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GEN-LARAC: A Generalized Approach to the Constrained Shortest Path Problem Under Multiple Additive Constraints

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Algorithms and Computation (ISAAC 2005)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 3827))

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Abstract

Given a network modeled as a graph G with each link associated with a cost and k weights, the Constrained Shortest Path (CSP(k)) problem asks for computing a minimum cost path from a source node s to a target node t satisfying pre-specified bounds on path weights. This problem is NP-hard. In this paper we propose a new approximation algorithm called GEN-LARAC for CSP(k) problem based on Lagrangian relaxation method. For k = 1, we show that the relaxed problem can be solved by a polynomial time algorithm with time complexity O((m + n log n)2). Using this algorithm as a building block and combing it with ideas from mathematical programming, we propose an efficient algorithm for arbitrary k. We prove the convergence of our algorithm and compare it with previously known algorithms. We point out that our algorithm is also applicable to a more general class of constrained optimization problems.

The work of K. Thulasiraman has been supported by NSF ITR grant ANI-0312435 The work of G. Xue has been supported by NSF ITR grant ANI-0312635.

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Author information

Authors and Affiliations

  1. School of Computer Science, University of Oklahoma, 200 Felgar Street, Norman, OK, 73019, USA

    Ying Xiao & Krishnaiyan Thulasiraman

  2. Arizona State University, Tempe, AZ, 85287, USA

    Guoliang Xue

Authors
  1. Ying Xiao
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  2. Krishnaiyan Thulasiraman
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  3. Guoliang Xue
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Editor information

Editors and Affiliations

  1. Department of Computer Science, City University of Hong Kong, Tat Chee Avenue, Kowloon , Hong Kong

    Xiaotie Deng

  2. Department of Computer Science, University of Texas at Dallas, EE/CS Building, 75083, Richardson, TX, USA

    Ding-Zhu Du

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© 2005 Springer-Verlag Berlin Heidelberg

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Xiao, Y., Thulasiraman, K., Xue, G. (2005). GEN-LARAC: A Generalized Approach to the Constrained Shortest Path Problem Under Multiple Additive Constraints. In: Deng, X., Du, DZ. (eds) Algorithms and Computation. ISAAC 2005. Lecture Notes in Computer Science, vol 3827. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11602613_11

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  • DOI: https://doi.org/10.1007/11602613_11

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-30935-2

  • Online ISBN: 978-3-540-32426-3

  • eBook Packages: Computer ScienceComputer Science (R0)

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