Skip to main content
SpringerLink
Log in

The Online Replacement Path Problem

  • Conference paper
Algorithms – ESA 2013 (ESA 2013)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8125))

Included in the following conference series:

Abstract

We study a new robust path problem, the Online Replacement Path problem (ORP). Consider the problem of routing a physical package through a faulty network G = (V,E) from a source s ∈ V to a destination t ∈ V as quickly as possible. An adversary, whose objective is to maximize the latter routing time, can choose to remove a single edge in the network. In one setup, the identity of the edge is revealed to the routing mechanism (RM) while the package is in s. In this setup the best strategy is to route the package along the shortest path in the remaining network. The payoff maximization problem for the adversary becomes the Most Vital Arc problem (MVA), which amounts to choosing the edge in the network whose removal results in a maximal increase of the s-t distance. However, the assumption that the RM is informed about the failed edge when standing at s is unrealistic in many applications, in which failures occur online, and, in particular, after the routing has started. We therefore consider the setup in which the adversary can reveal the identity of the failed edge just before the RM attempts to use this edge, thus forcing it to use a different route to t, starting from the current node. The problem of choosing the nominal path minimizing the worst case arrival time at t in this setup is ORP. We show that ORP can be solved in polynomial time and study other models naturally providing middle grounds between MVA and ORP. Our results show that ORP comprises a highly flexible and tractable framework for dealing with robustness issues in the design of RM-s.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Adjiashvili, D., Zenklusen, R.: An s - t connection problem with adaptability. Discrete Applied Mathematics 159(8), 695–705 (2011)

    Article  MathSciNet  MATH  Google Scholar 

  2. Aissi, H., Bazgan, C., Vanderpooten, D.: Approximation complexity of min-max (Regret) versions of shortest path, spanning tree, and knapsack. In: Brodal, G.S., Leonardi, S. (eds.) ESA 2005. LNCS, vol. 3669, pp. 862–873. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  3. Andreatta, G., Romeo, L.: Stochastic shortest paths with recourse. Networks 18(3), 193–204 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  4. Bar-Noy, A., Khuller, S., Schieber, B.: The complexity of finding most vital arcs and nodes. Technical report, Univ. of Maryland Institute for Advanced Computer Studies Report No. UMIACS-TR-95-96, College Park, MD, USA (1995)

    Google Scholar 

  5. Bar-Noy, A., Schieber, B.: The canadian traveller problem. In: SODA 1991, pp. 261–270. SIAM, Philadelphia (1991)

    Google Scholar 

  6. Bernstein, A.: A nearly optimal algorithm for approximating replacement paths and k shortest simple paths in general graphs. In: SODA 2010, pp. 742–755. SIAM, Philadelphia (2010)

    Google Scholar 

  7. Dhamdhere, K., Goyal, V., Ravi, R., Singh, M.: How to pay, come what may: Approximation algorithms for demand-robust covering problems. In: FOCS 2005, pp. 367–378. IEEE Computer Society, Washington, DC (2005)

    Google Scholar 

  8. Emek, Y., Peleg, D., Roditty, L.: A near-linear-time algorithm for computing replacement paths in planar directed graphs. ACM Trans. Algorithms 6, 64:1–64:13 (2010)

    Google Scholar 

  9. Fredman, M.L., Tarjan, R.E.: Fibonacci heaps and their uses in improved network optimization algorithms. J. ACM 34, 596–615 (1987)

    Article  MathSciNet  Google Scholar 

  10. Gotthilf, Z., Lewenstein, M.: Improved algorithms for the k simple shortest paths and the replacement paths problems. Inf. Process. Lett. 109, 352–355 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  11. Hassin, R.: Approximation schemes for the restricted shortest path problem. Mathematics of Operations Research 17(1), 36–42 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  12. Klein, P.N., Mozes, S., Weimann, O.: Shortest paths in directed planar graphs with negative lengths: A linear-space O(n log2 n)-time algorithm. ACM Trans. Algorithms 6, 30:1–30:18 (2010)

    Google Scholar 

  13. Malik, K., Mittal, A.K., Gupta, S.K.: The k most vital arcs in the shortest path problem. Operations Research Letters 8(4), 223–227 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  14. Moreno, A., Valls, A., Ribes, A.: Finding efficient organ transport routes using multi-agent systems. In: Proceedings of the IEEE 3rd International Workshop on Enterprise Networking and Computing in Health Care Industry (Healthcom), pp. 233–258 (2001)

    Google Scholar 

  15. Nardelli, E., Proietti, G., Widmayer, P.: Finding the detour-critical edge of a shortest path between two nodes. Information Processing Letters 67(1), 51–54 (1998)

    Article  MathSciNet  Google Scholar 

  16. Nardelli, E., Proietti, G., Widmayer, P.: Swapping a failing edge of a single source shortest paths tree is good and fast. Algorithmica 35, 2003 (1999)

    MathSciNet  Google Scholar 

  17. Nardelli, E., Proietti, G., Widmayer, P.: A faster computation of the most vital edge of a shortest path. Information Processing Letters 79(2), 81–85 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  18. Nardelli, E., Proietti, G., Widmayer, P.: Finding the most vital node of a shortest path. In: Wang, J. (ed.) COCOON 2001. LNCS, vol. 2108, pp. 278–287. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  19. Nikolova, E., Karger, D.R.: Route planning under uncertainty: the canadian traveller problem. In: AAAI 2008, pp. 969–974. AAAI Press (2008)

    Google Scholar 

  20. Nisan, N., Ronen, A.: Algorithmic mechanism design (extended abstract). In: STOC 1999, pp. 129–140. ACM, New York (1999)

    Google Scholar 

  21. Papadimitriou, C.H., Yannakakis, M.: Shortest paths without a map. In: Ausiello, G., Dezani-Ciancaglini, M., Della Rocca, S.R. (eds.) ICALP 1989. LNCS, vol. 372, pp. 610–620. Springer, Heidelberg (1989)

    Google Scholar 

  22. Roditty, L.: On the k-simple shortest paths problem in weighted directed graphs. In: SODA 2007, pp. 920–928. SIAM, Philadelphia (2007)

    Google Scholar 

  23. Roditty, L., Zwick, U.: Replacement paths and k simple shortest paths in unweighted directed graphs. In: Caires, L., Italiano, G.F., Monteiro, L., Palamidessi, C., Yung, M. (eds.) ICALP 2005. LNCS, vol. 3580, pp. 249–260. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  24. Tarjan, R.E.: Efficiency of a good but not linear set union algorithm. J. ACM 22(2), 215–225 (1975)

    Article  MathSciNet  MATH  Google Scholar 

  25. Vassilevska Williams, V.: Faster replacement paths. In: SODA 2011, pp. 1337–1346. SIAM (2011)

    Google Scholar 

  26. Wulff-Nilsen, C.: Solving the replacement paths problem for planar directed graphs in O(n logn) time. In: SODA 2010, pp. 756–765. SIAM, Philadelphia (2010)

    Google Scholar 

  27. Yu, G., Yang, J.: On the robust shortest path problem. Computers & Operations Research 25(6), 457–468 (1998)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute for Operations Research (IFOR), Eidgenössische Technische Hochschule (ETH) Zürich, Rämistrasse 101, 8092, Zürich, Switzerland

    David Adjiashvili

  2. Dipartimento di Ingegneria Civile ed Ingegneria Informatica, Università di Roma Tor Vergata, Via del Politecnico 1, 00133, Rome, Italy

    Gianpaolo Oriolo & Marco Senatore

Authors
  1. David Adjiashvili
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Gianpaolo Oriolo
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Marco Senatore
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Department of Computer Science, Utrecht University, Princetonplein 5, 3584 CC, Utrecht, The Netherlands

    Hans L. Bodlaender

  2. Dipartimento di Ingegneria Civile e Ingegneria Informatica, Università di Roma “Tor Vergata”, via del Politecnico 1, 00133, Rome, Italy

    Giuseppe F. Italiano

Rights and permissions

Reprints and permissions

Copyright information

© 2013 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Adjiashvili, D., Oriolo, G., Senatore, M. (2013). The Online Replacement Path Problem. In: Bodlaender, H.L., Italiano, G.F. (eds) Algorithms – ESA 2013. ESA 2013. Lecture Notes in Computer Science, vol 8125. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-40450-4_1

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-40450-4_1

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-40449-8

  • Online ISBN: 978-3-642-40450-4

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation