3,260 research outputs found
Memoryless Routing in Convex Subdivisions: Random Walks are Optimal
A memoryless routing algorithm is one in which the decision about the next
edge on the route to a vertex t for a packet currently located at vertex v is
made based only on the coordinates of v, t, and the neighbourhood, N(v), of v.
The current paper explores the limitations of such algorithms by showing that,
for any (randomized) memoryless routing algorithm A, there exists a convex
subdivision on which A takes Omega(n^2) expected time to route a message
between some pair of vertices. Since this lower bound is matched by a random
walk, this result implies that the geometric information available in convex
subdivisions is not helpful for this class of routing algorithms. The current
paper also shows the existence of triangulations for which the Random-Compass
algorithm proposed by Bose etal (2002,2004) requires 2^{\Omega(n)} time to
route between some pair of vertices.Comment: 11 pages, 6 figure
Void Traversal for Guaranteed Delivery in Geometric Routing
Geometric routing algorithms like GFG (GPSR) are lightweight, scalable
algorithms that can be used to route in resource-constrained ad hoc wireless
networks. However, such algorithms run on planar graphs only. To efficiently
construct a planar graph, they require a unit-disk graph. To make the topology
unit-disk, the maximum link length in the network has to be selected
conservatively. In practical setting this leads to the designs where the node
density is rather high. Moreover, the network diameter of a planar subgraph is
greater than the original graph, which leads to longer routes. To remedy this
problem, we propose a void traversal algorithm that works on arbitrary
geometric graphs. We describe how to use this algorithm for geometric routing
with guaranteed delivery and compare its performance with GFG
Improving Routing Efficiency through Intermediate Target Based Geographic Routing
The greedy strategy of geographical routing may cause the local minimum
problem when there is a hole in the routing area. It depends on other
strategies such as perimeter routing to find a detour path, which can be long
and result in inefficiency of the routing protocol. In this paper, we propose a
new approach called Intermediate Target based Geographic Routing (ITGR) to
solve the long detour path problem. The basic idea is to use previous
experience to determine the destination areas that are shaded by the holes. The
novelty of the approach is that a single forwarding path can be used to
determine a shaded area that may cover many destination nodes. We design an
efficient method for the source to find out whether a destination node belongs
to a shaded area. The source then selects an intermediate node as the tentative
target and greedily forwards packets to it, which in turn forwards the packet
to the final destination by greedy routing. ITGR can combine multiple shaded
areas to improve the efficiency of representation and routing. We perform
simulations and demonstrate that ITGR significantly reduces the routing path
length, compared with existing geographic routing protocols
Partitioning Graph Drawings and Triangulated Simple Polygons into Greedily Routable Regions
A greedily routable region (GRR) is a closed subset of , in
which each destination point can be reached from each starting point by
choosing the direction with maximum reduction of the distance to the
destination in each point of the path.
Recently, Tan and Kermarrec proposed a geographic routing protocol for dense
wireless sensor networks based on decomposing the network area into a small
number of interior-disjoint GRRs. They showed that minimum decomposition is
NP-hard for polygons with holes.
We consider minimum GRR decomposition for plane straight-line drawings of
graphs. Here, GRRs coincide with self-approaching drawings of trees, a drawing
style which has become a popular research topic in graph drawing. We show that
minimum decomposition is still NP-hard for graphs with cycles, but can be
solved optimally for trees in polynomial time. Additionally, we give a
2-approximation for simple polygons, if a given triangulation has to be
respected.Comment: full version of a paper appearing in ISAAC 201
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