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The Thief Orienteering Problem on Series-Parallel Graphs

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Combinatorial Optimization (ISCO 2024)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 14594))

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Abstract

In the thief orienteering problem an agent called a thief carries a knapsack of capacity W and has a time limit T to collect a set of items of total weight at most W and maximum profit along a simple path in a weighted graph \(G = (V, E)\) from a start vertex s to an end vertex t. There is a set I of items each with weight \(w_{i}\) and profit \(p_{i}\) that are distributed among \(V \setminus \{s,t\}\). The time needed by the thief to travel an edge depends on the length of the edge and the weight of the items in the knapsack at the moment when the edge is traversed.

There is a polynomial-time approximation scheme for the thief orienteering problem on directed acyclic graphs that produces solutions that use time at most \(T(1 + \epsilon )\) for any constant \(\epsilon > 0\). We give a polynomial-time algorithm for transforming instances of the problem on series-parallel graphs into equivalent instances of the thief orienteering problem on directed acyclic graphs; therefore, yielding a polynomial-time approximation scheme for the thief orienteering problem on this graph class that produces solutions that use time at most \(T(1 + \epsilon )\) for any constant \(\epsilon > 0\).

Andrew Bloch-Hansen and Roberto Solis-Oba were partially supported by the Natural Sciences and Engineering Research Council of Canada, grants 6636-548083-2020 and RGPIN-2020-06423, respectively.

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Notes

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    The full paper can be found at www.csd.uwo.ca/~ablochha/SeriesParallel.pdf.

References

  1. Abdelkader, R., Abdelkader, Z., Mustapha, R., Yamani, M.: Optimal allocation of reliability in series parallel production system. In: Search Algorithms for Engineering Optimization, pp. 241–258. InTechOpen, Croatia (2013)

    Google Scholar 

  2. Bloch-Hansen, A., Page, D., Solis-Oba, R.: A polynomial-time approximation scheme for thief orienteering on directed acyclic graphs. In: Hsieh, S.Y., Hung, L.J., Lee, C.W. (eds.) IWOCA 2023. LNCS, vol. 13889, pp. 87–98. Springer, Cham (2023). https://doi.org/10.1007/978-3-031-34347-6_8

    Chapter  Google Scholar 

  3. Bonyadi, M., Michalewicz, Z., Barone, L.: The travelling thief problem: the first step in the transition from theoretical problems to realistic problems. In: IEEE Congress on Evolutionary Computation (CEC), pp. 1037–1044. IEEE (2013)

    Google Scholar 

  4. Chagas, J., Wagner, M.: Ants can orienteer a thief in their robbery. Oper. Res. Lett. 48(6), 708–714 (2020)

    Article  MathSciNet  Google Scholar 

  5. Chagas, J., Wagner, M.: Efficiently solving the thief orienteering problem with a max-min ant colony optimization approach. Optim. Lett. 16(8), 2313–2331 (2022)

    Article  MathSciNet  Google Scholar 

  6. Chung, F., Leighton, F., Rosenberg, A.: Embedding graphs in books: a layout problem with applications to VLSI design. SIAM J. Algebraic Discrete Methods 1(8), 33–58 (1987)

    Article  MathSciNet  Google Scholar 

  7. Duffin, R.: Topology of series-parallel networks. J. Math. Anal. Appl. 2(10), 303–318 (1965)

    Article  MathSciNet  Google Scholar 

  8. Faêda, L., Santos, A.: A genetic algorithm for the thief orienteering problem. In: 2020 IEEE Congress on Evolutionary Computation (CEC), pp. 1–8. IEEE (2020)

    Google Scholar 

  9. Freeman, N., Keskin, B., Çapar, İ: Attractive orienteering problem with proximity and timing interactions. Eur. J. Oper. Res. 266(1), 354–370 (2018)

    Article  MathSciNet  Google Scholar 

  10. Gago, J., Hartillo, I., Puerto, J., Ucha, J.: Exact cost minimization of a series-parallel reliable system with multiple component choices using an algebraic method. Comput. Oper. Res. 40(11), 2752–2759 (2013)

    Article  MathSciNet  Google Scholar 

  11. Gunawan, A., Lau, H., Vansteenwegen, P.: Orienteering problem: a survey of recent variants, solution approaches and applications. Eur. J. Oper. Res. 255(2), 315–332 (2016)

    Article  MathSciNet  Google Scholar 

  12. Santos, A., Chagas, J.: The thief orienteering problem: formulation and heuristic approaches. In: IEEE Congress on Evolutionary Computation, pp. 1–9 (2018)

    Google Scholar 

  13. Valdes, J: Parsing flowcharts and series-parallel graphs. Ph.D. dissertation, Standford University (1978)

    Google Scholar 

  14. Wang, J., Wu, X., Fan, X.: A two-stage ant colony optimization approach based on a directed graph for process planning. Int. J. Adv. Manuf. Technol. 80, 839–850 (2015)

    Article  Google Scholar 

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Correspondence to Andrew Bloch-Hansen .

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Bloch-Hansen, A., Solis-Oba, R. (2024). The Thief Orienteering Problem on Series-Parallel Graphs. In: Basu, A., Mahjoub, A.R., Salazar González, J.J. (eds) Combinatorial Optimization. ISCO 2024. Lecture Notes in Computer Science, vol 14594. Springer, Cham. https://doi.org/10.1007/978-3-031-60924-4_19

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  • DOI: https://doi.org/10.1007/978-3-031-60924-4_19

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