Multihop wireless networks

Geographical Routing• Karp, B. and Kung, H.T., Greedy Perimeter Stateless Routing for

Wireless Networks, in MobiCom 2000.• Using node’s geographical information to route.• Assumes:

– Nodes know their locations, e.g., by having GPS– Nodes know their one-hop neighbors, e.g., by asking every node to

broadcast beacon signals periodically, and one-hop ONLY– Knows the location of the destination, e.g., by overhearing or

broadcasting– The connectivity is a unit disc (arguable)

• Advantage– Nodes do not have to store too many information. Given a constant

amount of information in the packet, it can make routing decisions– AODV and DSR need to ask nodes to store hop-by-hop routing tables

or complete routing paths

Greedy Routing

• First idea:– At node A, if the destination is t, pick the next hop

neighbor that is closest to t among all neighbors of A

• To implement greedy routing, the packet needs to carry the destination’s location

Greedy routing

• As many greedy algorithms, greedy routing may run into problems.

Planar Graphs• Consider routing in planar graphs.

– A planar graph is a graph where there is no crossing edges.– The area closed by a set of edges is called a “face.” The outside

is also called a face.– Faces are connected.– There are ways to construct planar graphs by deleting edges.

Face Routing• Keep left hand on the wall, walk until hit the straight line

connecting source to destination.• Then switch to the next face.• The point is that every time you are switching to a face closer to the

destination.

Face routing• Face Routing may fail only if there is

no path to the destination.– Face routing will forward the packet

to the face– Then it will circle around the face,

without finding a point intersecting the line from s to t other than the last intersection point Lf.

– Eventually it will hit the first edge when entered this face, e0, and will realize that the destination is unreachable

– So, face routing needs to store in the packet header• Destination location• The starting point location• Lf• e0

GPSR

• The idea is to first try greedy routing, which should cover most of the cases. In case greedy routing fails, try face routing.

Hierarchical Routing• AODV and DSR is suitable for

– small and flat networks, such as wireless ad hoc networks, where all nodes are the same, i.e., have similar processing power, similar battery.

– relatively small, such that the number of hop count is reasonable• In some other networks, nodes can be different.

– In wireless sensor networks, there may be cluster head nodes and the sensor nodes

– In wireless mesh networks, there are mesh routers and mesh clients– Forwarding message is costly, better let the nodes with more power

supply do it• In some networks, the size of the network can be very large

– A wireless sensors network for some applications should have thousands of nodes

Hierarchical Routing• Hierarchical routing is more efficient in these scenarios.• The basic idea is

– partition the entire network into regions or clusters. – Select one or more nodes as the cluster head – The routing is nodes -> cluster head A -> cluster head B ->

cluster head C -> nodes– The routing between cluster heads and the routing within a

cluster may follow different protocols, just as BGP and OSPF.• Achieves

– Better scalability – Removes the load to less powerful nodes

A Case Study of Intra-cluster Routing in Wireless Sensor networks

• Z. Zhang, M. Ma and Y. Yang, Energy Efficient Multi-Hop Polling in Clusters of Two-Layered Heterogeneous Sensor Networks ,  IEEE Transactions on Computers, vol. 57, no. 2, pp. 231-245, Feb. 2008

• Focusing on intra-cluster routing.• An example of cross-layer design. Merging

network layer with MAC layer.

Wireless Sensor Networks

• A large number of sensors are deployed in an area

• Challenges– the network must

be scalable– to reduce the cost,

sensors should be made as simple as possible

– must be energy efficient

Wireless Sensor Networks

• To make network scalable, introduce hierarchies.

• Sensors only communicate within a cluster. The inter-cluster communication is taken care of by the cluster head.

Wireless Sensor Networks

• Existing works such as LEACH, HEED, for cluster head selection.

• Disadvantage: Sensors become more complicated because every sensor could be elected as cluster head.

Wireless Sensor Networks

• First idea: Instead of selecting cluster head among the sensors, why not simply add some more powerful sensors to the network as cluster head?

Wireless Sensor Networks

• Advantage of such a two-layer heterogeneous network:– Better scalability – Majority of the sensors

can be made very simple

• Question: How does the cluster head collect data from the sensors in an energy efficient way?

Wireless Sensor Networks

• Data collecting can be done by letting sensors make their own decisions when to send packets.

• Problem – energy wasted in collision, collision avoidance, idle-listening, etc.

Wireless Sensor Networks• Second idea: Since we already have a powerful cluster head,

why not use it as a master and use polling to get data from sensors?

• Polling – Cluster head sends out polling messages, only those are polled will send packets.

• It is energy efficient because no energy will be wasted in collision and collision avoidance, and by designing a good polling schedule, the time needed in data collection is reduced so the idle listening time is reduced.

Routing

• With centralized control, can find the optimal routing paths.

• Optimal in the sense that the maximum load of the sensors is minimized, such that the minimum life time of the sensors are maximized.

S1

S2

S4

S3

S5

S6

t

S1 t

S2 S4

S3 S5 S6

t

t

Routing• The optimal forwarding path

problem. Given the topology and the traffic generated load at each node, find a set of forwarding paths such that the maximum transmission load of sensors is minimized.

• For example, given the load of A,B, C, D, E is 1,6,1,1,1, respectively, the traffic assignment should be as shown in the figure. NOT and tree.

• Solution: maximum flow algorithms.

C

E D

BA

H

1

3 3

1

4 4

Routing• Draw a graph which

– Breaks a node into two nodes, such as turning A into A->a. Let the link capacity be c for all such new links. A is called the receiving node and a is called the transmitting node.

– Introduce a source node s which connects to all receiving nodes, and let link between the source node and the receiving node has a capacity equal to the load of the original node.

– All other links have infinite capacity.• Set c=1 and run the maximum flow

algorithm (e.g., Ford-Fulkson). If the maximum flow is below the total load of the nodes, increment c by one. Otherwise quit.

c

E D

ba

H

cc

c

c

AB

C

e dc

s

1

61

11

Polling Schedule

• A poor schedule could take six time slots.

S1

S2

S3

S5

S4

S6

t

S1 t

time slot 1

S2

time slot 2

S4 S4

time slot 3

t S3

time slot 4

S5 S5

time slot 5

S6 S6

time slot 6

t

Polling Schedule

• To get a faster schedule, it is crucial to encourage spatial reuse: Allow simultaneous transmissions if they do not cause destructive interferences.

• Such transmission are called compatible.

S1

S2

S3

S5

S6

S4

t

S1 t

S2 S4S3 S5

Polling Schedule

S1

S2

S3

• A good schedule needs only three time slots.

S6

S5

S4

t

S1 t

time slot 1

S2 S4S3 S5

time slot 2

S4 t

S5 S6

time slot 3

S6 t

Optimal Polling Schedule

• The compatibilities of transmissions can be found by measuring the received signal strength.

• The Multi Hop Polling Problem: Given relaying paths and the compatibilities, find the minimum time schedule (optimal schedule).

Optimal Polling Schedule

• Use the Hamilton Path Problem. Given any instance of HP Problem, construct an MHP instance, called the two-level star.

• Each node in the graph corresponds to a branch.• Each sensor in the second level has exactly one packet to

send. Sensors in the first level have no packet to send.

Optimal Polling Schedule

• The connection pattern in the HP instance determines the compatibility in the two level star: If there is edge (v1,v2), S1–>t and S’

2–>S2 are compatible, so do S2–>t and S’

1–>S1.

v1

v2

v3

v4

v5

t

S2S1 S4S3 S5

S’1 S’5S’4S’3S’2

Optimal Polling Schedule

As a result of this construction, a schedule with k=n+1 will determine a Hamiltonian Path in the original graph.

Online Polling Algorithm

• Another challenge is that the algorithm must be able to run on-line.– Packet can be lost in some links, and the cluster

head must ask the sensor to send it again – new requests may arrive while data gathering is going on

Online Polling Algorithm

• The algorithm is simple: Check the requests in an arbitrary order, add a request to the schedule if it is compatible the current schedule.

• Time complexity: linear to input size.

Online Polling Algorithm

Reading• http://www.eecs.harvard.edu/~htk/publication/2000-mobi-karp-kung.pdf