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 ?