Lower Bounds for Compact Routing (Extended Abstract)

We study the complexity of compact routing on arbitrary networks. We give (1) networks on n vertices which for any interval routing scheme, Ω(n) routers of the network require Ω(n) intervals on some out-going link and (2) for each d≥ 3, networks of maximal degree d which for any interval routing scheme, Ω(n) routers each require Ω(n/ log n) intervals on some out-going link. Our results give the best known worst-case lower bounds for interval routing. For the case of universal routing schemes we give (3) networks on n vertices which for any near-optimal routing scheme with stretch factor<2 a total of Ω(n2) memory bits are required, and (4) for each d ≥3, networks of maximal degree d for which any optimal (resp., near-optimal) routing scheme (resp., with stretch factor <2) requires a total of Ω(n2/log n) (resp. Ω(n2/log2n)) memory bits.

[1]  Eli Upfal,et al.  A tradeoff between space and efficiency for routing tables , 1988, STOC '88.

[2]  Cyril Gavoille,et al.  On the Compactness of Bounded Degree Graphs for Shortest Path Interval Routing , 1995, SIROCCO.

[3]  Greg N. Frederickson,et al.  Efficient Message Routing in Planar Networks , 1989, SIAM J. Comput..

[4]  C. Q. Lee,et al.  The Computer Journal , 1958, Nature.

[5]  Jan van Leeuwen,et al.  Interval Routing , 1987, Computer/law journal.

[6]  Pierre Fraigniaud,et al.  Memory requirement for universal routing schemes , 1995, PODC '95.

[7]  Jan van Leeuwen,et al.  The Complexity of Interval Routing on Random Graphs , 1995, Comput. J..

[8]  Ming Li,et al.  An Introduction to Kolmogorov Complexity and Its Applications , 2019, Texts in Computer Science.

[9]  Cyril Gavoille,et al.  Worst Case Bounds for Shortest Path Interval Routing , 1998, J. Algorithms.

[10]  Jan van Leeuwen,et al.  The Complexity of Interval Routing on Random Graphs , 1995, MFCS.

[11]  Richard B. Tan,et al.  Computer Networks with Compact Routing Tables , 1986 .

[12]  Grzegorz Rozenberg,et al.  The Book of L , 1986, Springer Berlin Heidelberg.

[13]  Nicola Santoro,et al.  Labelling and Implicit Routing in Networks , 1985, Computer/law journal.

[14]  Eli Upfal,et al.  A trade-off between space and efficiency for routing tables , 1989, JACM.

[15]  Greg N. Frederickson,et al.  Space-Efficient Message Routing in c-Decomposable Networks , 1990, SIAM J. Comput..

[16]  Jaap-Henk Hoepman,et al.  Optimal routing tables , 1996, PODC '96.

[17]  Giorgio Gambosi,et al.  Boolean Routing , 1993, WDAG.