Upload
toni
View
31
Download
0
Tags:
Embed Size (px)
DESCRIPTION
Stateless and Guaranteed Geometric Routing on Virtual Coordinate Systems. Ke Liu and Nael Abu-Ghazaleh Dept. of CS, Binghamton University. Background and Motivation Virtual Coordinates System (VCS) Geometric Routing on VCS Contributions Dimensional Degradation - PowerPoint PPT Presentation
Citation preview
Stateless and Guaranteed Geometric Routing on Virtual Coordinate Systems
Ke Liu and Nael Abu-GhazalehDept. of CS, Binghamton University
Outlines Background and Motivation
Virtual Coordinates System (VCS) Geometric Routing on VCS
Contributions Dimensional Degradation Spanning Path Virtual Coordinate System
Conclusion
Geographic Routing (GPSR) Proposed by B. Karp (MobiCom 2000), kno
w as Greedy and Perimeter Stateless Routing (GPSR)
A similar one proposed by Hannes Frey, know as Greedy and Face routing (GFG)
Stateless: no path information, no (traditional) routing table. Only locations of neighborhood is used.
Geographic Routing Limitation Accurate Location
GPS is expensive Indoor application Localization Algorithm is not Accurate: 40%
localization error is common Perimeter Routing is not efficient
(Possible hundred) times longer than greedy forward. Fail facing Localization error
Virtual Coordinates System (VCS) Reference (anchor) nodes are served as bases of V
CS Each node sets up its VC as hop counts to referenc
e nodes As localization algorithm at first, later independen
tly used, replacing the physical coordinate system (GeoCS or PCS)
Only based on communication connectivity Physical voids are avoided -- mostly Virtual voids arise, NOT with physical voids
VCS Variants
Variant Dimensions Distance Backtracking
VCap 3 Euclidean Random Walk
LCR 4 Euclidean Universal Record
BVR N (>10, typically 80)
Manhattan Scoped Flooding
GSpring Dynamics Euclidean VC Upgrading
Virtual Anomaly: Broken Naming Uniqueness
Important Definitions Given a graph G(V, E) Component: C(V’,E’), |V’| >= 2 Node cut Vc: |Vc| >=2, and {Vc == V’, or removing Vc w
ould disconnect the rest of C(V’, E’) from G(V, E)} Network connectivity: the minimal size of any component Determinant Component: some anchor node in Vc Indeterminate Component Uniqueness Degree Ud: number of all unique virtual coord
inate values for all nodes in network
Dimensional Degradation: Dd
Maximal number of virtual dimensions (virtual anchors) which can increase the naming uniqueness (Ud)
if the Ud of a n-dimensional virtual coordinatesystem on a network is x, and the Ud of a (n+1)-dimensionalvirtual coordinate system is also x, we say the Dd of this network is n.
Theorem 1: The Dd of a 1-connected graph is 1(High dimensional VCS does not increase naming uniqueness)
A node cut Vc contains only this node, separate the network into 2 parts, one is determinant component, another is indeterminate component
Increasing the virtual dimension means select one more node in the determinant component as new anchor
Values for the new virtual dimension do not increase the naming uniqueness
Theorem 1: Proof
Lemma 2:
Theorem 3
Only (N-1)-Dimensional VCS maximize the naming uniqueness of a complete graph of N nodes
If using the current VCS set up procedure, then complete graph suffers most
It convergences to shortest path routing.
Spanning-Path VCS and Routing Why not use ONLY VCS – no localization at all Impossible? Possible?
Yes, it is impossible if using the same VCS setting up (multi-dimension, hop-count based virtual coordinates)
No, it is possible – if somehow we give each node unique name, with simple gradient between any pair of nodes
Current VCS setting up breaks the naming uniqueness of coordinate system Giving each node a unique ID (VC value) globally and
dynamically
Related Work Blind Searching: VCap, LCR
VCap: Random detour LCR: each node records each packet forwarded
Data Flooding: BVR Send the packet to the closest anchor node Anchor node scope floods the packet
VCS Upgrading: GSpring Elect one more node as a new anchor
Motivation: Spanning-Tree GEM: Using spanning-tree structure (VPCS), as lo
calization alogrithm GDSTR:
Spanning-Tree structure: Hull Tree Convex Hull: aggregate all descendent nodes as a conv
ex hull – a polygon covers the area of descendent nodes Negative false: failed to confirm some node in convex
hull – routing failure Although those Spanning-tree structure based solu
tion fail, we still believe it is a solution
Spanning-Path VCS One node is elected as anchor node DFS algorithm to set up a spanning-tree stru
cture Each node is assigned a unique ID (SPVC) Maximal Range: After all descendent nodes
are assigned SPVCs, the maximal SPVC is assigned to the root as its max range
Spanning-Path VCS Example
Spanning-Path Geometric Routing
Descendent Range: node’s SPVC node’s max range
Forwarding candidates: any node whose descendent range contains the destination’s SPVC
Using the one with the smallest descendent range as next hop
Aligned Greedy and Spanning Path (AGSP) Routing
Greedy forwarding mostly based on our previous work (aligned Virtual coordinate system – MASS 2006)– greedy forwarding succeeds 98%+ on VCS
If Greedy fowarding fails, using Spanning Path to route the data packets.
It is delivery guaranteed, stateless, no localization algorithm used.
AGSP Evaluation: Path stretch Better than almost all o
ther GR, both on VCS and GeoCS
Approaching the optimal performance, as shortest path routing
Deep alignment may not benefit much in high density
AGSP Evaluation: Odd deployment
LCR provides similar performance – it benefits from less choice during blind searching
AGSP is even better than random deployment
Conclusion Geometric Routing on VCS previously
Geographic Routing was impractical GR on VCS was not even good routing
Contribution Increasing Stateless delivery guaranteed GR on VCS Performance is not good as Greedy fowarding Easily to be used with any greedy forwarding, p
roviding the best performance.
Thank you
Questions ?