A survey on multi-constrained optimal path computation: Exact and approximate algorithms

The paper presents a survey on the techniques to solve the multi-constrained optimal path (MCOP) problem. Computing the MCOP is a task shared by many research areas, from transportation systems to telecommunication networks. In the latter, the MCOP is often related to the issue of Quality of Service (QoS) routing, which consists in finding a route between a couple of nodes that meets a series of QoS requirements such as bounded delay, packet loss, and other parameters. The MCOP problem has been faced by several authors and a plethora of solving methods is now available. In the present work, we draw the state of the art of exact and approximate MCOP computation algorithms, with particular attention to the networking area. We describe and analyse the most representative methods, and for each of them we derive the worst case computational complexity. In addition, we provide the reader with a uniform notation and with the detailed pseudo-code of various algorithms, so that the paper can indeed serve as a workable starting point for further studies on the MCOP problem.

[1]  Martin de Prycker,et al.  Asynchronous Transfer Mode, Solution for Broadband Isdn , 1991 .

[2]  Dave Katz,et al.  Traffic Engineering (TE) Extensions to OSPF Version 2 , 2003, RFC.

[3]  A. M. Geoffrion.  Proper efficiency and the theory of vector maximization , 1968 .

[4]  Fernando A. Kuipers,et al.  An overview of constraint-based path selection algorithms for QoS routing , 2002 .

[5]  Stefano Giordano,et al.  Multi-constrained path computation algorithms for Traffic Engineering over Wireless Mesh Networks , 2009, 2009 IEEE International Symposium on a World of Wireless, Mobile and Multimedia Networks & Workshops.

[6]  Gary B. Lamont,et al.  Multiobjective Evolutionary Algorithms: Analyzing the State-of-the-Art , 2000, Evolutionary Computation.

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

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

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

[10]  R. Musmanno,et al.  Label Correcting Methods to Solve Multicriteria Shortest Path Problems , 2001 .

[11]  Edsger W. Dijkstra,et al.  A note on two problems in connexion with graphs , 1959, Numerische Mathematik.

[12]  Xavier Gandibleux,et al.  A survey and annotated bibliography of multiobjective combinatorial optimization , 2000, OR Spectr..

[13]  Ronghui Hou,et al.  Approximation Algorithm for QoS Routing with Multiple Additive Constraints , 2009, 2009 IEEE International Conference on Communications.

[14]  Ossama Younis,et al.  Constraint-based routing in the internet: Basic principles and recent research , 2003, IEEE Communications Surveys & Tutorials.

[15]  Fan Chung Graham,et al.  On disjoint path pairs with wavelength continuity constraint in WDM networks , 2004, IEEE INFOCOM 2004.

[16]  Xavier Gandibleux,et al.  Martins' algorithm revisited for multi-objective shortest path problems with a MaxMin cost function , 2006, 4OR.

[17]  E. Martins.  On a multicriteria shortest path problem , 1984 .

[18]  Eric V. Denardo,et al.  Flows in Networks , 2011 .

[19]  Marta M. B. Pascoal,et al.  Deviation Algorithms for Ranking Shortest Paths , 1999, Int. J. Found. Comput. Sci..

[20]  Arunabha Sen,et al.  Finding a Path Subject to Many Additive QoS Constraints , 2007, IEEE/ACM Transactions on Networking.

[21]  Anthony Przybylski,et al.  Two phase algorithms for the bi-objective assignment problem , 2008, Eur. J. Oper. Res..

[22]  Matthias Ehrgott,et al.  A comparison of solution strategies for biobjective shortest path problems , 2009, Comput. Oper. Res..

[23]  Ralph E. Steuer,et al.  A Heuristic for Estimating Nadir Criterion Values in Multiple Objective Linear Programming , 1997, Oper. Res..

[24]  David L. Black,et al.  An Architecture for Differentiated Service , 1998 .

[25]  Sartaj Sahni,et al.  General Techniques for Combinatorial Approximation , 1977, Oper. Res..

[26]  R. Weiner.  Lecture Notes in Economics and Mathematical Systems , 1985 .

[27]  Jose Luis Esteves dos Santos,et al.  A new ranking path algorithm for the multi-objective shortest path problem , 2008 .

[28]  G. Xue,et al.  Polynomial Time Approximation Algorithms for Multi-Constrained QoS Routing , 2008, IEEE/ACM Transactions on Networking.

[29]  Xin Yuan.  Heuristic algorithms for multiconstrained quality-of-service routing , 2002, IEEE/ACM Trans. Netw..

[30]  Klara Nahrstedt,et al.  On finding multi-constrained paths , 1998, ICC '98. 1998 IEEE International Conference on Communications. Conference Record. Affiliated with SUPERCOMM'98 (Cat. No.98CH36220).

[31]  M. Ehrgott.  Approximation algorithms for combinatorial multicriteria optimization problems , 2000 .

[32]  T. Lindvall.  ON A ROUTING PROBLEM , 2004, Probability in the Engineering and Informational Sciences.

[33]  J. Paixão,et al.  LABELLING METHODS FOR THE GENERAL CASE OF THE MULTI-OBJECTIVE SHORTEST PATH PROBLEMA COMPUTATIONAL STUDY , 2007 .

[34]  Ernesto de Queirós Vieira Martins,et al.  Ranking multiobjective shortest paths , 2007 .

[35]  Zbigniew Tarapata,et al.  Selected Multicriteria Shortest Path Problems: An Analysis of Complexity, Models and Adaptation of Standard Algorithms , 2007, Int. J. Appl. Math. Comput. Sci..

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

[37]  Piet Van Mieghem,et al.  Performance evaluation of constraint-based path selection algorithms , 2004, IEEE Network.

[38]  Christos D. Zaroliagis,et al.  Multiobjective Optimization: Improved FPTAS for Shortest Paths and Non-Linear Objectives with Applications , 2006, Theory of Computing Systems.

[39]  T. N. Janakiraman,et al.  New Algorithms For Multi Objective Shortest Path Problem , 2003 .

[40]  Xavier Gandibleux,et al.  MultiObjective Programming and Goal Programming , 2003 .

[41]  Simon French,et al.  Multiple Criteria Decision Making: Theory and Application , 1981 .

[42]  Panos M. Pardalos,et al.  A survey of recent developments in multiobjective optimization , 2007, Ann. Oper. Res..

[43]  William R. McShane,et al.  A review of pedestrian safety models for urban areas in Low and Middle Income Countries , 2016 .

[44]  Graham Kendall,et al.  Search Methodologies: Introductory Tutorials in Optimization and Decision Support Techniques , 2013 .

[45]  I. Murthy,et al.  A parametric approach to solving bicriterion shortest path problems , 1991 .

[46]  E. Martins,et al.  A bicriterion shortest path algorithm , 1982 .

[47]  Piet Van Mieghem,et al.  On the complexity of QoS routing , 2003, Comput. Commun..

[48]  Xingming Liu,et al.  Heuristic algorithms for multi-constrained quality of service routing , 2001, Proceedings IEEE INFOCOM 2001. Conference on Computer Communications. Twentieth Annual Joint Conference of the IEEE Computer and Communications Society (Cat. No.01CH37213).

[49]  Vijay Srinivasan,et al.  RSVP-TE: Extensions to RSVP for LSP Tunnels , 2001, RFC.

[50]  João C. N. Clímaco,et al.  A bicriterion approach for routing problems in multimedia networks , 2003, Networks.

[51]  Ashish Goel,et al.  Efficient computation of delay-sensitive routes from one source to all destinations , 2001, Proceedings IEEE INFOCOM 2001. Conference on Computer Communications. Twentieth Annual Joint Conference of the IEEE Computer and Communications Society (Cat. No.01CH37213).

[52]  Arthur Warburton,et al.  Approximation of Pareto Optima in Multiple-Objective, Shortest-Path Problems , 1987, Oper. Res..

[53]  Sartaj Sahni,et al.  Approximation algorithms for multiconstrained quality-of-service routing , 2006, IEEE Transactions on Computers.

[54]  Piet Van Mieghem,et al.  Non-dominance in QoS routing: an implementational perspective , 2005, IEEE Communications Letters.

[55]  Karsten Weihe,et al.  On the cardinality of the Pareto set in bicriteria shortest path problems , 2006, Ann. Oper. Res..

[56]  Kim Allan Andersen,et al.  A label correcting approach for solving bicriterion shortest-path problems , 2000, Comput. Oper. Res..

[57]  Clarisse Dhaenens,et al.  Parallel partitioning method (PPM): A new exact method to solve bi-objective problems , 2007, Comput. Oper. Res..

[58]  Mihalis Yannakakis,et al.  On the approximability of trade-offs and optimal access of Web sources , 2000, Proceedings 41st Annual Symposium on Foundations of Computer Science.

[59]  Ariel Orda,et al.  Precomputation schemes for QoS routing , 2003, TNET.

[60]  Sartaj Sahni,et al.  Two techniques for fast computation of constrained shortest paths , 2004, IEEE Global Telecommunications Conference, 2004. GLOBECOM '04..

[61]  Paolo Dell'Olmo,et al.  On finding dissimilar Pareto-optimal paths , 2005, Eur. J. Oper. Res..

[62]  Alexander Schrijver,et al.  Combinatorial optimization. Polyhedra and efficiency. , 2003 .

[63]  E. Martins,et al.  An algorithm for the ranking of shortest paths , 1993 .

[64]  Klara Nahrstedt,et al.  An overview of quality of service routing for next-generation high-speed networks: problems and solutions , 1998, IEEE Netw..

[65]  D. Shier,et al.  An empirical investigation of some bicriterion shortest path algorithms , 1989 .