1 research outputs found
Routing in Histograms
Let be an -monotone orthogonal polygon with vertices. We call
a simple histogram if its upper boundary is a single edge; and a double
histogram if it has a horizontal chord from the left boundary to the right
boundary. Two points and in are co-visible if and only if the
(axis-parallel) rectangle spanned by and completely lies in . In the
-visibility graph of , we connect two vertices of with an edge
if and only if they are co-visible.
We consider routing with preprocessing in . We may preprocess to
obtain a label and a routing table for each vertex of . Then, we must be
able to route a packet between any two vertices and of , where each
step may use only the label of the target node , the routing table and
neighborhood of the current node, and the packet header.
We present a routing scheme for double histograms that sends any data packet
along a path whose length is at most twice the (unweighted) shortest path
distance between the endpoints. In our scheme, the labels, routing tables, and
headers need bits. For the case of simple histograms, we obtain a
routing scheme with optimal routing paths, -bit labels, one-bit
routing tables, and no headers.Comment: 18 pages, 11 figure