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Prize-Collecting TSP with a Budget Constraint

Authors Alice Paul, Daniel Freund, Aaron Ferber, David B. Shmoys, David P. Williamson

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  • approximation algorithms
  • traveling salesman problem

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Abstract

We consider constrained versions of the prize-collecting traveling salesman and the minimum spanning tree problems. The goal is to maximize the number of vertices in the returned tour/tree subject to a bound on the tour/tree cost. We present a 2-approximation algorithm for these problems based on a primal-dual approach. The algorithm relies on finding a threshold value for the dual variable corresponding to the budget constraint in the primal and then carefully constructing a tour/tree that is just within budget. Thereby, we improve the best-known guarantees from 3+epsilon and 2+epsilon for the tree and the tour version, respectively. Our analysis extends to the setting with weighted vertices, in which we want to maximize the total weight of vertices in the tour/tree subject to the same budget constraint.

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Alice Paul, Daniel Freund, Aaron Ferber, David B. Shmoys, and David P. Williamson. Prize-Collecting TSP with a Budget Constraint. In 25th Annual European Symposium on Algorithms (ESA 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 87, pp. 62:1-62:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017) https://doi.org/10.4230/LIPIcs.ESA.2017.62

Author Details

Alice Paul
Daniel Freund
Aaron Ferber
David B. Shmoys
David P. Williamson

References

  1. Aaron Archer, MohammadHossein Bateni, MohammadTaghi Hajiaghayi, and Howard Karloff. Improved approximation algorithms for prize-collecting Steiner tree and TSP. SIAM Journal on Computing, 40(2):309-332, 2011. Google Scholar
  2. Sunil Arya and Hariharan Ramesh. A 2.5-factor approximation algorithm for the k-MST problem. Information Processing Letters, 65(3):117-118, 1998. Google Scholar
  3. G. Ausiello, M. Demange, L. Laura, and V. Paschos. Algorithms for the on-line quota traveling salesman problem. Information Processing Letters, 92(2):89-94, 2004. Google Scholar
  4. Avrim Blum, Ramamurthy Ravi, and Santosh Vempala. A constant-factor approximation algorithm for the k-MST problem. In Proceedings of the Twenty-Eighth Annual ACM Symposium on Theory of Computing (STOC), pages 442-448. ACM, 1996. Google Scholar
  5. Chandra Chekuri and Nitish Korula. Approximation algorithms for orienteering with time windows. arXiv preprint arXiv:0711.4825, 2007. Google Scholar
  6. Chandra Chekuri, Nitish Korula, and Martin Pál. Improved algorithms for orienteering and related problems. ACM Transactions on Algorithms (TALG), 8(3):23, 2012. Google Scholar
  7. Chandra Chekuri and Martin Pal. A recursive greedy algorithm for walks in directed graphs. In 46th Annual IEEE Symposium on Foundations of Computer Science (FOCS), pages 245-253. IEEE, 2005. Google Scholar
  8. Ke Chen and Sariel Har-Peled. The orienteering problem in the plane revisited. In Proceedings of the Twenty-Second Annual Symposium on Computational Geometry, pages 247-254. ACM, 2006. Google Scholar
  9. Joan Feigenbaum, Christos H. Papadimitriou, and Scott Shenker. Sharing the cost of multicast transmissions. Journal of Computer and System Sciences, 63(1):21-41, 2001. Google Scholar
  10. Greg N. Frederickson and Barry Wittman. Approximation algorithms for the traveling repairman and speeding deliveryman problems. Algorithmica, 62(3-4):1198-1221, 2012. Google Scholar
  11. Daniel Freund, Ashkan Norouzi-Fard, Alice Paul, Shane G. Henderson, and David B. Shmoys. Data-driven rebalancing methods for bike-share systems. Working Paper, 2017. Google Scholar
  12. N. Garg. A 3-approximation for the minimum tree spanning k vertices. In Proceedings of the 37th Annual Symposium on Foundations of Computer Science, FOCS'96, pages 302-, Washington, DC, USA, 1996. IEEE Computer Society. Google Scholar
  13. Naveen Garg. Saving an epsilon: a 2-approximation for the k-MST problem in graphs. In Proceedings of the Thirty-Seventh Annual ACM Symposium on Theory of Computing (STOC), pages 396-402. ACM, 2005. Google Scholar
  14. Michel X. Goemans and David P. Williamson. A general approximation technique for constrained forest problems. SIAM Journal on Computing, 24(2):296-317, 1995. Google Scholar
  15. Anupam Gupta, Ravishankar Krishnaswamy, Viswanath Nagarajan, and R. Ravi. Approximation algorithms for stochastic orienteering. In Proceedings of the Twenty-Third Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), pages 1522-1538. SIAM, 2012. Google Scholar
  16. David S. Johnson, Maria Minkoff, and Steven Phillips. The prize collecting Steiner tree problem: theory and practice. In Proceedings of the Eleventh Annual ACM-SIAM Symposium on Discrete Algorithms (SODA), pages 760-769. Society for Industrial and Applied Mathematics, 2000. Google Scholar
  17. Mor Kaspi, Tal Raviv, and Michal Tzur. Detection of unusable bicycles in bike-sharing systems. Omega, 65:10-16, 2016. Google Scholar
  18. Asaf Levin. A better approximation algorithm for the budget prize collecting tree problem. Operations Research Letters, 32(4):316-319, 2004. Google Scholar
  19. Viswanath Nagarajan and R. Ravi. Approximation algorithms for distance constrained vehicle routing problems. Networks, 59(2):209-214, 2012. Google Scholar
  20. Gerhard Reinelt. TSPLIB - a traveling salesman problem library. ORSA Journal on Computing, pages 376-384, 1991. Google Scholar
  21. Shalabh Vidyarthi and Kaushal K. Shukla. Approximation algorithms for P2P orienteering and stochastic vehicle routing problem. arXiv preprint arXiv:1501.06515, 2015. Google Scholar
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