Wireless Networks

, Volume 13, Issue 3, pp 323–334 | Cite as

Finding multi-constrained feasible paths by using depth-first search



An extended depth-first-search (EDFS) algorithm is proposed to solve the multi-constrained path (MCP) problem in Quality-of-Service (QoS) routing, which is NP-Complete when the number of independent routing constraints is more than one. EDFS solves the general k-constrained MCP problem with pseudo-polynomial time complexity O(m2 · EN + N2), where m is the maximum number of non-dominated paths maintained for each destination, E and N are the number of links and nodes of a graph, respectively. This is achieved by deducing potential feasible paths from knowledge of previous explorations, without re-exploring finished nodes and their descendants in the process of the DFS search. One unique property of EDFS is that the tighter the constraints are, the better the performance it can achieve, w.r.t. both time complexity and routing success ratio. This is valuable to highly dynamic environment such as wireless ad hoc networks in which network topology and link state keep changing, and real-time or multimedia applications that have stringent service requirements. EDFS is an independent feasible path searching algorithm and decoupled from the underlying routing protocol, and as such can work together with either proactive or on-demand ad hoc routing protocols as long as they can provide sufficient network state information to each source node. Analysis and extensive simulation are conducted to study the performance of EDFS in finding feasible paths that satisfy multiple QoS constraints. The main results show that EDFS is insensitive to the number of constraints, and outperforms other popular MCP algorithms when the routing constraints are tight or moderate. The performance of EDFS is comparable with that of the other algorithms when the constraints are loose.


Multi-constrained path selection Depth-first search Success ratio Existence percentage Competitive ratio 


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  1. 1.
    H. Badis and K. Agha, Quality of Service for Ad-hoc Optimized Link State Routing Protocol (QOLSR), IETF Internet Draft, draft-badis-manet-qolsr-01.txt, April 2005.Google Scholar
  2. 2.
    S. Chen and K. Nahrstedt, Distributed Quality-of-Service Routing in Ad-Hoc Networks. IEEE Journal on Selected Areas in Communications, Vol. 17, No. 8. (August 1999).Google Scholar
  3. 3.
    S. Chen and K. Nahrstedt, On Finding Multi-constrained Paths. In Proceedings of IEEE International Conference of Communications (ICC'98), pp. 874–879. Springer-Verlag, June, 1998.Google Scholar
  4. 4.
    T. Clausen and P. Jacquet, Optimized Link State Routing Protocol, IETF RFC 3626 (Experimental), October. 2003.Google Scholar
  5. 5.
    T. H. Cormen, C. E. Leiserson, R. L. Rivest, and C. Stein, Introduction to Algorithms, Second Edition. McGraw-Hill Companies, 2003.Google Scholar
  6. 6.
    J.J. Garcia-Luna-Aceves and Marcelo Spohn. Transmission-Efficient Routing in Wireless Networks Using Link-State Information. Mob. Netw. Appl., Vol. 6, No. 3 (2001) pp. 223–238.Google Scholar
  7. 7.
    J. M. Jaffe, Algorithms for Finding Paths with Multiple Constraints. IEEE Networks, 14:95–116, 1984.MATHMathSciNetGoogle Scholar
  8. 8.
    A. Juttner, B. Szviatovszki, I. Mecs, and Z. Rajko, Lagrange Relaxation Based Method for the QoS Routing Problem. In Proceedings of IEEE INFOCOM, 2001.Google Scholar
  9. 9.
    T. Korkmaz, M. Krunz, and S. Tragoudas, An Efficient Algorithm for Finding a Path Subject to Two Additive Constraints. In Proceedings of the ACM SIGMETRICS, pp. 318–327, 2000.Google Scholar
  10. 10.
    F. A. Kuipers and P. V. Mieghem, The Impact of Correlated Link Weights on Qos Routing. In Proceedings of IEEE INFOCOM, 2003.Google Scholar
  11. 11.
    X. Lin and N.B. Shroff, An Optimization Based Approach for QoS Routing in High-Bandwidth Networks. In Proceedings of IEEE INFOCOM, 2004.Google Scholar
  12. 12.
    Q. Ma and P. Steenkiste, Quality-of-Service Routing for Traffic with Performance Guarantees. In Proceedings of the IFIP Fifth International Workshop on Quality of Service, pp. 115–126, May, 1997.Google Scholar
  13. 13.
    P. V. Mieghem and F. A. Kuipers, Concepts of Exact Qos Routing Algorithms. IEEE/ACM Trans. Netw., Vol. 12, No. 5 (2004) pp. 851–864.CrossRefGoogle Scholar
  14. 14.
    H. D. Neve and P. V. Mieghem, TAMCRA: A Tunable Accuracy Multiple Constraints Routing Algorithm. Computer Communications, Vol. 23 (2000) pp. 667–679.CrossRefGoogle Scholar
  15. 15.
    C. Perkins, E. Royer, and S. Das, Quality of Service in Ad-hoc On-demand Distance Vector Routing, IETF Internet Draft (work in progress), draft-perkins-manet-aodvqos-00.txt, July 2000.Google Scholar
  16. 16.
    C. Perkins, E. Royer, and S. Das, Ad Hoc On Demand Distance Vector (AODV) Routing, IETF RFC 3561 (Experimental). July 2003.Google Scholar
  17. 17.
    H. Rangarajan and J.J. Garcia-Luna-Aceves, Using Labeled Paths for Loop-free On-demand Routing in Ad Hoc Networks. In Proceedings of the 5th ACM International Symposium on Mobile ad hoc Networking and Computing (MobiHoc'04), pp. 43–54, Roppongi Hills, Tokyo, Japan, 2004. ACM Press.Google Scholar
  18. 18.
    B. Smith and J.J. Garcia-Luna-Aceves, Efficient Policy-Based Routing without Virtual Circuits. In Proceedings of the First International Conference on Quality of Service in Heterogeneous Wired/Wireless Networks (QSHINE'04), Dallas, Texas, October, 2004.Google Scholar
  19. 19.
    Z. Wang and J. Crowcroft, Quality-of-Sservice Routing for Supporting Multimedia Applications. IEEE Journal of Selected Areas in Communications, Vol. 14, No. 7 (1996) pp. 1228–1234.CrossRefGoogle Scholar
  20. 20.
    X. Yuan, Heuristic Algorithms for Multiconstrained Quality-of-Service Routing. IEEE/ACM Trans. Netw., Vol. 10, No. 2 (2002) 244–256.CrossRefGoogle Scholar

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© Springer Science + Business Media, LLC 2006

Authors and Affiliations

  1. 1.Department of Computer EngineeringUniversity of CaliforniaSanta CruzUSA
  2. 2.Palo Alto Research Center (PARC)Palo AltoUSA

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