Routing Algorithms: Shortest Path, Widest Path, and Spanning Tree

In this chapter, we first describe two classes of routing algorithms: shortest path routing and widest path routing. They appear in network routing in many ways and have played critical roles in the development of routing protocols. For example, shortest path routing is used in IP networks is based on the addition cost property. Widest path routing is used for call routing in circuit-switched networks and MPLS networks and is based on the non-additive concave cost property. Widest path routing is also part of quality-of-service (QoS) routing.

[1]  João C. N. Clímaco,et al.  An algorithm for ranking quickest simple paths , 2005, Comput. Oper. Res..

[2]  J. Kruskal On the shortest spanning subtree of a graph and the traveling salesman problem , 1956 .

[3]  M. Pollack Letter to the Editor—The Maximum Capacity Through a Network , 1960 .

[4]  A. Khanna,et al.  The revised ARPANET routing metric , 1989, SIGCOMM 1989.

[5]  D. R. Fulkerson,et al.  Maximal Flow Through a Network , 1956 .

[6]  Y. H. Chin,et al.  The quickest path problem , 1990, Comput. Oper. Res..

[7]  Michel X. Goemans,et al.  A catalog of steiner tree formulations , 1993, Networks.

[8]  Robert Sedgewick,et al.  Algorithms in Java, Part 5: Graph Algorithms , 2003 .

[9]  Eric C. Rosen,et al.  The New Routing Algorithm for the ARPANET , 1980, IEEE Trans. Commun..

[10]  Kurt Mehlhorn,et al.  A Faster Approximation Algorithm for the Steiner Problem in Graphs , 1988, Inf. Process. Lett..

[11]  Antonio Sedeño-Noda,et al.  On the K shortest path trees problem , 2010, Eur. J. Oper. Res..

[12]  Jon Crowcroft,et al.  Quality-of-Service Routing for Supporting Multimedia Applications , 1996, IEEE J. Sel. Areas Commun..

[13]  David C. Walden,et al.  The ARPA Network Design Decisions , 1977, Comput. Networks.

[14]  Richard Bellman,et al.  ON A ROUTING PROBLEM , 1958 .

[15]  J. Ben Rosen,et al.  Algorithms for the quickest path problem and the enumeration of quickest paths , 1991, Comput. Oper. Res..

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

[17]  I. Richer,et al.  A Review of the Development and Performance of the ARPANET Routing Algorithm , 1978, IEEE Trans. Commun..

[18]  L. R. Ford,et al.  NETWORK FLOW THEORY , 1956 .

[19]  George Markowsky,et al.  A fast algorithm for Steiner trees , 1981, Acta Informatica.

[20]  J. Y. Yen Finding the K Shortest Loopless Paths in a Network , 1971 .

[21]  R. Prim Shortest connection networks and some generalizations , 1957 .

[22]  Ernesto de Queirós Vieira Martins,et al.  An algorithm for the quickest path problem , 1997, Oper. Res. Lett..

[23]  Eric C. Rosen,et al.  The Updating Protocol of ARPANET's New Routing Algorithm , 1980, Comput. Networks.

[24]  T. C. Hu Letter to the Editor---The Maximum Capacity Route Problem , 1961 .

[25]  Toshihide Ibaraki,et al.  An Algorithm for Finding K Minimum Spanning Trees , 1981, SIAM J. Comput..