Constraint-based routing for ad-hoc networks

Abstract

Future large-scale networks, such as sensor networks, will consist of hundreds and even thousands of wirelessly connected sensor and actuator nodes. The nodes are typically highly resource-constrained (processor, memory, and power), have limited communication range, and are prone to failure. Furthermore, there is no global information about the exact location and connectivity of the nodes. Consequently, the explicit consideration of network and task constraints and objectives will be an important part of routing algorithms for these networks. We present a distributed constraint-based routing approach that represents destination conditions as well as routing constraints and objectives explicitly. We further present an efficient routing algorithm, CB-LRTA*, that extends traditional Learning Real-Time A* (LRTA*) with back-propagation. We evaluate CB-LRTA* using simulation and demonstrate that it improves convergence to the optimal route over LRTA*.

Full text

Constraint-based Routing for Ad-hoc Networks
Yi Shang
Dept. of Computer Engineering/Science
Univ. of Missouri-Columbia
Columbia, MO 65211
shangy@missouri.edu
Markus P.J. Fromherz, Ying Zhang and Lara S. Crawford
Palo Alto Research Center
3333 Coyote Hill Road
Palo Alto, CA 94304, U.S.A.
{fromherz,yzhang,lcrawford}@parc.com
Abstract—Future large-scale networks, such as sensor net-
works, will consist of hundreds and even thousands of wirelessly
connected sensor and actuator nodes. The nodes are typically
highly resource-constrained (processor, memory, and power),
have limited communication range, and are prone to failure.
Furthermore, there is no global information about the exact
location and connectivity of the nodes. Consequently, the explicit
consideration of network and task constraints and objectives will
be an important part of routing algorithms for these networks.
In this paper, we present a distributed constraint-based routing
approach that represents destination conditions as well as routing
constraints and objectives explicitly. We further present an
efficient routing algorithm, CB-LRTA*, that extends traditional
Learning Real-Time A* (LRTA*) with back-propagation. We
evaluate CB-LRTA* using simulation and demonstrate that it
improves convergence to the optimal route over LRTA*.
I. INTRODUCTION
Large-scale networks with hundreds and even thousands of
very small, battery-powered and wirelessly connected sensor
and actuator nodes are becoming a reality [4]. The sheer
number of devices in such networks, the resource constraints
of the nodes, and the dynamics of the environment call for
adaptive, robust, scalable, and constraint-aware algorithms
for discovery, routing, and aggregation of information. The
algorithms should be localized, use minimal storage, adapt to
changes, and have minimal communication cost.
Imagine a network of sensors sprinkled across a large
building or an area such as a forest. Typical tasks considered
for such networks are to send a message to a node at a
given location (without knowing which node or nodes are
there, or how to get there), to retrieve sensor data (e.g., sound
or temperature levels) from nodes in a given region, and to
find nodes with sensor data in a given range without any
geographical information. In some cases, one is interested in
passing on a single message and thus simply wants to find
a good path, maybe sub-optimal, to the destination quickly,
since finding the optimal path could be much more time and
energy consuming. In other cases, many packets are to be
sent between source and destination (e.g., updates on sensor
readings), and it would be better to establish a lowest cost path
or the shortest path between them. When the energy levels of
the nodes are very limited, multiple different paths may be
preferable to distribute energy usage and prolong the lifetime
of the network. Some applications add further requirements
to message routing, such as avoiding compromised regions of
the network in military applications.
In the past, algorithms proposed for discovery and routing
tasks in sensor networks [7], [12], especially those with
energy awareness, use a variant of dynamic programming, in
particular search algorithms related to Learning Real-Time A*
(LRTA*) [9], [10].
Implicitly, these algorithms encode various constraints and
objectives about the task, often in a task-specific manner.
Task representations and routing algorithms are inevitably
linked and can be hard to change as the requirements of
the task change. In this paper, we propose a constraint-based
approach for routing in ad-hoc networks. It consists of a
generic, constraint-based task representation of the discovery
problem and constraint-aware routing protocols. The approach
is a generalization of existing sensor network routing and
geographical routing protocols. The representation does not
assume a particular routing algorithm, and in fact the choice
of algorithm can be embedded in the message as well. In addi-
tion, we present a variant of LRTA*, Constraint-based Back-
propagating LRTA* (CB-LRTA*), which extends traditional
LRTA* in three ways: explicit inclusion of hard constraints,
node heuristics in addition to connection heuristics, and par-
allel learning with a distributed memory.
II. RELATED WORK
A. Ad-hoc routing protocols
Many previous ad-hoc routing protocols require greater
energy resources of the nodes and higher bandwidth than what
is available in sensor networks. For example, Dynamic Source
Routing (DSR) [6] floods a route request packet throughout the
network. Location Aided Routing (LAR) [8] improves DSR
and uses geographic location information to limit the route
request flooding to a smaller region, where it is most probable
the destination is located.
Geographic location information has been used to develop
efficient, scalable routing protocols. Geographic routing allows
routers to be stateless and requires propagation of topology
information for only a single hop. Most geographic ad-hoc
routing protocols use greedy algorithms to forward the packet
to the destination. They differ in how they recover when
greedy forwarding is impossible, e.g., at communication holes
or when avoiding obstacles.
Finn [2] proposes flooding search for recovering from local
maxima. Karp and Kung propose Greedy Perimeter Stateless
0-7803-7724-9/03/$17.00
c
° 2003 IEEE 500

Routing (GPSR) [7] to have better scalability. GPSR recovers
from local maxima by deriving a planar graph out of the
original network graph and then routing around the perimeter
of the region containing a local maximum. A drawback of
GPSR is that it tends to concentrate traffic on the perimeter
when it routes around holes or obstacles, thus burning out the
nodes on the perimeter sooner.
Geographical and Energy Aware Routing (GEAR) [12]
achieves good energy efficiency. GEAR is based on a
real-time heuristic search method, Learning Real-Time A*
(LRTA*) [10]. It uses energy aware and geographically in-
formed neighbor selection to route a packet towards the target
region. The strategy attempts to balance energy consump-
tion and thereby increase network lifetime. In related work,
CADR [1] uses a sophisticated information metric derived
from sensor data to guide the routing process.
Directed diffusion [5] is a data-centric paradigm for sensor
network applications. All communication is for named data
and all nodes are application aware. This enables diffusion
to achieve energy savings by selecting good paths. It uses
initial and periodic data flooding throughout the network. Data
generated by sensor nodes is named using attribute-value pairs.
An issue common to these algorithms is that expectations
about both the task (e.g., find the destination) and algorithm
properties (e.g., conserve energy) are built into the algorithms
and cannot be changed easily. Since routing algorithms cannot
be uploaded repeatedly onto thousands of already deployed
nodes, a more general, programmable approach is highly
desirable.
B. Real-time search methods
Real-time (heuristic) search methods interleave planning
and plan execution and restrict planning to a local area. LRTA*
is a popular real-time search method [11]. It not only acts
in real time, but also converges to a shortest path when it
solves the same planning task repeatedly. A related algorithm
is FALCONS [3], which differs in the selection of successors
and has been shown to converge to a shortest path faster than
LRTA*.
Starting from a source node, LRTA* traverses the graph
in search of the destination by using local information only.
Concretely, at current node i, a decision is made about which
node to move on to next based on information about the node
and its neighbors (Fig. 1). This information includes the known
cost c(i, j) to move to node j and the estimated cost h(j)
to move from node j to the destination. (Costs are usually
distances.) Node i chooses neighbor j with minimum value
f(j) = c(i, j) + h(j), updates its own heuristic value h(i) to
f(j), and moves on to node j.
Real-time search methods similar to LRTA* differ in two
dimensions: the size of their local search spaces and the
informedness of the initial state values. For exploration and
goal-directed search in unknown terrain, the local search space
may contain only the current state or all the known (visited)
parts of the state space. Heuristic information may or may
not be available to estimate the state values for goal-directed
received (s, find(goal)) at node i do
if found(goal) then return; end
for all j ∈ N
i
do f(j) ← c(i, j) + h(j); end
j ← argmin
j∈N
i
f(j);
h(i) ← f (j);
send(j, find(goal));
end
Fig. 1. LRTA* – Nodes i receive find request messages, compute successors
j among their neighbors N
i
, and forward the messages to these successors.
The command send(j, m) in node i sends message m to node j, which leads
to event received(i, m) in node j. In a distributed network, multiple nodes
may execute this code in parallel.
search.
III. CONSTRAINT-BASED ROUTING
We make the following assumptions about a distributed
sensor and actuator network: The system consists of a large
number of nodes that are distributed geographically, each able
to communicate with a small subset of neighbor nodes, and
equipped with a processor and a number of sensors (e.g.,
light, sound, temperature). Nodes know their own items of
interests and locations, as well as those of their neighbors
(e.g., through a publish-and-subscribe connection), but they
have no knowledge about nodes outside their neighborhood.
Items of interest include sensor values, battery level, available
memory, etc.
Typical tasks are sending and retrieving data between nodes.
There are constraints both on the destinations and the routes:
finding nodes in a certain geographic region or with sensor
readings in a given range or avoiding nodes with low battery
levels or near loud objects. The goal is to find the shortest route
to a destination node while also satisfying the route constraints
and optimizing the route objectives.
A. Constraint-based Task Representation
A sensor and actuator network is defined by a graph hV, Ei,
with V the set of n nodes and E the set of edges. Each node i
has a set of neighbors N
i
⊆ V with which it can communicate.
Nodes are described by sets of attributes. These may denote
any interesting node characteristic, such as node position and
sensor values. Data is generated by sensor nodes in the form
of attribute-value pairs. For example, a node i has positions
x
i
and y
i
, light sensor value l
i
, temperature sensor value t
i
,
energy level e
i
, etc.
Specifically, a routing task T (V, E, s, O
d
, C
r
, O
r
) is defined
by a network graph hV, Ei, a source node s, a set of destination
objectives O
d
, a set of route constraints C
r
, and a set of
route objectives O
r
. Starting at the source node s, the goal
of the search is to find a destination node that minimizes the
destination objectives, as well as a route that satisfies the route
constraints and minimize the route objectives. Constraints and
objectives are defined on node attributes.
Examples for destination objectives are location-based ob-
jectives, e.g., finding the node in region R, and sensor-based

objectives, e.g., finding a node with temperature level below
t
d
.
Examples for route constraints are constraints to avoid
obstacles or “risky” areas, e.g., avoid nodes in the light,
C
r
= {l ≤ l
t
}, where l
t
is a threshold below which the node
is considered to be in the dark, or constraints to use only nodes
with energy level above a certain level e
t
, C
r
= {e ≥ e
t
}.
Route objectives can be used to describe preferences between
alternative paths, e.g., prefer nodes with high remaining energy
levels, O
r
= {e
max
−e}. where e
max
is the maximum possible
energy level.
The requesting node initiates an interest in the form of
T (V, E, s, O
d
, C
r
, O
r
) and sends it to one of its neighbor
nodes. Intermediate nodes in the network forward the mes-
sage until it reaches a destination. Each node maintains an
interest cache, containing one entry for each distinct interest.
Each entry has several fields: destination objectives, routing
constraints, routing objectives, time stamp of the last received
matching interest, parent field specifying where the interest
comes from and requested data rate, a duration field indicating
the approximate lifetime of the interest, information about its
neighbor nodes, such as heuristic values estimating the best
cost going through a neighbor node, and others.
B. Heuristic Functions in LRTA*
Route discovery is carried out by agent-based search al-
gorithms, such as LRTA*. The heuristic function used for
selecting successor nodes is f (j) = c(i, j) + h(j) where the
heuristic function h(j) estimates the true cost from node j to
a destination node.
Let c(i, j) represent the total cost of going from node i
to j, which consists of the route objective values of node j
and the costs of moving a message to node j from node i
and processing the message at node j. Assuming the message
transmission and processing costs are constant C, i.e., the same
for all nodes, we have
c(i, j) = C +
X
o
l
∈O
r
w
l
o
l
(j),
where w
l
are weights.
There are various h functions. When the cost of future nodes
cannot be estimated, we set h(j) to 0. Alternatively, we can
use the route objectives in h, such as in a weighted sum form
h(j) =
X
o
k
∈O
d
w
k
o
k
(j) (1)
where o
k
(j) is the value of an destination objective o
k
at
node j and w
k
is a weight. Examples of objective functions
are |x(j) − p| (the coordinate of the destination is at p),
and max(x(j) − u, 0) + max(l − x(j), 0) (the coordinate of
the destination is between l and u). The objectives may be
normalized by the attribute domain ranges.
As an example, consider the following task:
O
d
= {|x − x
d
|, |y − y
d
|}, C
r
= {l ≤ l
t
}, O
r
= {e
max
− e}.
(2)
start (id, O
d
, C
r
, O
r
) at node i do
record source(id);
send(i,find(id, O
d
, C
r
, O
r
));
end
received (s,find(id, O
d
, C
r
, O
r
)) at node i do
if no record sender(id) exists then
record (sender(id) = s);
end
if the values of O
d
at i satisfy stopping criteria then
send(sender(id),back(id, O
d
, C
r
, O
r
));
return;
end
N
0
i
← {j ∈ N
i
| satisfied(C
r
, j)};
for all j ∈ N
0
i
do
f(j) ← c(i, j) + h(j);
end
j ← argmin
j∈N
0
i
f(j);
h(i) ← f (j);
send(j, find(id, O
d
, C
r
, O
r
));
end
received (s,back(id, O
d
, C
r
, O
r
)) at node i do
if source(id) then return; end
N
0
i
← {j ∈ N
i
| satisfied(C
r
, j)};
for all j ∈ N
0
i
do
f(j) ← c(i, j) + h(j);
end
j ← argmin
j∈N
0
i
f(j);
h(i) ← f (j);
send(sender(id),back(id, O
d
, C
r
, O
r
));
end
Fig. 2. CB-LRTA* – Command start() in the source node starts the search.
Command send(j, m) in node i leads to event received(i, m) in node j. Here,
the message includes a message identifier id as well as the constraints and
objectives. Since different messages with unrelated constraints and objectives
may be passing through, the identifier is used to distinguish h entries for these
different messages.
The initial value of h(j) is |x
j
− x
d
| + |y
j
− y
d
| and f(j) =
C + (e
max
− e
j
) + h(j). The successor nodes must satisfy the
route constraints in C
r
, which are not included in f.
IV. CB-LRTA*
CB-LRTA* is a variation of LRTA* using the generalized,
attribute-based heuristic functions for neighbor evaluation
(Fig. 2). CB-LRTA* uses the route objectives and constraints
in node selection and the destination objectives to determine
termination. Decisions for forwarding a message are made
locally at each node based on the task specification, O
d
, C
r
,
and O
r
.
Here, we illustrate the behavior of CB-LRTA* using some
simple examples, assuming the nodes know their locations.
Example 1. O
d
= {|x−x
d
|, |y −y
d
|}, C
r
= {}, O
r
= {}. CB-
LRTA* becomes geographic routing and moves to a neighbor
node closest to the destination.

Example 2. O
d
= {x−x
d
|, |y −y
d
|}, C
r
= {}, O
r
= {e
max
−
e}. CB-LRTA* tends to move to a neighbor node closer to the
destination and with higher energy level. Its behavior is similar
to GEAR.
Example 3. O
d
= {max(t − t
d
, 0)}, C
r
= {l ≤ l
t
}, O
r
=
{e
max
− e}. CB-LRTA* tends to move to a neighbor node
with lower temperature and higher energy level, which must
have a light sensor value less than l
t
.
Furthermore, CB-LRTA* includes a back-propagation
mechanism that goes back from the destination to the source
node along the forwarding route with redundant loops re-
moved, updating heuristic values of the nodes on the way. As
will be shown, this can significantly speed up convergence to
the optimal route from source to destination. Back-propagation
is particularly appropriate for tasks in sensor networks, where
acknowledgments and retrieved sensor data often have to be
sent back from destination to source anyway. By piggybacking
the heuristic values on reverse messages, no additional packets
need to be sent, and the amount of additional communication
and computation can be kept minimal.
V. EXPERIMENTS
We call a “message” the data to be sent from source to
destination, with acknowledgment sent back to the source. We
call a “packet” the exchange between two nodes to forward a
message. We count both the number of packets from source
to destination (“forward”) and the total number of packets for
both forwarding and acknowledging a message (“total”).
The performance measure is the cost incurred until conver-
gence to the optimal route. All data is averaged over 100 runs
per experiment, using a packet-level simulator shown in Fig. 3.
A. Scaling with obstacles
Fig. 4 shows the scaling of sending messages in a 400
node network with increasing number of obstacles. The task is
defined as in Eq. (2) but without the route objectives. Obstacles
(nodes with high light sensor values) are chosen randomly
such that a path from source to destination exists.
Fig. 4a compares CB-LRTA* with LRTA* on the number
of forward and total packets until convergence to the optimal
path. The number of packets for the first path is shown for
reference. The result shows that back-propagation significantly
improves convergence, whether comparing forward or total
number of packets. The total number of packets of CB-LRTA*
is comparable to the forward number of packets of LRTA*.
This makes CB-LRTA* competitive even in a non-distributed
context, where LRTA* would restart directly at the source for
multiple trials, while CB-LRTA* needs to trace the path back
to the source. The poor performance of LRTA* in Fig. 4a is
due to LRTA* needing many extra messages (up to twice as
many) for small improvements before it converges. Finally,
we observe at least one phase transition around 40%, from
where it becomes easier to find the route due to the decreasing
number of route options.
Fig. 3. Front end (upper) and animation (lower) of the routing simulation
environment
B. Scaling with size
Fig. 5 shows the scaling of sending messages in networks
with increasing size, while holding the ratio of obstacles
constant at 30%. The same task as before is used. Again,
CB-LRTA* and LRTA* are compared, showing the number
of forward and total packets until convergence to the optimal
path, as well as the number of packets for the first path.
Again, CB-LRTA* performs significantly better and the
large difference between CB-LRTA* and LRTA* is primarily
due to additional messages (or retries) needed by LRTA*
before search converges.
C. Performance with message interleaving
A distributed network offers the option to release multi-
ple messages with short delays instead of waiting for the

0 10 20 30 40 50 60 70 80
0
200
400
600
800
1000
1200
% Obstacles
Packets
Forward (first path)
Forward (no bp)
Total (no bp)
Forward (bp)
Total (bp)
Fig. 4. Scaling with increasing number of obstacles: average number of
packets until convergence with and without back-propagation (“bp”) (400
nodes, random source and destination nodes at least 20 hops apart)
200 300 400 500 600 700 800 900 1000
0
500
1000
1500
2000
2500
3000
3500
4000
Network Size
Packets
Forward (first path)
Forward (no bp)
Total (no bp)
Forward (bp)
Total (bp)
Fig. 5. Scaling with increasing number of nodes: average number of packets
until convergence (random source and destination nodes at least (w + l)/4
hops apart (width w, length l), 30% random obstacles)
acknowledgment of each message. Fig. 6 compares results
with increasing release delay (in simulation time units) for
100 messages. The case of waiting for acknowledgment is not
shown, but would be similar to a release delay of 80. As can
be seen, shorter release delays incur a very small amount of
overhead in the total number of packets to be sent, but the
total time to deliver all the messages is significantly shorter.
D. Load-balancing through route objectives
Route objectives can effectively balance the usage of nodes
in message routing. For example, without a route objective
of using higher energy nodes, repeated messages are routed
through the most direct path and quickly use up the nodes’ en-
ergies, which erects a significant barrier for messages between
other source and destination nodes in the network. Adding the
route objective, in contrast, leads to a much more preferable
distribution of energy usage in the network.
VI. CONCLUSIONS
The research presented here is a first step towards a generic
approach of representing and solving routing tasks in resource-
constrained, ad-hoc networks as constraint problems. We
present an explicit representation of routing and destination
0 10 20 30 40 50 60 70 80
0
1000
2000
3000
4000
5000
6000
7000
8000
Release Delay
Packets; Time
Total Packets
Total Time
Fig. 6. Scaling with increasing release delay between messages: average total
number of packets and simulation time for 100 messages and 30% random
obstacles. )
constraints and objectives, as well as CB-LRTA*, a constraint-
based, real-time search method that extends LRTA* and con-
verges faster than LRTA*. We have successfully implemented
this method on a real sensor network.
In future work, an extension is to make the routing al-
gorithm time-aware, so that secondary objectives (such as
load-balancing) can be traded off against primary objectives
(such as reaching the destination) when routing messages
with deadlines. Furthermore, other real-time search algorithms,
such as FALCONS, may be extended for routing applications.
VII. ACKNOWLEDGEMENTS
This work was partially supported by DARPA under con-
tract F33615-01-C-1904.
REFERENCES
[1] M. Chu, H. Haussecker, and F. Zhao. Scalable information-driven sensor
querying and routing for ad hoc heterogeneous sensor networks. Int.
Journal on High Performance Computing Applications, June 2002.
[2] G. G. Finn. Routing and addressing problems in large metropolitan-scale
internetworks. Technical report isi/rr-87-180, USC/ISI, March 1987.
[3] D. Furcy and S. Koenig. Speeding up the convergence of real-time
search. In Proc. 17th National Conf. on Artificial Intelligence, pages
891–897, 2000.
[4] D. Ganesan, B. Krishnamachari, A. Woo, D. Culler, D. Estrin, and
S. Wicker. An empirical study of epidemic algorithms in large scale mul-
tihop wireless networks. Technical report ucla/csd-tr-02-0013, UCLA
Computer Science Department, 2002.
[5] C. Intanagonwiwat, R. Govindan, and D. Estrin. Directed diffusion:
A scalable and robust communication paradigm for sensor networks.
In Proc. 6th Int’l Conf. on Mobile Computing and Networks (ACM
Mobicom), Boston, MA, 2000.
[6] D. B. Johnson and D. B. Maltz. Dynamic source routing in ad hoc
wireless networks. In T. Imielinski and H. Korth, editors, Mobile
Computing, pages 153–181. Kluwer Academic, 1996.
[7] B. Karp and H. T. Kung. GPSR: Greedy perimeter stateless routing for
wireless networks. In Proc. 6th Int’l Conf. on Mobile Computing and
Networks (ACM Mobicom), Boston, MA, 2000.
[8] Y. Ko and N. Vaidya. Location-aided routing in mobile adhoc networks.
In Proc. 4th Annual ACM/IEEE Int’l Conf. on Mobile Computing and
Networks (Mobicom), Dallas, TX, 1998.
[9] S. Koenig. Agent-centered search. AI Magazine, 22(4):109–131, 2001.
[10] R. Korf. Real-time heuristic search. Artificial Intelligence, 42(2-3):189–
211, 1990.

[11] M. Yokoo and T. Ishida. Search algorithms for agents. In G. Weiss,
editor, Multiagent Systems: A Modern Approach to Distributed Artificial
Intelligence, chapter 4, pages 165–199. The MIT Press, Cambridge, MA,
1999.
[12] Y. Yu, R. Govindan, and D. Estrin. Geographical and energy aware
routing: a recursive data dissemination protocol for wireless sensor net-
works. Technical report ucla/csd-tr-01-0023, UCLA Computer Science
Department, May 2001.