1 research outputs found
New routing techniques and their applications
Let be an undirected graph with vertices and edges. We
obtain the following new routing schemes:
- A routing scheme for unweighted graphs that uses space at each vertex and -bit headers, to route a message between any pair of vertices
on a -stretch path, i.e., a path of length at most
. This should be compared to the -stretch
and space distance oracle of Patrascu and Roditty [FOCS'10
and SIAM J. Comput. 2014] and to the -stretch routing scheme of Abraham
and Gavoille [DISC'11] that uses space at each vertex.
- A routing scheme for weighted graphs with normalized diameter , that
uses space at each vertex and
-bit headers, to route a message between
any pair of vertices on a -stretch path. This should be compared
to the -stretch and space distance oracle of Thorup and
Zwick [STOC'01 and J. ACM. 2005] and to the -stretch routing scheme of
Thorup and Zwick [SPAA'01] that uses space at each vertex.
Since a -stretch routing scheme must use tables of space
our result is almost tight.
- For an integer , a routing scheme for unweighted graphs that uses
space at each vertex
and -bit headers, to route a message between any
pair of vertices on a -stretch path.
- A routing scheme for weighted graphs, that uses space at each vertex and -bit headers, to route a message between any pair
of vertices on a -stretch path