We give complete characterizations for the classes of graphs with uniform cost links that admit optimum all shortest paths 1-SLIRS (strict linear interval routing schemes) and 1-LIRS (linear interval routing schemes). The characterization of all the interval routing schemes with uniform cost links that represent only a single shortest path is known to be NP-complete, For any integer k > 0, we also show that the class of graphs with dynamic cost links that admit optimum all shortest paths L-IRS (SIRS, LIRS, SLIRS) is equivalent to the class of graphs with dynamic cost links that admit an optimum single shortest path l-IRS (SIRS, LIRS, SLIRS) and also equivalent to the class of graphs with dynamic cost links that admit single paths up to any constant stretch factor k-IRS (SIRS, LIRS, SLIRS). (C) 2001 John Wiley & Sons, Inc.
Flammini, M., Gambosi, G., Nanni, U., Tan, R.b. (2001). Characterization results of all shortest paths interval routing schemes. NETWORKS, 37(4), 225-232 [10.1002/net.1017].
Characterization results of all shortest paths interval routing schemes
GAMBOSI, GIORGIO;
2001-01-01
Abstract
We give complete characterizations for the classes of graphs with uniform cost links that admit optimum all shortest paths 1-SLIRS (strict linear interval routing schemes) and 1-LIRS (linear interval routing schemes). The characterization of all the interval routing schemes with uniform cost links that represent only a single shortest path is known to be NP-complete, For any integer k > 0, we also show that the class of graphs with dynamic cost links that admit optimum all shortest paths L-IRS (SIRS, LIRS, SLIRS) is equivalent to the class of graphs with dynamic cost links that admit an optimum single shortest path l-IRS (SIRS, LIRS, SLIRS) and also equivalent to the class of graphs with dynamic cost links that admit single paths up to any constant stretch factor k-IRS (SIRS, LIRS, SLIRS). (C) 2001 John Wiley & Sons, Inc.Questo articolo è pubblicato sotto una Licenza Licenza Creative Commons
