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Approximation algorithms for constructing some required structures in digraphs

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  • Li, Jianping
  • Ge, Yu
  • He, Shuai
  • Lichen, Junran

Abstract

We consider a new problem of constructing some required structures in digraphs, where all arcs installed in such required structures are supposed to be cut from some pieces of a specific material of length L. Formally, we consider the model: a digraph D=(V, A; w), a structure S and a specific material of length L, where w: A→R+, we are asked to construct a subdigraph D′ from D, having the structure S, such that each arc in D′ is constructed by a part of a piece or/and some whole pieces of such a specific material, the objective is to minimize the number of pieces of such a specific material to construct all arcs in D′.

Suggested Citation

  • Li, Jianping & Ge, Yu & He, Shuai & Lichen, Junran, 2014. "Approximation algorithms for constructing some required structures in digraphs," European Journal of Operational Research, Elsevier, vol. 232(2), pages 307-314.
    • Handle: RePEc:eee:ejores:v:232:y:2014:i:2:p:307-314
    DOI: 10.1016/j.ejor.2013.07.033
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    References listed on IDEAS

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    1. Vardges Melkonian & Éva Tardos, 2005. "Primal-Dual-Based Algorithms for a Directed Network Design Problem," INFORMS Journal on Computing, INFORMS, vol. 17(2), pages 159-174, May.
    2. Arthur Warburton, 1987. "Approximation of Pareto Optima in Multiple-Objective, Shortest-Path Problems," Operations Research, INFORMS, vol. 35(1), pages 70-79, February.
    3. Refael Hassin, 1992. "Approximation Schemes for the Restricted Shortest Path Problem," Mathematics of Operations Research, INFORMS, vol. 17(1), pages 36-42, February.
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    Cited by:

    1. Junran Lichen & Jianping Li & Ko-Wei Lih & Xingxing Yu, 2022. "Approximation algorithms for constructing required subgraphs using stock pieces of fixed length," Journal of Combinatorial Optimization, Springer, vol. 44(3), pages 1774-1795, October.
    2. Junran Lichen & Jianping Li & Ko-Wei Lih & Xingxing Yu, 0. "Approximation algorithms for constructing required subgraphs using stock pieces of fixed length," Journal of Combinatorial Optimization, Springer, vol. 0, pages 1-22.

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