Routing with bounded buffers and hotpotato routing in vertexsymmetric networks
Abstract

O(log n · D), with high probability (w.h.p.), if constant size buffers are available for each edge,

O(log n · Dlog^{1+∈}D) for any ε > 0, w.h.p., if for each vertex buffers of size 3, independent of the degree of the network, are available.
The schedule for the second result can be converted into a hotpotato routing schedule, if a selfloop is added to each vertex.
E.g., for any bounded degree vertexsymmetric network with selfloops and diameter O(log n) (among them expanders) we obtain a hotpotato routing protocol that needs time O(log^{2}n(log log n)^{1+∈}) for any ε > 0 to route a randomly chosen function and any permutation, w.h.p.
Our protocols also allow bounds on the space requirements for vertices and packets in the network: we show that O(D(log log D+log d)) space suffices for storing routing information in the vertices and O(log D) space suffices for storing routing information in the packets.
This is the first result about spaceefficient routing where both the buffer size and the space for storing routing information is strongly bounded. Previous results are only known about routing protocols that either can reduce the buffer size or the space for storing routing information. For spaceefficient hotpotato routing no general results are known.
In order to prove the results above we introduce a new offline routing protocol for arbitrary networks which is fast even for vertex buffers of size 1. This bound can not be reached by any other nontrivial offline routing protocol yet.
Keywords
Buffer Size Output Buffer Arbitrary Network Path System Local LemmaPreview
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