Restricted Shortest Path in Temporal Graphs

The restricted shortest path RSP problem on directed networks is a well-studied problem, and has a large number of applications such as in Quality of Service routing. The problem is known to be NP-hard. In certain cases, however, the network is not static i.e., edge parameters vary over time. In light of this, we extend the RSP problem for general networks to that for temporal networks. We present several exact algorithms for this problem, one of which uses heuristics, and is similar to the $$A^*$$ algorithm. We experimentally evaluate these algorithms by simulating them on both existing temporal networks, and synthetic ones. Furthermore, based on one of the pseudo-polynomial exact algorithms, we derive a fully polynomial time approximation scheme.

[1]  Funda Ergün,et al.  An improved FPTAS for Restricted Shortest Path , 2002, Inf. Process. Lett..

[2]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[3]  Johannes O. Royset,et al.  Lagrangian relaxation and enumeration for solving constrained shortest‐path problems , 2008, Networks.

[4]  Jon M. Kleinberg,et al.  Spatial gossip and resource location protocols , 2001, JACM.

[5]  Andrew V. Goldberg,et al.  Computing the shortest path: A search meets graph theory , 2005, SODA '05.

[6]  Paul G. Spirakis,et al.  Traveling salesman problems in temporal graphs , 2014, Theor. Comput. Sci..

[7]  Janelle J. Harms,et al.  Fast Exact MultiConstraint Shortest Path Algorithms , 2007, 2007 IEEE International Conference on Communications.

[8]  Ariel Orda,et al.  QoS routing in networks with uncertain parameters , 1998, Proceedings. IEEE INFOCOM '98, the Conference on Computer Communications. Seventeenth Annual Joint Conference of the IEEE Computer and Communications Societies. Gateway to the 21st Century (Cat. No.98.

[9]  David M. Ryan,et al.  Flight Attendant Rostering for Short-Haul Airline Operations , 1997, Oper. Res..

[10]  Danny Raz,et al.  A simple efficient approximation scheme for the restricted shortest path problem , 2001, Oper. Res. Lett..

[11]  Chak-Kuen Wong,et al.  Time-varying shortest path problems with constraints , 1997, Networks.

[12]  Marwan Krunz,et al.  Multi-constrained optimal path selection , 2001, Proceedings IEEE INFOCOM 2001. Conference on Computer Communications. Twentieth Annual Joint Conference of the IEEE Computer and Communications Society (Cat. No.01CH37213).

[13]  Refael Hassin,et al.  Approximation Schemes for the Restricted Shortest Path Problem , 1992, Math. Oper. Res..

[14]  Yi Lu,et al.  Path Problems in Temporal Graphs , 2014, Proc. VLDB Endow..

[15]  Piet Van Mieghem,et al.  Concepts of exact QoS routing algorithms , 2004, IEEE/ACM Transactions on Networking.

[16]  K. Nachtigall.  Time depending shortest-path problems with applications to railway networks , 1995 .

[17]  Nils J. Nilsson,et al.  A Formal Basis for the Heuristic Determination of Minimum Cost Paths , 1968, IEEE Trans. Syst. Sci. Cybern..