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

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

Wireless Ad-Hoc Network Set of transceivers communicating by radio

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

Wireless Ad-Hoc Network Transceiver receives transmission from only if

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

Definition A set of transceivers

Definition A set of transceivers is the power assignment

Definition A set of transceivers is the power assignment

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

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

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

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

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

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

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

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

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

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

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

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

How TDMA comes to business? Time f Frequency

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.

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

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)

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