Solving the Shortest Path Problem with Interval Arcs

Sengupta, Atanu; Pal, Tapan Kumar

doi:10.1007/s10700-005-4916-y

Cited by 29 publications

(5 citation statements)

References 9 publications

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“…This problem is prevalent in diverse fields, including transportation, road mapping, and other applications. SPP can be classified into three types according to Sengupta et al [12]: determining the minimum (shortest) path from a single source, calculating the shortest path from the origin vertex to all other vertices in the graph, and solving the singlesource shortest path problem, where the decision-maker's goal is to identify the shortest paths among all connected nodes in the network. Another variant involves determining the shortest path between any two vertices, aiming to compute the shortest paths for all pairs in a given transportation problem (TP).…”

Section: Application Review Of Neutrosophic Setmentioning

confidence: 99%

Heuristic Incident Edge Path Algorithm for Interval-Valued Neutrosophic Transportation Network

2024

Contemp. Math.

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Neutrosophic Set is an extension of Fuzzy set theory dealts with uncertain environments in Transportation, Decision-making etc. Finding the shortest path for an uncertain environment is one of the most challenging tasks, many heuristic algorithms play a vital role in releasing this task. This research article an heuristic algorithmic approach using graph theoretical methods helps the researcher to crack the challenge and which type of algorithm can use the type of score functions are discussed. especially, the interval-valued Neutrosophic transportation problem (IVNTP) is considered for finding the shortest path which is a real-world decision-making problem in an ambiguous (uncertain) environment. Providing the shortest and finest way to address this ambiguity leads to the success of researcher to the organization. The algorithm used has been introduced for determination of interval-valued Neutrosophic shortest path (IVNSP) from the origin node to all other nodes by de-neutrosophicated edges using score functions. An illustrative Interval-valued neutrosophic transportation problem explains the algorithm’s efficacy and authenticity to find optimum result; this research article discusses about the nature of score functions, and some score function were taken into consideration. Further, the heuristic algorithm used is applicable for both positive and negative weighted edges; it was elaborated and compared with existing algorithm results also it provided all pair of shortest path. Future study and brief study of this article was disclosed in conclusion.

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Section: Application Review Of Neutrosophic Setmentioning

confidence: 99%

Heuristic Incident Edge Path Algorithm for Interval-Valued Neutrosophic Transportation Network

2024

Contemp. Math.

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“…Gent et al investigated the possibility of using genetic algorithms to solve shortest path problems [10]. Gupta and Pal presented an algorithm for the shortest path problem when the connected arcs in a transportation network are represented as interval numbers [11]. In this paper some basic definitions and Preliminaries of networks and CE algorithm are presented then the modified algorithm is proposed.…”

Section: Literature Reviewmentioning

confidence: 99%

Finding shortest path in static networks

Abbasi¹,

Moosavi²

2012

IJFBS

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This paper considers the problem of finding the shortest path in a static network, where the costs are constant. The CE Algorithm based strategy that is presented by Rubinstein to solving rare event and combinatorial optimization problem is modified to finding shortest path in this research. To analyze the efficiency of the used algorithm three sets of small, medium and large sized problems that generated randomly are solved. The results on the set of problems show that the modified algorithm produces good solutions and time saving in computation of large-scale network.

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“…The Fuzzy Shortest Path Problem (FSPP) 18,23,25,[33][34][35][36][37][39][40][41][42][43][44][45][46][47][48] is a generalization of the classical SPP for applications in ill-defined environment and has been found important to many applications such as Communication or Transportation Network, Computational Geometry, Graph Algorithms, Geographical Information Systems (GIS), Network Optimization, etc. In traditional shortest path problems, the arc length of the network takes precise numbers, but in the real-world problem, the arc length may represent transportation time or cost which can be known only approximately due to vagueness of information, and hence it can be considered a fuzzy number or an intuitionistic fuzzy number.…”

Section: Introductionmentioning

confidence: 99%

“…The main results obtained from their studies were that the shortest path in the fuzzy sense corresponds to the actual paths in the network, and the fuzzy shortest path problem is an extension of the crisp case. Nayeem and Pal 38 have proposed an algorithm based on the acceptability index introduced by Sengupta and Pal 46 which gives a single fuzzy shortest path or a guideline for choosing the best fuzzy shortest path according to the decision maker's viewpoint. Thus, numerous papers have been published in different journals/books on the fuzzy shortest path problem (FSPP).…”

Section: Introductionmentioning

confidence: 99%

Z-Dijkstra’s Algorithm to solve Shortest Path Problem in a Z-Graph

Biswas

2017

Orient. J. Chem

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In this paper the author introduces the notion of Z-weighted graph or Z-graph in Graph Theory, considers the Shortest Path Problem (SPP) in a Z-graph. The classical Dijkstra's algorithm to find the shortest path in graphs is not applicable to Z-graphs. Consequently the author proposes a new algorithm called by Z-Dijkstra's Algorithm with the philosophy of the classical Dijkstra's Algorithm to solve the SPP in a Z-graph.

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Solving the Shortest Path Problem with Interval Arcs

Cited by 29 publications

References 9 publications

Heuristic Incident Edge Path Algorithm for Interval-Valued Neutrosophic Transportation Network

Heuristic Incident Edge Path Algorithm for Interval-Valued Neutrosophic Transportation Network

Finding shortest path in static networks

Z-Dijkstra’s Algorithm to solve Shortest Path Problem in a Z-Graph

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