Map medial axis based geometric routing in sensor networks
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MAP: Medial Axis Based Geometric Routing in Sensor Networks. MobiCom’05 Jehoshua Bruck, Jie Gao, Anxiao(Andrew) Jiang Ku Dara. Contents. Introduction Medial axis Medial Axis based naming and routing Protocol (MAP) In continuous region in the Euclidean plane In discrete sensor field

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MAP: Medial Axis Based Geometric Routing in Sensor Networks

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Map medial axis based geometric routing in sensor networks

MAP: Medial Axis Based Geometric Routing in Sensor Networks

MobiCom’05

Jehoshua Bruck, Jie Gao, Anxiao(Andrew) Jiang

Ku Dara


Contents

Contents

  • Introduction

    • Medial axis

  • Medial Axis based naming and routing Protocol (MAP)

    • In continuous region in the Euclidean plane

    • In discrete sensor field

  • Simulation

  • Summary

MAP


Introduction 1 2

Introduction(1/2)

  • Design of Routing algorithm

    • Routing is elementary in all communication networks

    • is tightly coupled with auxiliary infrastructure that abstracts the network connectivity

      • Stable link & powerful nodes (Internet) : routing table

      • Fragile links & constantly changing topologies &nodes with less resouceful h/w (ad-hoc mobile wireless networks) : flooding

Too energy-expensive for sensor networks

Flooding for route discovery

Light infrastructure of sensor networks for efficient and localized routing

Medial Axis

MAP


Introduction 2 2

Introduction(2/2)

  • Medial Axis

    • Set of points with at least two closest neighbors on the boundaries of the shape

    • ‘Skeleton’ of a region

    • Capture both geometric and topological features by using the connectivity information

  • MAP

    • Medial axis based naming and routing protocol as a routing infrastructure

    • Depend only connectivity graph

    • Consist of 2 protocols

      • Madial Axis Construction Protocol(MACP)

      • Medial Axis based Routing Protocol(MARP)

MAP


Medial axis definition

Medial Axis - Definition

  • Given a bounded region R, boundary

  • A is the collection of points with two or more closest points in

  • A cord is a line segment on the medial axis and its closest points on

  • A point on the medial axis with 3 or more closest points on is called a medial vertex

  • Canonical cell : the medial axis, 2 chords,

MAP


Naming w r t medial axis

Naming w.r.t. medial axis

  • Point p is named by the chord x(p)y(p) it stays on (x(p), y(p), d(p))

    • x(p) is a point on the medial axis

    • y(p) is the closest point of x(p) on ∂R

    • d(p) is height. i.e. relative distance from x(p): |px(p)|/|x(p)y(p)|

Theorem: Every point is given a unique name

MAP


Routing between canonical cells 1 2

Routing between canonical cells(1/2)

  • The naming system naturally builds a Cartesian coordinate system

    • x-longitude curve --The chord with medial point x

    • h-latitude curve --The collection of points with the height h (0 ≤ h ≤ 1)

  • The canonical cells are glued together by the medial axis.

  • With the knowledge of the medial axis – route from cells to cells by checking only local neighbor information

MAP


Routing between canonical cells 1 21

C2

C2

C1

C1

Routing between canonical cells(1/2)

  • Two canonical cells adjacent to the same medial vertex may not share a chord

  • Build rotary systems around medial vertices

  • Polar coordinate system: (|ap|/r, ), r is the maximum radius of a ball centered at a medial vertex a

MAP


Routing scheme 1 2

Routing scheme(1/2)

  • Routing is done in 2 steps

    • Check the medial axis graph, find a route connecting the corresponding points on the medial axis as guidance

    • Realize the route by local gradient descending, in either the Cartesian coordinate system inside a canonical piece, or a polar coordinate system around a medial vertex

MAP


Routing scheme 2 2

Routing scheme(2/2)

  • Routing is done in 2 steps

    • Check the medial axis graph, find a route connecting the corresponding points on the medial axis as guidance

    • Realize the route by local gradient descending, in either the Cartesian coordinate system inside a canonical piece, or a polar coordinate system around a medial vertex

MAP


Map in discrete networks naming 1 5

MAP in discrete networks – naming(1/5)

  • Detect boundaries of the sensor field

    • Find sample nodes on boundaries

      • By manual identification, or automatic detection [Fekete’04, funke’05]

MAP


Map in discrete networks naming 2 5

MAP in discrete networks – naming(2/5)

  • Detect boundaries ( the curve construction problem)

    • Use local flooding to connect nearby boundary nodes

    • Include nodes on the shortest path between them as boundary nodes

MAP


Map in discrete networks naming 3 5

MAP in discrete networks – naming(3/5)

  • Construct the media axis graph

    • Detect medial nodes (the sensors with 2 or more closest boundary nodes) by restricted flooding

      • Flooding message: Sensor’s ID, boundary, hop count

MAP


Map in discrete networks naming 4 5

MAP in discrete networks – naming(4/5)

  • Construct the medial axis graph

    • Connect medial nodes into a graph and clean it up

      • Remove very short branches

Broadcast this simple graph to all sensors

MAP


Map in discrete networks naming 5 5

MAP in discrete networks – naming(5/5)

  • Assign names to sensors for discrete networks

    • Replace chords by approximate shortest path trees

      • “Medial axis with dangling trees”

    • Shortest path forest rooted at the medial axis

    • Nodes are assigned names w.r.t. where it lies in the tree

All the computation is

simple and local

MAP


Medial axis based routing

Medial axis based routing

  • Medial Axis based Routing Protocol

    • Find the shortest path in the medial axis graph A

    • Route in parallel to the shortest path

    • Route along the shortest path trees rooted at that medial point to reach the destination q

  • Guaranteed delivery

    • If there is no better choice, route toward the medial axis

  • Maintain balanced load

    • Try to route in parallel with the medial axis as much as possible to avoid overloading nodes near the medial axis

  • MAP


    Simulation 1 2

    Simulation (1/2)

    • Outdoor sensor field: Campus(650mX620m) 5735 nodes

    The simple medial axis graph: 18nodes, 27edges

    MAP


    Simulation 2 2

    Simulation (2/2)

    Routing path comparison

    Load balance comparison

    MAP

    destination

    source

    GPSR

    Normalized standard deviation of traffic load on sensors

    MAP


    Summary

    Summary

    • MAP

      • Topology-enabled naming and routing schemes that based purely on link connectivity information

    • Advantage

      • Takes only connectivity graph as input

      • Infrastructure is lightweight

      • Routing is efficient and local

    MAP


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