5 research outputs found
Routing in Polygonal Domains
We consider the problem of routing a data packet through the visibility graph of a polygonal domain P with n vertices and h holes. We may preprocess P to obtain a label and a routing table for each vertex. Then, we must be able to route a data packet between any two vertices p and q of Pwhere each step must use only the label of the target node q and the routing table of the current node.
For any fixed eps > 0, we pre ent a routing scheme that always achieves a routing path that exceeds the shortest path by a factor of at most 1 + eps. The labels have O(log n) bits, and the routing tables are of size O((eps^{-1} + h) log n). The preprocessing time is O(n^2 log n + hn^2 + eps^{-1}hn). It can be improved to O(n 2 + eps^{-1}n) for simple polygons
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