Finding Your Way: Shortest Paths on Networks

Traveling to different destinations is a major part of our lives. We visit a variety of locations both during our daily lives and when we are on vacation. How can we find the best way to navigate from one place to another? Perhaps we can test all of the different ways of traveling between two places, but another method is to use mathematics and computation to find a shortest path between them. In this article, we discuss how to construct shortest paths and introduce Dijkstra’s algorithm to minimize the total cost of a path, where the cost may be the travel distance, the travel time, or some other quantity. We also discuss how to use shortest paths in the real world to save time and increase traveling efficiency.

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Finding Your Way: Shortest Paths on Networks

10.31235/osf.io/s34uv ◽

2020 ◽

Author(s):

Teresa Rexin ◽

Mason A. Porter

Keyword(s):

Travel Time ◽

Shortest Path ◽

Real World ◽

Shortest Paths ◽

Travel Distance ◽

Dijkstra’S Algorithm ◽

Total Cost ◽

The Real ◽

Dijkstra's Algorithm ◽

The Cost

Traveling to different destinations is a big part of our lives. How do we know the best way to navigate from one place to another? Perhaps we could test all of the different ways of traveling between two places, but another method is using mathematics and computation to find a shortest path. We discuss how to find a shortest path and introduce Dijkstra’s algorithm to minimize the total cost of a path, where the cost may be the travel distance or travel time. We also discuss how shortest paths can be used in the real world to save time and increase traveling efficiency.

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The Cost-Effectiveness of Pre-school Peanut Oral Immunotherapy in the Real World Setting

The Journal of Allergy and Clinical Immunology In Practice ◽

10.1016/j.jaip.2021.02.058 ◽

2021 ◽

Author(s):

Marcus Shaker ◽

Edmond S. Chan ◽

Jennifer LP. Protudjer ◽

Lianne Soller ◽

Elissa M. Abrams ◽

...

Keyword(s):

Cost Effectiveness ◽

Real World ◽

Oral Immunotherapy ◽

The Real ◽

Real World Setting ◽

The Cost

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Kajian Literatur : Etnografi Digital Sebagai Cara Baru Dalam Pencarian Data Dalam Proses Perencanaan Arsitektur

AKSEN ◽

10.37715/aksen.v6i1.2103 ◽

2021 ◽

Vol 6 (1) ◽

pp. 19-31

Author(s):

Andrey Caesar Effendi ◽

LMF Purwanto

Keyword(s):

Real World ◽

Digital Technology ◽

Ethnographic Methods ◽

Daily Lives ◽

The Real ◽

Face To Face ◽

Architectural Programming ◽

Programming Process ◽

The Way

The use of digital technology today can be said to be inseparable in our daily lives. Digital technology isslowly changing the way we communicate with others and the environment. Socialization that is usuallyface-to-face in the real world now can be done to not having to meet face-to-face in cyberspace. Thisliterature review aims to see a change in the way of obtaining data that is growing, with the use of digitaltechnology in ethnographic methods. The method used in this paper is to use descriptive qualitativeresearch methods by analyzing the existing literature. So it can be concluded that the use of digitalethnography in the architectural programming process can be a new way of searching for data at thearchitectural programming stage.

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The Effect of Route-choice Strategy on Transit Travel Time Estimates

10.31235/osf.io/3r4p6 ◽

2019 ◽

Author(s):

Nate Wessel ◽

Steven Farber

Keyword(s):

Travel Time ◽

Shortest Path ◽

Imperfect Information ◽

Optimal Path ◽

Shortest Paths ◽

Route Choice ◽

Travel Times ◽

Selection Strategies ◽

Time Estimates ◽

Average Travel Time

Estimates of travel time by public transit often rely on the calculation of a shortest-path between two points for a given departure time. Such shortest-paths are time-dependent and not always stable from one moment to the next. Given that actual transit passengers necessarily have imperfect information about the system, their route selection strategies are heuristic and cannot be expected to achieve optimal travel times for all possible departures. Thus an algorithm that returns optimal travel times at all moments will tend to underestimate real travel times all else being equal. While several researchers have noted this issue none have yet measured the extent of the problem. This study observes and measures this effect by contrasting two alternative heuristic routing strategies to a standard shortest-path calculation. The Toronto Transit Commission is used as a case study and we model actual transit operations for the agency over the course of a normal week with archived AVL data transformed into a retrospective GTFS dataset. Travel times are estimated using two alternative route-choice assumptions: 1) habitual selection of the itinerary with the best average travel time and 2) dynamic choice of the next-departing route in a predefined choice set. It is shown that most trips present passengers with a complex choice among competing itineraries and that the choice of itinerary at any given moment of departure may entail substantial travel time risk relative to the optimal outcome. In the context of accessibility modelling, where travel times are typically considered as a distribution, the optimal path method is observed in aggregate to underestimate travel time by about 3-4 minutes at the median and 6-7 minutes at the \nth{90} percentile for a typical trip.

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A MODIFIED GENETIC ALGORITHM FOR FINDING FUZZY SHORTEST PATHS IN UNCERTAIN NETWORKS

ISPRS - International Archives of the Photogrammetry, Remote Sensing and Spatial Information Sciences ◽

10.5194/isprsarchives-xli-b2-299-2016 ◽

2016 ◽

Vol XLI-B2 ◽

pp. 299-304 ◽

Cited By ~ 4

Author(s):

A. A. Heidari ◽

M. R. Delavar

Keyword(s):

Genetic Algorithm ◽

Shortest Path ◽

Shortest Paths ◽

The Body ◽

Shortest Path Problems ◽

Conventional Procedure ◽

Path Lengths ◽

The Cost ◽

Uncertain Networks ◽

Exploration Exploitation

In realistic network analysis, there are several uncertainties in the measurements and computation of the arcs and vertices. These uncertainties should also be considered in realizing the shortest path problem (SPP) due to the inherent fuzziness in the body of expert's knowledge. In this paper, we investigated the SPP under uncertainty to evaluate our modified genetic strategy. We improved the performance of genetic algorithm (GA) to investigate a class of shortest path problems on networks with vague arc weights. The solutions of the uncertain SPP with considering fuzzy path lengths are examined and compared in detail. As a robust metaheuristic, GA algorithm is modified and evaluated to tackle the fuzzy SPP (FSPP) with uncertain arcs. For this purpose, first, a dynamic operation is implemented to enrich the exploration/exploitation patterns of the conventional procedure and mitigate the premature convergence of GA technique. Then, the modified GA (MGA) strategy is used to resolve the FSPP. The attained results of the proposed strategy are compared to those of GA with regard to the cost, quality of paths and CPU times. Numerical instances are provided to demonstrate the success of the proposed MGA-FSPP strategy in comparison with GA. The simulations affirm that not only the proposed technique can outperform GA, but also the qualities of the paths are effectively improved. The results clarify that the competence of the proposed GA is preferred in view of quality quantities. The results also demonstrate that the proposed method can efficiently be utilized to handle FSPP in uncertain networks.

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A Generic Approach on How to Formally Specify and Model Check Path Finding Algorithms: Dijkstra, A* and LPA*

International Journal of Software Engineering and Knowledge Engineering ◽

10.1142/s0218194020400215 ◽

2020 ◽

Vol 30 (10) ◽

pp. 1481-1523

Author(s):

Kazuhiro Ogata

Keyword(s):

Model Checking ◽

Shortest Path ◽

Formal Specification ◽

Model Check ◽

Shortest Paths ◽

Path Finding ◽

Property A ◽

Goal Node ◽

The Cost ◽

Start Node

The paper describes how to formally specify three path finding algorithms in Maude, a rewriting logic-based programming/specification language, and how to model check if they enjoy desired properties with the Maude LTL model checker. The three algorithms are Dijkstra Shortest Path Finding Algorithm (DA), A* Algorithm and LPA* Algorithm. One desired property is that the algorithms always find the shortest path. To this end, we use a path finding algorithm (BFS) based on breadth-first search. BFS finds all paths from a start node to a goal node and the set of all shortest paths is extracted. We check if the path found by each algorithm is included in the set of all shortest paths for the property. A* is an extension of DA in that for each node [Formula: see text] an estimation [Formula: see text] of the distance to the goal node from [Formula: see text] is used and LPA* is an incremental version of A*. It is known that if [Formula: see text] is admissible, A* always finds the shortest path. We have found a possible relaxed sufficient condition. The relaxed condition is that there exists the shortest path such that for each node [Formula: see text] except for the start node on the path [Formula: see text] plus the cost to [Formula: see text] from the start node is less than the cost of any non-shortest path to the goal from the start. We informally justify the relaxed condition. For LPA*, if the relaxed condition holds in each updated version of a graph concerned including the initial graph, the shortest path is constructed. Based on the three case studies for DA, A* and LPA*, we summarize the formal specification and model checking techniques used as a generic approach to formal specification and model checking of path finding algorithms.

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How Much of What We Learn in Virtual Reality Transfers to Real-World Navigation?

Multisensory Research ◽

10.1163/22134808-20201445 ◽

2020 ◽

Vol 33 (4-5) ◽

pp. 479-503 ◽

Cited By ~ 1

Author(s):

Lukas Hejtmanek ◽

Michael Starrett ◽

Emilio Ferrer ◽

Arne D. Ekstrom

Keyword(s):

Virtual Reality ◽

Real World ◽

Information Transfer ◽

Spatial Knowledge ◽

Desktop Computer ◽

The Real ◽

Head Mounted Display ◽

Spatial Environment ◽

The Cost ◽

Study Participants

Abstract Past studies suggest that learning a spatial environment by navigating on a desktop computer can lead to significant acquisition of spatial knowledge, although typically less than navigating in the real world. Exactly how this might differ when learning in immersive virtual interfaces that offer a rich set of multisensory cues remains to be fully explored. In this study, participants learned a campus building environment by navigating (1) the real-world version, (2) an immersive version involving an omnidirectional treadmill and head-mounted display, or (3) a version navigated on a desktop computer with a mouse and a keyboard. Participants first navigated the building in one of the three different interfaces and, afterward, navigated the real-world building to assess information transfer. To determine how well they learned the spatial layout, we measured path length, visitation errors, and pointing errors. Both virtual conditions resulted in significant learning and transfer to the real world, suggesting their efficacy in mimicking some aspects of real-world navigation. Overall, real-world navigation outperformed both immersive and desktop navigation, effects particularly pronounced early in learning. This was also suggested in a second experiment involving transfer from the real world to immersive virtual reality (VR). Analysis of effect sizes of going from virtual conditions to the real world suggested a slight advantage for immersive VR compared to desktop in terms of transfer, although at the cost of increased likelihood of dropout. Our findings suggest that virtual navigation results in significant learning, regardless of the interface, with immersive VR providing some advantage when transferring to the real world.

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Centrality Metrics-Based Connected Dominating Sets for Real-World Network Graphs

Strategic Innovations and Interdisciplinary Perspectives in Telecommunications and Networking - Advances in Wireless Technologies and Telecommunication ◽

10.4018/978-1-5225-8188-8.ch001 ◽

2019 ◽

pp. 1-29

Author(s):

Natarajan Meghanathan ◽

Md Atiqur Rahman ◽

Mahzabin Akhter

Keyword(s):

Shortest Path ◽

Real World ◽

Degree Centrality ◽

Dominating Sets ◽

Eigenvector Centrality ◽

Connected Dominating Sets ◽

The Real ◽

Centrality Metrics ◽

Local Clustering Coefficient ◽

Node Size

The authors investigate the use of centrality metrics as node weights to determine connected dominating sets (CDS) for a suite of 60 real-world network graphs of diverse degree distribution. They employ centrality metrics that are neighborhood-based (degree centrality [DEG] and eigenvector centrality [EVC]), shortest path-based (betweenness centrality [BWC] and closeness centrality [CLC]) as well as the local clustering coefficient complement-based degree centrality metric (LCC'DC), which is a hybrid of the neighborhood and shortest path-based categories. The authors target for minimum CDS node size (number of nodes constituting the CDS). Though both the BWC and CLC are shortest path-based centrality metrics, they observe the BWC-based CDSs to be of the smallest node size for about 60% of the real-world networks and the CLC-based CDSs to be of the largest node size for more than 40% of the real-world networks. The authors observe the computationally light LCC'DC-based CDS node size to be the same as the computationally heavy BWC-based CDS node size for about 50% of the real-world networks.

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Shortest Path Method for Hardware/Software Partitioning Problems

International Journal of Information Systems and Social Change ◽

10.4018/ijissc.2021070104 ◽

2021 ◽

Vol 12 (3) ◽

pp. 40-57

Author(s):

Adil Iguider ◽

Oussama Elissati ◽

Abdeslam En-Nouaary ◽

Mouhcine Chami

Keyword(s):

Embedded System ◽

Shortest Path ◽

High Performance ◽

Accurate Information ◽

Daily Lives ◽

Smart Systems ◽

Partitioning Problems ◽

Main Component ◽

The Right ◽

The Cost

Smart systems are becoming more present in every aspect of our daily lives. The main component of such systems is an embedded system; this latter assures the collection, the treatment, and the transmission of the accurate information in the right time and for the right component. Modern embedded systems are facing several challenges; the objective is to design a system with high performance and to decrease the cost and the development time. Consequently, some robust methodologies like the Codesign were developed to fulfill those requirements. The most important step of the Codesign is the partitioning of the systems' functionalities between a hardware set and a software set. This article deals with this problem and uses a heuristic approach based on shortest path optimizations to solve the problem. The aim is to minimize the total hardware area and to respect a constraint on the overall execution time of the system. Experiments results demonstrate that the proposed method is very fast and gives better results compared to the genetic algorithm.

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