Mobile Advanced Networks Introduction - EURECOM

Mobile Advanced Networks Introduction

Navid Nikaein

Mobile Communication Department

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INTERNET TODAY

©Navid Nikaein 2011 6

htpp://www.eurecom.fr/

Source: R. Haynal



Possible E2E Network Interconnections

©Navid Nikaein 2011 - p 8


The Big Picture User Equipments: Multi-Media PCs equipped to send and receive all variety

of multimedia User Communication Equipments: Connects the Users' PC(s) to the "Local

Loop" Local Loop Carriers: Connects the User location to the ISP's Point of Presence

(POP). ISP’s POP: Connections from the user are accepted and authenticated by the

ISP User Services Provided by the ISP: Used by the User for access (DNS, EMAIL,

etc). Core network / ISP backbone: Interconnects the ISP's POPs, AND

interconnects the ISP to other ISP's and online content. Online Contents: These are the host sites / servers that the user interacts

with. Origins of online contents: This is the original "real-world" sources for the

online information.



BASICS



Illustration


Backbone

RAN RAN


Simple Example

V ={1,2,3,4,5,6}

E={{1,2},{1,5},{2,3},{2,5},{3,4},{4,5},{4,6}}



What is a Graph?

Mathematical structure used to model relations between objects

Each graph G(V,E) is pair consisting of a set of nodes/vertices : V(G) a set of links/edges that connect pairs of nodes E(G)

Graph representation : Drawing: several ways to draw a given graph Data structure

List : used mainly for sparse graph Matrix : used mainly for dense graph



Communication network

The infrastructure that allows two or more nodes to communicate with each other Requires a set of standard communication rules, called

protocol, to exchange information over the common medium PDU and SDU format Interfaces

Generally divided into three planes Control plane Data plane Management plane



Network design

• Iterative process of defining the architecture, components, modules, interfaces, and data for a network to satisfy specified requirements

– Topological design – Network architecture and services

• Includes physical, datalink, network, and transport layer – Network realization

• But what are those requirements in MANET?

• How they influence protocol design ?



Network design requirements

• Applications and environments – e.g. commercial or emergency, wired or wireless, indoor, urban, rural

• User requirements and groups – e.g. user organization and priority, civilian or governmental

• Reference scenarios and services – e.g. concentration or random, rich multimedia application

• Technical goals and trade-offs – e.g. scalability, reliable, reconfigurable, rapidly deployable, security performance

• Internetworking – e.g. internet connection

• Network traffics (flow, load, behavior, and QoS) – e.g. interactive real-time, quality-of-service,

– Medium – E.g. wireless, underwater, cable



PROTOCOL STACK



Network Architecture

• Network Architecture: – Layered: separate communication task, triggers – Cross-layer: information sharing, joint deign, interactions – Integrated : unique communication task – Service oriented: connectivity, mediation, and application services

• Issues: compatibility, interactions, configuration • Example: OSI • Impact:

– Complexity – Performance – Resources – Upgradeability – Interoperability – Standardization



Transport Layer

• Unit: segment/datagram

• Example of Services: • Connection(less)-oriented, same-order delivery • Reliable data, flow control, error control, congestion avoidance,

reservation • (De)Fragmentation, byte-orientation, port numbering • Authentication, E2E encryption

• Example of protocol: TCP, UDP, RTP

• Impact: – Performance(delay, throughput, loss rate) – Fairness – Recovery latency



Network Layer

• Unit: Packet

• Example of Services: • Connection(less)-oriented, routing/forwarding • Fragmentation, host address, metric • mobility management, QoS, error control, security, internetworking

• Example: OSPF, RIP, AODV

• Impact: – Performance – Scalability – Load distribution and congestion – Resource consumption



Data link layer

• Unit: frame • Example of LLC services :

• Reliable transmission, link management, resource control, fragmentation, address resolution, error control, flow control,

• Header compression, ciphering • Example of MAC services:

• Channel access, resource allocation, feedback/measurement mechanisms, QoS support, MAC address

• Example: ATM, Ethernet, PPP, 802.11/16 • Impact:

– Performance (delay and throughput, loss rate ) – Fairness – Resource consumption – Scalability



Physical Layer-Base Band

Unit: bit Medium, frequency, bandwidth, energy

Example of Services: Synchronization, randomizer, inter-leaver, encoder, modulator, flow

control, Equalizer, shape filter, waveform

Example: WiFi, WiMax, LTE Impact:

Bit rate Bit error rate Physical topology Serial or parallel communication Duplex transmission mode Security



http://en.wikipedia.org/wiki/Image:Fibreoptic.jpg

http://en.wikipedia.org/wiki/Image:Fibreoptic.jpg

http://en.wikipedia.org/wiki/Image:Ethernet_RJ45_connector_p1160054.jpg

http://en.wikipedia.org/wiki/Image:Montreal-tower-top.thumb2.jpg

Physical Layer – RF Subsystem

Unit : signal Medium, frequency, bandwidth, energy

Example of Services: ADDC, filter, AGC, (de)modulator, (de)coding, power

amplifier, waveform

Impact: Interference Receive signal level BER



Antenna

Unit: Signal Example of Services: Transmit and received electromagnetic waves (convert to current

and vice versa) Omni-directional, directional, switched lobe, dynamically phased

array, adaptive array, MIMO, DAS Metric: EIRP (effective isotropic radiated power)

Examples: dipole, yagi-uda, horn Impact: Transmit power Capacity Spatial (freq) reuse Range vs. interference



Hardware

Unit: IC/Gates (AND and XOR), clock Example of Services: Speed, power consumption, processing, interface Hard chipset, soft chipset, full costume

Example: x86PC, ASIC, adaptive ASIC, FPGA, design-specific FPGA

Impact: Cost Size Performance Power consumption Flexibility Usage



Hardware cont’d

• Form factor – Layout: board size, mounting, connector, height – Examples: ATX, EATX, EmbATX, ITX, PC/104 – Impact:

• Cost • Power supply • System resources • Category of applications • Hardware architecture • Ports and interfaces



http://en.wikipedia.org/wiki/Image:Atxscale.svg

http://en.wikipedia.org/wiki/Image:Atxscale.svg

MOBILE ADVANCE NETWORK



Mobile Advanced Networks

Mobile Ad Hoc Networks: MANET

Wireless Mesh Networks: WMN

Wireless (Multimedia) Sensor Networks and Machine to Machine Communication: WSN, WMSN, M2M, IoT

Vehicular Ad Hoc networks: VANET

Delay-tolerant networks : DTN

Cognitive Radio Ad Hoc networks : CRAHN



Original Motivation of MANET

Military needs for battlefield survivability [leiner87] No restrictions imposed by a fixed platform The military cannot rely on access to a fixed, pre-placed

communication infrastructure in battlefield environment Unavailable or unreliable of access due to the destruction of the local

infrastructure or eavesdropping of the information Lack of terrestrial communication infrastructure

Packet Radio Networks Term invented by US military research @ 70 First cellular networks 1G was launched in Japon @79 Second cellular networks 2G GSM was launched in Europe

@82



Complexity of Packet Radio Networks


Highly Dynamic Network

Requires rapid response to

topology changes

Many updates generated by typical routing

algorithms

Requires multiple algorithms at different time

scales

Interest in efficiency

Use of multiple routing algorithms

Relatively scarce radio spectrum

Relatively low bandwidth

Shared Channel

Access to “overheard” information

Control over transmission parameters

Use of integrated algorithms which can be complex and may violate layering


Definition

A collection of nodes forming one or potentially several dynamic autonomous networks Nodes may be mobile or fixed Nodes communicate

using wireless medium without necessarily the intervention of any fixed infrastructure, i.e.

AP/BS Multi-hop fashion (store-and-forward), i.e. transmit range

Nodes acts as a host, and may act as a router

Packet Radio – Multihop - MANET



Backbone

MANET Characteristics

Multihop forwarding Network disconnection

due to Node mobility Traffic load (congestion) Lack of resource Transmission range Obstacle

Render route changes


RAN RAN


MANET Characteristics Cont’d

Wireless Medium Broadcast nature of the medium May render collision and contention

Node Mobility Time-varying topology and resources May render a link failure

Self-Organized Lack of infrastructure May render a (quasi-) distributed operation

Small Devices Limited resources May render Multihop operation



Wireless Network Models


Backbone Network

Single-hop network model e.g. Cellular

Network

Obstacle

Multi-hop network model

e.g. ad hoc networks

Backbone Network Hybrid ad hoc

network model e.g. sensor

network


Architectural Convergence ?

©Navid Nikaein 2011

2G - GSM

2.5 G - EDGE/GPRS

3G - UMTS(WCDMA/HSPA)

4G – LTE/LTE-A Source: J. Erfanian & LOLA Project

- p 35


Network Protocol Convergence


- Evolution from separate packet-switched and circuit-switched core sub-domains to one common IP core - New IP-based flat mobile core introduced in LTE: Toward ALL-IP-Architecture

Source: ALU

- p 36


Example of MANET Connectivity Graph

Does this graph correctly represents MANET topology?


S D

End-to-end path


Example of MANET Connectivity Graph


S D

End-to-end path S

DX X path

disruption!

time Space-time path Conceptual Graph over time and space

aggregate

Source: T. Spyropoulos


Applications of Ad Hoc Networks [chlamtek,hoebeke] Tactical networks

Military communication and operations

Public safety networks Rescue operation, disaster recovery (firefighters, police, doctors)

Commercial and civilian services Vehicular services such as road, weather, and accident information, inter-vehicle

communication Spontaneous network for group collaboration Sport stadiums, trade-fairs, and shopping mall

Home, office, and university networking Smart Home, Conference, meeting room, virtual classroom

Entertainments Multiuser game, wireless P2P networking, Robotic pets

Sensor Networks Intelligent environments Body area networks Data tracking of environment conditions (weather, earthquake, bridge)



User Mobility


Source: M. I. Rahman

- p 40


Coverage Area



Wireless Technology: Range vs. data rate


Data Rate (Mbps)

Ra

ng

e

ZigBee 802.15.4 802.15.3

802.15.3a 802.15.3c

WPAN

WLAN

WMAN

WWAN

WiFi 802.11

0.01 0.1 1 10 100 1000

Bluetooth 802.15.1

802.22

LTE / WiMax 802.16 HSPA

802.20

NFC


WIRELESS MESH NETWORKS



Wireless Mesh Network


Routers

Gateways

Printers, servers

Mobile clients

Stationary clients

Intra-mesh wireless links

Stationary client access

Mobile client access

Internet access links

Node Types Link Types

• Extend the coverage • Transit networks • Do not originate and/or terminate data flows

Access link Backbone links Backhaul links


How it Works : Data flows


User to internet and User to user traffic


Wireless Mesh Networks

Can you think of any application?


Source: I. Akyldiz




Broadband Internet Access




Law Enforcement

Intelligent Transport System


http://www.intel.com/update/contents/nc11032.htm

http://www.intel.com/update/contents/nc11032.htm



Rapidly Deployable Public Safety Network




Military Communication


Comparison

Mobile Ad Hoc Networks

Multihop

Nodes are wireless, possibly mobile

Nodes have the same capabilities/responsibilities

It does not rely on infrastructure

Most traffic is user-to-user

Wireless Mesh Networks Multihop

Nodes are wireless, some mobile, some fixed

Nodes can be routers, gateway, or users

It relies on infrastructure

Most traffic is user-to-gateway



Companies

Aerial Broadband

BelAir Networks

Firetide

Intel

Kiyon

LamTech (ex. Radiant)

Locust World

Mesh Dynamics

Microsoft

Motorola (ex. Mesh Networks)

Nokia Rooftop

Nortel Networks

Packet Hop

Ricochet Networks

SkyPilot Networks

Strix Systems

Telabria

Tropos Networks

52 ©Navid Nikaein 2011


Recent Mesh Products

53

Motorola: IAP4300 – Intelligent Access Point for

MOTOMESH Duo Motorola: MESH Wireless Video Camera

Tropos 5320 Outdoor MetroMesh Router

Mekari MR58 PacketHop Mesh Exchange



54

IEEE 802.11s

IEEE 802.15.1,2.3

IEEE 802.15.4

IEEE 802.15.5

IEEE 802.16a

Proprietary

Wireless Mesh Standards



http://www.ieee.org/

WIRELESS SENSOR NETWORKS



Wireless Sensor Networks

Need to monitor and measure various physical phenomena: Temperature, fluid levels, vibration, strain, humidity, acidity,

pumps, generators to manufacturing lines, aviation, building maintenance, vehicular movement, lightning condition, pressure, noise levels, presence or absence of certain types of objects, mechanical stress levels on attached objects, current characteristics (speed, direction, size) of an object, etc.

Common to many areas including structural engineering, agriculture and forestry, healthcare, logistics and transportation, and military applications.




Connected sensing device that are capable of retrieving data and potentially interacting with the environment

Why Inexistent of wired infrastructure for instance in a remote and/or

hostile environment Cost reduction for installing, terminating, testing, maintaining,

trouble-shooting, and upgrading

Challenge Self-organize networking Energy efficiency Variable channel capacity In-network processing QoS support



Wireless (Multimedia) Sensor Networks



Data Aggregation

The process of Aggregating the data from multiple sensors Eliminate redundant transmission Fuse information at intermediate nodes Transmit the processed data to the sink, e.g. base station



Type of Sensors

Passive, omnidirectional sensors Measure a physical quantity at the point of the sensor node Examples: thermometer, light sensors, vibration, microphones, humidity,

mechanical stress or tension in materials, smoke detectors

Passive, narrow-beam sensors Well-defined direction of measurement Examples: camera which can “take measurements” in a given direction,

but has to be rotated if need be

Active sensors actively probes the environment, for example, a sonar of some types of

seismic sensors, which generate shock waves by small explosions

Actuation capable Receive commands and perform a predefined operation



View of a Sensor

Sensing unit sensors and ADC

Processing unit (CPU) Communication subsystem: composed of transceiver and

interfaces the devices with n/w

Coordination subsystem co-ordinates different n/w

devices

A storage unit (memory) Optional mobility/ actuation

unit





• Can you think of any application?




Power Processor

Radio

Sensors Memory

Source: ETH-DCG



Habitat monitoring – Great Duck Island Gather temp, IR, humidity, and other readings from bird nests

on island Determining occupancy of nests to understand breeding &

migration behavior Live readings at http://www.greatduckisland.net



http://www.greatduckisland.net/


Health Applications Telemonitoring of human physiological data, tracking and

monitoring patients and doctors inside a hospital, and assistance of the elderly

Wearable and implantable sensors can monitor a broad variety of conditions of the patients continuously at all times

Pre-hospital, in-hospital, and ambulatory monitoring possible



Wireless Multimedia Networks


Multimedia surveillance Networks

Health Care delivery Systems

Industrial Process Control

Environmental Monitoring control Systems Traffic monitoring systems


Evolution toward IoT

Smart interconnected sensing objects embedding pervasive information processing connectivity medium Service enabler

Evolution towards “Internet of Things” RFID/tags WSN/WMSN M2M IoT


RFID

WSN M2M

IoT


Machine To Machine Communication

Essentially add intelligent to wireless multimedia sensors and connect devices and remote system Communicating object and Internet of things (IoT)



Toward Smart City


Smart Elec. Smart Water

Appliances

Temperature

Light

Wind Turbine

Solar Panel

Smart Gas

Meters Coms

Home displays TV, Computer

In-Home Energy Display

Breaker Valves

Gateway

Data Center

Wan Communication

Source: ETSI


Comparison


Bandwidth is generous (>1Mbps)

Some nodes mobile, some fixed

Normally not energy limited

Resources are not an issue



Bandwidth is limited (tens of kbps)

In most applications, fixed nodes

Energy efficiency is an issue

Resource constrained




VEHICULAR AD HOC NETWORKS



Motivation

In 2004, the European Commission triggered a socio-economic study (SeiSS) on the impact of intelligent vehicular systems: 5 to 15% reduction in fatalities 10 % to 20% reduction in traffic congestion 40% stand-still reduction with dynamic and real time traffic management …

According to the American Automotive Association study, the cost for the US economy of traffic accident is 160 billion $ yearly Approx $1000 per citizen per year

There is a clear benefit to make cars able to talk and exchange data ! A large set of applications have been defined and are ranked in three classes

Traffic safety Accident avoidance Traffic Efficiency

Congestion avoidance Real-time optimal path

Infotainment Internet access, advertisement and P2P


Source: J. Harri


Vehicular Ad Hoc Networks

Dedicated interconnection of cars to form a network Supporting connection to roadsides and existing wireless

infrastructures


Source: J.-C. Kao




Reduce CRASHES

Increase

Automation?

- Automatic Driver Assistance? - Emergency Vehicle Warning

- Inter-Vehicle warning

Minimize effects

of Driver Error

- Intersection collision avoidance

- Curve speed Deceleration

Improve Driver

Situational Awareness

Safer Roads Source: F. Kargl




Reduce CONGESTION

Improve Traffic

Information

Improve Situational

Roadway Awareness

- Real time traffic information

- Alternative route guidance

- Dynamic roadway condition info.

- Emergency situation management

Manage Traffic

Flow?

- Dynamic flow control?

- Dynamic roadway pricing?

More Efficient Driving Source: F. Kargl




Source: F. Kargl


Application Ranking

Active safety Accident avoidance Cooperative emergency applications

Real-time traffic control and monitoring Vehicular traffic monitoring and congestion avoidance Optimal path computation

Infotainment Cooperative files download (cartorrent) and Internet access

Parking assistance: Find a park place easily in a city Air pollution emission measurement and reduction Law enforcement Internet access in cars



Communication Paradigm

I: infrastructure: in general fixed (WiFi/WAVE APs) but it can be mobile (specific police cars)

V: Vehicle: in general cars but it can be trucks, busses, trains, etc.


V2I: Vehicle to Infrastructure

V2V: Vehicle to Vehicle

V2V2I: Vehicle to Vehicle to Infrastructure

I2V : Infrastructure to Vehicle

I2V2V: Infrastructure to vehicle to vehicle

I2V2I ?

In-vehicle communication


VANET Requirements


WLAN has been designed to provide Internet-grade communication ITS Communications have different requirements

But they are investigated as if similar !

Internet Communication Traffic Safety

Mostly Unicast

Bursty Traffic

Throughput Oriented

Delay ‘tolerant’

Large-scale

Mostly Broadcast

Mostly Periodic Traffic

Message Oriented

Delay Centric

Local Scale


Heterogeneous Vehicular Networks


Always Best Connected/Served? May involve lots of technologies ?

Source: F. Kargl


Heterogeneous Vehicular Networks

From Vehicular Ad Hoc Networks (VANET) Dedicated interconnection of cars to and form a network Supporting connection to roadside infrastructure

To Heterogeneous Vehicular Networks Extension of VANET considering cellular and satellite

networks When dedicated communication cannot be established When multi-hop communication is not possible or efficient

Trade-off between cellular/satellite systems and WLAN in ad hoc mode



ETSI ITS Scenario



Intelligent Vehicle / Transport


Motocycle Warning Emergency Vehicle

Source: BMW F&T & J. Harri

Source:


http://www.car-2-car.org/index.php?id=152

http://www.car-2-car.org/index.php?id=153


How to notify congestion and manage road traffics ? Sensor-based collection: Costly (install everywhere), Centralized Vanet-based collection: The vehicle IS the sensor (CHEAP); Disseminate

traffic data only when/where necessary (SCALABLE)




Manet & Vanet




Unlike other adhoc and sensor networks CPU and power are NOT key resources

Bandwidth is the key information network resource Bandwidth and delay guarantees depend on applications’

requirements

Links between peers will be dynamic and unstable Notion of platoons

Move as one simultaneously increase the capacity without additional lanes)

Nodes dynamically leave and join platoons

Links with fixed and mobile (enhanced probe vehicles) Mobility is constrained and directional



DELAY-TOLERANT NETWORKS



Delay-Tolerant Networks

There is no direct path from node S to node D at any given time.

Packets from node S can be delivered to node D if intermediate nodes can hold/carry the packets. At 8:00 am, node S sends the packets to node 2; at 10:00am node 2 forwards the packets to node 3; and at 11:30 am node 3 forwards the packets to node D.



Delay-Tolerant Networks Intermittent link (dis)connection No guarantees on End-to-End path Predictable / Opportunistic disconnection Opposed to assumptions in today’s Internet always connected, low round trip time, etc.

89

A B

E

D

F

C




Intermittent link (dis)connection High latency : signal propagation and/or intermittent connectivity Low data rate Long queuing times Lack of resource at end nodes

Opposed to the assumptions of the Internet today always connected, low round trip time, etc.


S D

End-to-end path S

DX X path

disruption!


Terminology for DTNs

There are many different terminologies used for DTNs in the literature, such as eventual connectivity space-time routing partially connected transient connection opportunistic networking extreme networks delay-tolerant network disruption-tolerant networks Sparse networks





time (days)

Connectivity: Village – City band

wid

th bike

satellite phone

Connection Availability BW Delay cost Satellite 3-4 times per day Low Msec High Bike Once per day High Hours Medium phone On demand Medium Msec High(day)

Low(night)







Location-dependent Services Current events within 1km of where I am? Any media? Any good Asian restaurants around with a wait less than 15min? Anybody nearby with tickets to sell for today’s Real Madrid game?

Social Networking Services Are any of my friends (e.g. from Facebook) nearby, in the same bar/train? Who else is on this train, and what are their profiles?

Extending the realm of Existing ones File-sharing, downloading popular content, cached web access

Power constrained networks

Why not using the existing applications, e.g. iPhone apps? Note: Not a replacement of the existing infrastructure




COGNITIVE RADIO AD HOC NETWORKS



Cognitive Radio Ad Hoc Networks

CR is a radio that can tune its radio based on the interaction with its environment Learn and adapt Reconfigurability : SDR concept

Spectrum-aware communication Limited available radio spectrum Inefficiency spectrum usage

Goal is to find the best available spectrum holes Requires cooperation among systems and networks

Spectrum sensing: detect spectrum opportunities Spectrum management: analysis and decision Spectrum mobility: switch the frequency of operation Spectrum sharing: cooperation with license user



Cognitive Radio Ad Hoc Networks


Source: I.F. Akyildiz


Simulation Tools for MANET

NS-2/3 http://www.isi.edu/nsnam/ns/ TCL-TK for scenario setup C++ for protocol design

GloMoSim http://pcl.cs.ucla.edu/projects/gl

omosim/ C and parsec (parallel simulation

capability)

Qualnet http://www.scalable-

networks.com/ Commercial version of GloMoSim

Matlab http://www.mathworks.com/

Omnet http://www.omnetpp.org/ C++ for protocol design

GTNET http://www.ece.gatech.edu/rese

arch/labs/MANIACS/GTNetS/ C++

Opnet http://www.opnet.com/solutions

/network_rd/modeler.html C++

Sinalgo http://www.dcg.ethz.ch/projects

/sinalgo/ java



http://www.isi.edu/nsnam/ns/

http://pcl.cs.ucla.edu/projects/glomosim/

http://pcl.cs.ucla.edu/projects/glomosim/

http://www.scalable-networks.com/

http://www.scalable-networks.com/

http://www.mathworks.com/

http://www.omnetpp.org/

http://www.ece.gatech.edu/research/labs/MANIACS/GTNetS/

http://www.ece.gatech.edu/research/labs/MANIACS/GTNetS/

http://www.opnet.com/solutions/network_rd/modeler.html

http://www.opnet.com/solutions/network_rd/modeler.html

http://www.dcg.ethz.ch/projects/sinalgo/

http://www.dcg.ethz.ch/projects/sinalgo/

A brief Comparison

Simulation No interaction with the external entities (closed environment) Part or all of the elements of a network/system is modeled or abstracted

Emulation Bring the external elements with their I/O streams (open environment) Decision on which element is real or modeled depends on the use case

and purpose of the experiments At least one thing is modeled

Real testbed All the elements are real Part of the testbed maybe controlled

100


A brief Comparison

Experiment

Scenario Setup

Abstraction / Modeling

Reproducibility

Scalability / Costs

Limitation

Net Traffic & Mobility

Analytical +++ - +++ +++ CPU/ Abstracted/ Modeled

Simulation ++ + +++ ++ Abstraction Modeled

Emulation + ++ ++ ++ CPU/Cost Modeled / Real

Real Testbed - NA - - Cost Real

101


Expectation from the Validation Platforms

Analytical

• UML • FreeMat

• IDL • Matlab • SciLab • Octave

Simulation

• Sinalgo • NetSim

• GloMoSim/Qualnet • NS-3 • Opnet

• Omnet++

Emulation

• NS3 • NistNEt • CORE • USPR2 • WARP

• CMU-DSR • ORBIT • OAI

Real Testbed

• PlanetLab/OneLab • NITOS

• GnuRadio • WARP • ORBIT

• Sundance, BEE2, WiTestLab • USPR2 • OAI

Scalability Reproducibility Applicability

Abstraction Level Realism Level

102


AD HOC NETWORK MODELING



Seven Bridges of Königsberg (Kaliningrad, RU)

Problem is to find a walk through the city that would cross each bridge exactly once

Alternative problem is to find a path that traverses all bridges and also has the same starting and ending point


What matters is the sequence of bridge crossed

Solution exists iff ?


What is a Graph?

Mathematical structure used to model relations between objects

Each graph G(V,E) is pair consisting of a set of nodes/vertices : V(G) a set of links/edges that connect pairs of nodes E(G)

Graph representation : Drawing: several ways to draw a given graph Data structure

List : used mainly for sparse graph Matrix : used mainly for dense graph



Simple Example

V ={1,2,3,4,5,6}

E={{1,2},{1,5},{2,3},{2,5},{3,4},{4,5},{4,6}}



Type of graphs

Undirected graph and directed graph (digraph) Directed graph FSM

Symmetric and asymmetric

Simple graph vs. multigraph (loop and multiple edges)

Weighted graph Such weight may represent cost, length, capacities Examples:

Dijkastra algorithm Minimum cost spanning tree, shortest path maximal flow

Q: Weights are assigned to edges or vertices?



Classes of graphs

K-Regular graph Each vertex has the same k neighbor Example: 0-regular to 3 regular

Complete graph each pair of vertices has an edge connecting them Example: K1 to K5

Connected graph vs. disconnected graph If there is a path between any pair of vertices

K-vertices and k-edges connected graph



Classes of Graph

Bipartite graph The vertices set can be partitioned into two sets

Complete bipartite graph

Path Graph Ordered list of vertices

Cycle Graph Connected 2-regular



Classes of graph

Planner Graph Vertices and edges can be drawn in a plane such that no two

edges intersects, i.e. embedded in the plane Any cycle that surrounds a region without any edges forms a

face

Tree Connected graph with no cycle

Forest Graph with no cycle, distinct union of trees



Subgraphs

A subgraph H of graph G is a graph if V(H) in V(G) and E(H) in E(G) G contains H, and is a supergraph of H

H is a spanning subgraph of graph G if it has the same number of vertex as G. We say that H spans G

H is a k-spanner subgraph of G if any two vertex u,v are at most k times far apart in H than on G K is referred as dilatation number

H is an induced subgraph of graph G if xy is an edge of H iff xy is an edge of G



Walks

Sequence of vertices and edges, where the vertices that precede and follow an edge are the end vertices of that edge Closed walk: first and last vertices are the same opened walk

Path is an opened walk where no edges and vertices are repeated

Length of a walk Number of edges used for a walk



Other Properties

Degree of a vertex V is the number of vertices incident to V Total degree of a graph = 2x|E|, where n is number of edges Degree sequence : list of degrees in non-increasing order Maximum degree: largest degree over all vertices

Adjacency: two vertices u and v are called adjacent if an edge exists between them

Neighborhood: all vertices adjacent to v (induced subgraph of G) Closed: when v is included Opened: when v is not included

distance : the length of a shortest path between any two vertices u, v d= 0 , when u=v d=∞ , when u and v are unreachable Eccentricity of v is the maximum distance from v to any other vertex u

Graph diameter has the maximum eccentricity and graph radius is the minimum



Graph Eccentricity

Eccentricity of node 2 is the maximum distance from node 2 to vertex 3 and 4

Max/Min eccentricity for all nodes give the graph diameter/radius



Dominating sets

Dominating set DS of a graph is a vertex subset whose closed neighborhood includes all vertices of the graph DS is a subset of nodes such that each node is

either in DS or has at least one neighbor in DS

DS can be Weakly connected dominating set WCDS Connected Dominating set CDS Minimum CDS



Independent set

Independent set is a set of vertices of which no pair is adjacent Pair-wise disjoint or mutually nonadjacent

A graph can be decomposed into independent sets in the sense that the entire vertex set of the graph can be partitioned into pair-wise disjoint independent subsets



Problems in graph

Graph coloring/labeling Edge/vertex/face coloring Four-color theorm

Route problems Minimum spanning tree Shortest path Seven bridge of konigsberg Three cottage problem Travelling salesman problem

Network flow Max flow min cut

Visibility graph Museum guard

Covering problem Max clique and independent set



- p 119

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