4期6卷 345-361页

作者： Winter, S Vienna Tech Univ Inst Geoinformat A-1040 Vienna Austria

In this paper a model that handles costs of turns in route planning is defined, investigated and discussed. Costs are traditionally attached to edges in a graph. For some important route planning problems other costs can be identified, namely costs that appear when leaving one edge and entering the next. Examples are turn restrictions, the turning angle, or the simple necessity to turn. Such costs cannot be stored as attributes of nodes or edges in the graph, and they cannot be handled correctly by shortest path algorithms without modifications. Turn costs can be represented by a pseudo-dual graph in a way that shortest path algorithms run without modifications. Although the idea is not new, it has not found much interest in the literature. The pseudo-dual graph is defined here in a new way, it is systematically investigated, and some practical applications are shown. Concentrating strictly on topology, it turns out that the pseudo-dual graph is conceptually cleaner and more efficient in route planning than alternative, currently used ways to deal with turn costs. The discussed applications are from the field of pedestrian navigation, which gave rise to this research.

关键词： shortest path algorithm turn costs turn restrictions route planning pedestrian navigation location-based services

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An integrated multi-objective model to determine the optimal rescue path and traffic controlled arcs for disaster relief operations under uncertainty environments

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JOURNAL OF ADVANCED TRANSPORTATION 2008年第4期42卷 493-519页

作者： Chiou, Yu-Chiun Lai, Yu-Hsuan Natl Chiao Tung Univ Inst Traff & Transportat Taipei Taiwan

This study proposes an integrated multi-objective model to determine the optimal rescue path and traffic controlled arcs for disaster relief operations under uncertainty environments. The model consists of three sub-models: rescue shortest path model, post-disaster traffic assignment model, and traffic controlled arcs selection model to minimize four objectives: travel time of rescue path, total detour travel time, number of unconnected trips of non-victims, and number of police officers required. Since these sub-models are inter-related with each other, they are solved simultaneously. This study employs genetic algorithms incorporated with traffic assignment and K-shortest path methods to determine optimal rescue path and controlled arcs. To cope with uncertain information associated with the damaged network, fuzzy system reliability theory (weakest t-norm method) is used to measure the access reliability of rescue path. To investigate the validity and applicability of the proposed model, studies on an exemplified case and a field case of Chi-Chi earthquake in Taiwan are conducted. The performances of three rescue strategies: without traffic control, selective traffic control (i.e. the proposed model) and absolute traffic control are compared. The results show that the proposed model can maintain the efficiency of rescue activity with minimal impact to ordinary trips and number of police officers required.

关键词： Chi-Chi earthquake disaster relief operations fuzzy access reliability genetic algorithms shortest path algorithm

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Online Semantic Object Segmentation for Vision Robot Collected Video

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IEEE ACCESS 2019年 7卷 107602-107615页

作者： Li, Kunqian Tao, Wenbing Liu, Liman Ocean Univ China Coll Engn Qingdao 266100 Shandong Peoples R China Huazhong Univ Sci & Technol Sch Artificial Intelligence & Automat Natl Key Lab Sci & Technol Multispectral Informat Wuhan 430074 Hubei Peoples R China South Cent Univ Nationalities Sch Biomed Engn Wuhan 430074 Hubei Peoples R China

Video segmentation is the foundation of many senior computer vision applications. For robotic vision applications, video object segmentation is facing more difficulties. Since the videos are usually collected from those complicated scenes and the camera perspective may be static for some time, object saliency and motion clues which are widely used in traditional video segmentation approaches could be unreliable. Besides, its online processing ability is of crucial importance. In this paper, we propose an online video object segmentation method, which is organized as a segmentation-by-detection framework. It first effectively segments out meaningful objects in short video frame batches with the help of object detectors, and then the segmentation of different batches can be associated with each other via bi-directional notebook based connecting strategy. Experiments conducted on public available datasets verify the above-mentioned property and show good performance of the proposed method.

关键词： Online video segmentation object segmentation object detection object tracklets object proposal shortest path algorithm

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Finding the most reliable path with and without link travel time correlation: A Lagrangian substitution based approach

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TRANSPORTATION RESEARCH PART B-METHODOLOGICAL 2011年第10期45卷 1660-1679页

作者： Xing, Tao Zhou, Xuesong Univ Utah Dept Civil & Environm Engn Salt Lake City UT 84112 USA

path travel time reliability is an essential measure of the quality of service for transportation systems and an important attribute in travelers' route and departure time scheduling. This paper investigates a fundamental problem of finding the most reliable path under different spatial correlation assumptions, where the path travel time variability is represented by its standard deviation. To handle the non-linear and non-additive cost functions introduced by the quadratic forms of the standard deviation term, a Lagrangian substitution approach is adopted to estimate the lower bound of the most reliable path solution through solving a sequence of standard shortest path problems. A subgradient algorithm is used to iteratively improve the solution quality by reducing the optimality gap. To characterize the link travel time correlation structure associated with the end-to-end trip time reliability measure, this research develops a sampling-based method to dynamically construct a proxy objective function in terms of travel time observations from multiple days. The proposed algorithms are evaluated under a large-scale Bay Area, California network with real-world measurements. (C) 2011 Elsevier Ltd. All rights reserved.

关键词： shortest path algorithm path travel time reliability Reliable route Lagrangian relaxation method

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Parallel Voronoi Computation for Physics-Based Simulations

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COMPUTING IN SCIENCE & ENGINEERING 2016年第3期18卷 88-94页

作者： Toss, Julio Comba, Joao Raffin, Bruno Univ Fed Rio Grande do Sul BR-90046900 Porto Alegre RS Brazil Univ Grenoble Alpes INRIA Grenoble France

Voronoi diagrams are fundamental data structures in computational geometry, with applications in areas such as physics-based simulations. For non-Euclidean distances, the Voronoi diagram must be performed over a grid-graph, where the edges encode the required distance information. The major bottleneck in this case is a shortest path algorithm that must be computed multiple times during the simulation. The authors present a GPU algorithm for solving the shortest path problem from multiple sources using a generalized distance function. Their algorithm was designed to leverage the grid-based nature of the underlying graph that represents the deformable objects. Experimental results report speed-ups up to 65x over a current reference sequential method.

关键词： computational geometry data structures digital simulation graph theory graphics processing units parallel processing physics GPU algorithm Voronoi diagrams computational geometry data structures generalized distance function grid-based nature grid-graph nonEuclidean distances parallel Voronoi computation physics-based simulations shortest path algorithm algorithm design and analysis Computational modeling Graphics processing units Interpolation Three-dimensional displays Topology Physics scientific computing simulation

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Graph Theory Modeling Approach for Optimal Operation of Water Distribution Systems

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JOURNAL OF HYDRAULIC ENGINEERING 2016年第3期142卷 4015061-1-4015061-15页

作者： Price, Eyal Ostfeld, Avi Technion Israel Inst Technol Fac Civil & Environm Engn IL-32000 Haifa Israel

A graph theory-based algorithm is demonstrated for optimal pump scheduling of two example application water networks. The hydraulic part of the problem is solved using a dedicated and efficient hydraulic solver. The pump scheduling part of the problem is solved using a skeletonized operational graph, representing only the basic logic operational relations existing in the network required for pump selection: the pumping units (with nominal operating costs), water tanks and clustered demand nodes. The hydraulic solver advances one time step at a time. After each time step advance, the nodes of the model are checked to see if satisfy minimum service pressure and minimum water tank level. For nodes not satisfying the service constraints, the Dijkstra's shortest path algorithm is applied to the skeletonized graph to determine the optimal pumping unit to be activated and then updating the pumps operation pattern in the model. The hydraulic solver is then reinitialized to resolve and recheck the time steps one by one. The algorithm ends when the solver reaches the last time step with all nodes meeting service constraints. The algorithm returns an optimal minimal cost pump-scheduling pattern under greater-than constraints over the examined time period, such as (1)minimal consumer service pressure, and (2)water balance closure at the water tanks. The algorithm returns discrete pump operation scheduling with minimal pump switching and minimal water age in the tanks, demonstrating short solution times (28s to schedule 11 pumps over a 168-hour period). The algorithm may be applicable for real-time pump scheduling. Future research may include water quality constraints and variable frequency drive pump scheduling. Pump selection is based on the assumption that the optimal pump operation order is not affected by changes in the network's hydraulic conditions, such as water tank levels and location along the pump efficiency curve (assuming constant efficiency). If hydraulic conditio

关键词： Graph theory shortest path algorithm Water distribution network optimal operation Water distribution Optimization

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The urban traffic noise monitoring system based on LoRaWAN technology

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WIRELESS NETWORKS 2022年第1期28卷 441-458页

作者： Dobrilovic, Dalibor Brtka, Vladimir Jotanovic, Gordana Stojanov, Zeljko Jausevac, Goran Malic, Milan Univ Novi Sad Tech Fac Mihajlo Pupin Zrenjanin Serbia Univ East Sarajevo Fac Transport & Traff Engn Doboj Bosnia & Herceg Schneider Elect DMS NS Novi Sad Serbia

Noise and air pollution are among the most important problems and challenges in urban environments. Noise can cause several problems in functioning within urban settlements and may result in a variety of health problems. Continuous monitoring, prevention, and active work on solving these problems are in the focus of research communities, local and national agencies and organizations, and many international organizations. Traffic noise on city roads has been identified as one of the major problems in urban settlements. Fortunately, it can be monitored and controlled in a way that can reduce its level and negative effects. One of the most effective and cheapest ways to monitor and control traffic noise is to use wireless sensor networks, IoT technology, and cloud-based architectures. This article presents an approach in designing urban traffic noise monitoring system based on LoRaWAN and microservices oriented architecture supported with open-source hardware and software solutions. Design of the system includes planning LoRaWAN network and development of the IoT system layered architecture. Methods for traffic routing and rerouting in urban areas, based on experiments that uses Dijkstra and Floyd-Warshall algorithms are presented. The system implementation and evaluation of the proposed routing modifications are presented in the case of the city of Zrenjanin in Serbia. Discussion of extensions and improvements of the presented system, as well as future research directions, are also presented.

关键词： Urban road traffic noise Planning LoRaWAN Traffic routing shortest path algorithm IoT layered architecture

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Distribution Network Expansion Planning Approach for Large Scale Electric Vehicles Accommodation

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IEEE TRANSACTIONS ON SUSTAINABLE ENERGY 2023年第2期14卷 906-919页

作者： Wang, Xiaowen Shi, Xiaoying Xu, Yinliang Shen, Xinwei Tsinghua Univ Tsinghua Berkeley Shenzhen Inst Tsinghua Shenzhen Int Grad Sch Shenzhen 518055 Peoples R China

The increased power demand incurred by electric vehicles (EVs) has imposed new challenges on the distribution network. One significant responsibility of the distribution network operator (DNO) is to design and expand the distribution network periodically to accommodate the ever-increasing demand. The previous researches mainly use relaxation techniques to enhance the problem tractability, which would involve additional binary variables and incur computation burden to the optimization problem, or even worse, may lead to an intractable problem. This paper develops a mixed-integer non-linear programming (MINLP) model considering various network constraints for the distribution network expansion planning under a high penetration level of EVs. The stochastic characteristics of demands are addressed through set of scenarios. A distributed biased min-consensus algorithm based approach is proposed to solve the MINLP model. Finally, comparison tests are conducted on three different scales of distribution networks to validate the effectiveness of the proposed approach. Simulation results demonstrate that the computation time of the proposed approach is reduced by 42.46% on average for different systems compared with that of the traditional shortest path algorithm based approach.

关键词： Biased min-consensus algorithm network cons-traint shortest path algorithm distribution network expansion planning computation efficiency

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Designing Skid-Trail Networks to Reduce Skidding Cost and Soil Disturbance for Ground-Based Timber Harvesting Operations

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FOREST SCIENCE 2016年第1期62卷 48-58页

作者： Contreras, Marco A. Parrott, David L. Chung, Woodam Univ Kentucky Dept Forestry Lexington KY 40546 USA Univ Kentucky Lexington KY 40506 USA Oregon State Univ Corvallis OR 97331 USA

Skid-trail locations directly influence the economics and environmental impacts of harvesting operations. Typically, field managers design skid-trail networks manually based on field observations of vegetation and terrain conditions. We designed a model to automatically design skid-trail networks to reduce skidding costs and soil disturbances. The model simulates tree-bunch locations, creates a feasible skid-trail network across the harvest unit, estimates skidding cost and soil recovery cost for each feasible skid-trail segment, and finds the network design that connects each tree bunch to landings while reducing skidding and soil recovery costs. The model was applied to a 24-ha hypothetical harvest unit to test its ability to design optimal networks under different scenarios representing conditions commonly found in timber harvesting operations (e.g., skidding pattern, uneven volume distribution, skidding obstacles, and different weights given to skidding and soil recovery costs). It was also applied to an actual 124-ha harvest unit to evaluate its ability to design skid-trail networks considering more realistic conditions with multiple design factors. The model successfully created optimized skid-trail networks for all scenarios considered, and results suggest that it provides a useful tool to help forest engineers and field managers design economically efficient and environmentally sound ground-based timber harvesting operations.

关键词： forest operations planning shortest path algorithm forest optimization network programming

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