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Number of Shortest Paths in Triangular Grid for 1- and 2-Neighborhoods

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Book cover Combinatorial Image Analysis (IWCIA 2015)

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Abstract

This paper presents a novel formulation to determine the number of shortest paths between two points in triangular grid in 2D digital space. Three types of neighborhood relations are used on the triangular grid. Here, we present the solution of the above mentioned problem for two neighborhoods—1-neighborhood and 2-neighborhood. To solve the stated problem we need the coordinate triplets of the two points. This problem has theoretical aspects and practical importance.

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Author information

Authors and Affiliations

  1. Department of Computer Science and Engineering, International Institute of Information Technology, Naya Raipur, India

    Mousumi Dutt

  2. Department of Information Technology, Indian Institute of Engineering Science and Technology, Shibpur, India

    Arindam Biswas

  3. Department of Computer Science, Faculty of Informatics, University of Debrecen, Debrecen, Hungary

    Benedek Nagy

  4. Department of Mathematics, Faculty of Arts and Sciences, Eastern Mediterranean University, Mersin-10, Famagusta, North Cyprus, Turkey

    Benedek Nagy

Authors
  1. Mousumi Dutt
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  2. Arindam Biswas
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  3. Benedek Nagy
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Corresponding author

Correspondence to Mousumi Dutt .

Editor information

Editors and Affiliations

  1. SUNY Fredonia, Fredonia, New York, USA

    Reneta P. Barneva

  2. Advanced Computing and Microelectronics, Indian Statistical Institute, Kolkata, Germany

    Bhargab B. Bhattacharya

  3. SUNY Buffalo State, Buffalo, New York, USA

    Valentin E. Brimkov

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Dutt, M., Biswas, A., Nagy, B. (2015). Number of Shortest Paths in Triangular Grid for 1- and 2-Neighborhoods. In: Barneva, R., Bhattacharya, B., Brimkov, V. (eds) Combinatorial Image Analysis. IWCIA 2015. Lecture Notes in Computer Science(), vol 9448. Springer, Cham. https://doi.org/10.1007/978-3-319-26145-4_9

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  • DOI: https://doi.org/10.1007/978-3-319-26145-4_9

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-26144-7

  • Online ISBN: 978-3-319-26145-4

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