1. Research: algorithmic solutions for networking
Prof. Michael Segal
Research: algorithmic solutions for networking
Clustering of networks: spanners
Minimal-energy solutions (saving battery life-time)
Efficient information routing/switching with QoS
Identification of core nodes in networks
Fast scheduling for load balancing and throughput

2. Techniques Keeping local information in hosts
Finding good geometric structures in the network.
Distributed solutions for updating structures.
Graph algorithmic theoretic/experimental network analysis.

3. Wireless Ad-Hoc Network
Set of transceivers communicating by radio

4. Wireless Ad-Hoc Network
Each transceiver has a transmission power
which results in a transmission range

5. Wireless Ad-Hoc Network
Transceiver receives transmission from only if

6. Wireless Ad-Hoc Network
As a result a directed communication graph is
induced

7. Definition
A set of transceivers

8. Definition
A set of transceivers
is the power assignment

9. Definition
A set of transceivers
is the power assignment

10. Definitions A set of transceivers is the power assignment
is the communication graph

11. Definitions A set of transceivers is the power assignment
is the communication graph
is the cost of the assignment

12. Example: Broadcast A graph is a h-bounded-hop broadcast
graph rooted at if there is a path from to any
and the number of hops is limited by
4-bounded-hop
broadcast

13. Example: Broadcast A graph is a k-h-broadcast graph if
it remains h-bounded-hop broadcast graph
even with the removal of up to nodes
2-4-bounded-hop
broadcast

14. Example: Broadcast A graph is a k-h-broadcast graph if
it remains h-bounded-hop broadcast graph
even with the removal of up to nodes
2-vertex disjoint
paths under 4 hops

15. Example: Broadcast A graph is a k-h-broadcast graph if
it remains h-bounded-hop broadcast graph
even with the removal of up to nodes
2-vertex disjoint
paths under 4 hops

16. Spanners What is a spanner? A spanning subgraph that approximates
some measure of the original graph

17. Spanners What is a spanner? A spanning subgraph that approximates
some measure of the original graph
E.g., Euclidean distance

18. Spanners What is a spanner? A spanning subgraph that approximates
some measure of the original graph
E.g., Euclidean distance

19. Spanners What is a spanner? A spanning subgraph that approximates
some measure of the original graph
E.g., Euclidean distance
Shortest path is at most
times longer than in

20. Spanners What is a spanner? A spanning subgraph that approximates
some measure of the original graph
E.g., Euclidean distance
Shortest path is at most
times longer than in
stretch factor

21. Spanners optimization measures
Distance – reducing transmission latency
Energy – increasing network lifetime
Hop-diameter – latency
Number of interferences

22. How TDMA comes to business?
Time f
Frequency

23. Example: Convergecast
Every node sends to his child its number from [0..d] and the total number of children d. When sending information back, use a time slot i mod d.
How to find a good tree? Depends on constraints.

24. Flooding Time Synchronization Protocol (FTSP)
Each node maintains both a local and a global time
Global time is synchronized to the local time of a reference node
Node with the smallest id is elected as the reference node
Reference time is flooded through the network periodically
reference node 4 5 1 7 6 2 3

25. Gradient Time Synchronization Protocol (GTSP)
Synchronize with all neighboring nodes
Broadcast periodic time beacons, e.g., every 30 s
No reference node necessary
How to synchronize clocks without having a leader?
Follow the node with the fastest/slowest clock?
Idea: Go to the average clock value/rate of all neighbors (including node itself)

26. Variants of Clock Synchronization Algorithms
Tree-like Algorithms Distributed Algorithms
e.g. FTSP e.g. GTSP
Bad local skew
All nodes consistently average errors to all neigbhors