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```									 QoS Topology Control and
Energy Efficient Routing

Prof. Xiaohua Jia
Dept of Computer Science,
City Univ of Hong Kong

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What’s a mobile ad hoc network?
1) Mobility
2) No wired infrastructure

S

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Power function:
p(u,v) = dα(u,v), 2 ≤ α ≤ 4

Two special features of radio transmission:
2) p(u,w) + p(w,v) < p(u,v),
relaying messages by a third node may result in
a smaller energy cost.
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Topology Control Problem

Given a set of wireless nodes V in a plane,
for each node u, adjust its transmission
power to p(u), such that the network is fully
connected and                is minimized.

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R. Ramanathan, R. Rosales-Hain, “Topology control of
multihop wireless networks using transmit power

Greedy algorithm (based on Kruskal’s MST algorithm)

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5
3
C                D
1                        1
A                B
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Side-effect edge problem
Distributed algorithms: LINT and LILT
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R. Wattenhofer, L. Li, P. Bahl and Y.M. Wang, “Distributed
topology control for power efficient operation in multihop

G: topology by max power; G’: topology by min power.
Algorithm:
1) Divide uniformly a node’s region into cones with angle α;
2) Increase a node-power until there is a neighbor in each
cone, or it reaches max power of the node.

Theorem. Let α ≤ 2π/3. G’ is connected if G is connected.

u        α

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N. Li, J. Hou and Lui Sha, “Design and Analysis of an MST-based
Topology Control Algorithm”, IEEE INFOCOM’03.
N. Li and J. Hou, “Topology control in heterogeneous wireless networks:
problems and solutions”, IEEE INFOCOM’04.

Algorithm:
1)  Collect information about maximally reachable neighbors;
2)  Construct a local MST (in terms of transmission power) among
neighbors by each node;
3)  Determine the actual power of each node (the neighbors of u in
G’ are 1-hop nodes in u’s local MST).

Theorem 1. G’ is connected if G is connected.

Theorem 2. The degree of any node in G’ is bounded by 6.

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QoS topology control

Given a set of nodes in a plane:
B, max bandwidth capacity at a node.
λs,d, end-end traffic demand between s, d.
Δs,d, maximal hop-count allowed between s, d.

Problem. Find transmission power p(i) for 0  i  n,
such that λs,d, for all pairs (s,d), can be routed within Δs,d,
and Pmax is minimized, where Pmax = max{p(i) | 0  i  n}.

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Traffic Non-splittable Formulations

Variables:
xi,j - boolean, xi,j = 1 if there is a link from node i to
node j; otherwise, xi,j = 0.
- boolean, = 1 if the route from s to d goes
through the link (i,j); otherwise         = 0.
Pmax - the maximum transmitting power of nodes.

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Traffic non-splittable
Objective : Min Pmax
Topology constraints:
i
j’       j
Transmission power constraint:

Delay constraint:                     i

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Traffic non-splittable

Bandwidth constraint:

Flow constraints:

Binary constraint:

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Traffic non-splittable

Topology of six nodes and six requests

Non-splittable case              Splittable case
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Trarffic Splittable Formulation

Variables:
and Pmax remain the same.

- amount of (s, d)’s traffics going through link (i, j).

Objective : Min Pmax

Topology constraints:
i
j’   j
Transmission power constraint:

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Formulation (cont’d)

Bandwidth constraint:

Flow constraints:

Variable constraints:

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Two steps of solution

Problem. Given a network graph G and traffic
demands between node pairs, route these
traffics in this graph, such that Lmax minimized.

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Formulation of QoS routing problem

Objective : Min Lmax
Constraints:

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Step 2. QoS topology control

Algorithm:
1) sort all node-pairs (i,j) in ascending order
according to their distance d(i,j).
2) pick up the node-pair with closest distance but
not yet connected and increase the power to
make them connected.
3) run the QoS routing algorithm on G to obtain
Lmax. If Lmax ≤ B, then stop; otherwise repeat (b)
and (c).

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Experimental results

(a) λ = 0.02B    (b) = 0.1B

(c) λ = 0.2B     (d) λ = 0.32B   18
Experimental results

max               avg            min

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node degree   12
10
8
6
4
2
0
0.025B

0.05B

0.075B

0.1B

0.125B

0.15B

0.175B

0.2B

0.225B
λm

Node-degrees versus λm

X. Jia, D. Li, and D. Du, “QoS topology control in ad
hoc wireless networks” , INFOCOM’04.
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Networks
•   Proactive protocols (routing table based), such as
DSDV (Destination Sequenced Distance Vector),
OLSR (Optimized Link State Routing), etc.
•   On-demand protocols (reactive protocols), such
as DSR (Dynamic Source Routing), AODV (Ad-
hoc On-demand Distance Vector), etc.
•   Virtual backbone based protocols, such as
Spine-based method, clustering method,
hierarchical protocols, etc.
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D. B. Johnson, D. A. Maltz, Y.C. Hu, and J. G. Jetcheva, The
Dynamic Source Routing Protocol for Mobile Ad Hoc Networks,
http://www.ietf.org, draft-ietf-manet-dsr-05.txt, Mar 01.

Dynamic Source Routing (DSR):
1.  Source s finds a route to
destination d by flooding a Rreq
packet.
2.  d replies a Rrep packet to s by
reversing the route appended to
the Rreq.
3.  s includes the route to d in each
data packet to d (called source
routing).

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Route Caching in DSR

•   Each node learns routing
information from both Rreq
and Rrep packets and
caches the routes.
•   When a node receives a
Rreq to d and it has a valid
route in its cache, it replies
the route to s.
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Charles E. Perkins, E. M. Royer and Samir R. Das, “Ad-hoc
On-Demand Distance Vector (AODV) Routing”, draft-ietf-
manet-aodv-08.txt, http://www.ietf.org, Mar 2001.

•   It is similar to DSR in route
discovery, but improves DSR by
keeping routing tables (next-hop) at
nodes (no route info in data packets).
•   When a node receives a Rreq, it sets
up a reverse path to the source in its
routing table.
•   Rrep travels along the reverse set-up
path to s and the forward-path (i.e.,
the route from s to d) is set up as the
Rrep travels to s.
•   Entries in routing table are purged
after a timeout.
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C. E. Perkins and Pravin Bhagwat, “Highly Dynamic
Destination-Sequenced Distance-Vector Routing (DSDV) for
Mobile Computers”, ACM SIGCOMM, Oct 1994, pp.234-244.

Destination Sequence Distance Vector Routing:
• It mimics the Distance Vector Routing.
• Each node keeps a routing table: next-hop and
distance to each destination, and dest-sequnce-no.
• Each node periodically exchange the routing table
with neighbors.
• Data packets are forwarded towards destinations
by using the next-hop info in routing tables on the
way.

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Power-Aware Routing

•   Define optimization goals on energy cost
for routing, e.g., minimum energy cost per
maximum minimum residual energy.
•   Assign a weight to each link according to
optimization goal, e.g., energy cost over a
•   Perform routing with minimum weight.

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Ts: broadcast tree rooted from source s;
NL(Ts): set of non-leaf nodes of Ts.
Problem. Given a set of nodes in a plane, for each node u,
adjust its transmission power p(u), to form a Ts, such that:

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To determine, for each node u:
1) Transmission power of u, and
2) The children of u.
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J. Cartigny, D.Simplot, and I. Stojmenovic, “Localized minimum-energy

Algorithm:
1)  Construct a connected topology that has min total energy.
2)  Derive the broadcast tree from the min-energy topology
using neighbor elimination scheme.

S

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J.E. Wieselthier, G. D. Nguyen, and A. Ephremides, “On the
Construction of Energy-Efficient Broadcast and Multicast
Trees in Wireless Networks”, IEEE Infocom’00.

1) It is based on Prim’s MST algorithm.
2) Starting from s, each time a new node that can be
connected by a tree-node with least incremental power is
added to the tree, until all nodes are in the tree.

s

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Given Transmission Power

p(v): transmission power of node v;
Ts: broadcast tree rooted from source s;
NL(Ts): set of non-leaf nodes of Ts.
Problem. Given a set of nodes in a plane
and p(v) for each node v, find a Ts that:

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Transforming the problem to the
Steiner tree problem

The broadcast routing problem is transformed to: finding a
directed tree Ts’ in G’ that spans all nodes in V’ and the
total weights of Ts’ is minimized.
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A Greedy Heuristic

U: uncovered set; D: covered set;
Vi: set of outgoing neighbors of node i;
1) D ←Vs; U ← V – Vs;
2) Pick from D a node i that has the largest
value of: | Vi∩U|/p(i);
D ← D + Vi; U ← U - Vi;
3) Repeat step 2 until D = V.
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A Node-weighted Steiner Tree Based Heuristic

Theorem 1. Given G(V, E) and s, this heuristic
can output a broadcast tree in time O(n4).

Theorem 2. The approximation ratio is at most
2ln(n-1)+1.

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Experimental Results

4000                                                    4000
NST-h                                                   NST-h
3750        Greedy-h                                    3750        Greedy-h
SPT-h                                                   SPT-h
3500
3500
energy cost

energy cost
3250
3250
3000
2750                                                    3000

2500                                                    2750
2250                                                    2500
2000
2250
0   20     40     60    80   100
0   20     40     60    80   100
the num ber of nodes
the num ber of nodes

D. Li , Xiaohua Jia and H. Liu, "Energy efficient broadcast routing in ad
hoc wireless networks", IEEE Trans on Mobile Computing, Vol. 3, No.
2, Apr - Jun, 2004, pp.144-151.

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Energy-Balanced Multicast Routing

Given a wireless network G(V,E):
Ei – initial energy at node i.
wi,j – power cost per time-unit on link li,j, wi,j = dαi,j.
Problem. For a multicast request (s, D, t), find a routing tree,
such that the minimal remaining energy of nodes is
maximized after the multicast session.

S. Cheng, X. Jia, F. Hung, and Y. Wang, “Energy efficient broadcasting
and multicasting in static wireless ad hoc networks”, IEEE Trans on
Wireless Communications.

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duration routing

Given a wireless network G(V,E):
Ei – initial energy at node i;
wi,j – power cost per time-unit on link li,j.

Problem. Find a set of broadcast / multicast
trees, such that the duration of the broadcast /
multicast session is maximized.

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The End

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