Geographic Routing with Minimal Local Geometry

2016 International Conference on Distributed Computing in Sensor Systems (DCOSS)

2016

Self Cite

Abstract-Geographic routing is an appealing routing strategy that uses the location information of the nodes to route the data. This technique uses only local information of the communication graph topology and does not require computational effort to build routing table or equivalent data structures. A particularly efficient implementation of this paradigm is greedy routing, where along the data path the nodes forward the data to a neighboring node that is closer to the destination. The decreasing distance to the destination implies the success of the routing scheme. A related problem is to consider an abstract graph and decide whether there exists an embedding of the graph in a metric space, called a greedy embedding, such that greedy routing guarantees the delivery of the data. A common approach to assign geographic coordinates is to measure distances (for instance the distances between neighboring nodes) and compute (virtual) coordinates.The rationale of the Virtual raw Anchor Coordinate System (VRAC) is to use the (raw) measured distances as coordinates in order to avoid further computations. More precisely, each node needs to measure three distances. In this paper, we investigate the existence of greedy routing in the VRAC coordinate system using a metric free characterization of greedy paths that is more general than in previous works. We show that if the graph is saturated (see definition in the text) then the greedy algorithm guarantees delivery. Interestingly, the approach of greediness here applies to Schnyder drawings of planar triangulations. Indeed, by choosing the measured distances appropriately Schnyder drawings of planar triangulations are always saturated and hence our greedy routing algorithm succeeds.The VRAC coordinates have conditions to satisfy to make greedy routing successful. These conditions can be inferred from geometric considerations. However, we formulate these conditions in an abstract way in order to avoid geometric considerations and in order to make possible further derivation of virtual VRAC coordinate systems, i.e. using only the abstract graph description. In particular using only local information would lead to distributed algorithm.

Section: Discussionmentioning

confidence: 99%

Section: Schnyder Characterization and Saturated Communication Graphmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Greedy Routing on Virtual Raw Anchor Coordinate (VRAC) System

2016 International Conference on Distributed Computing in Sensor Systems (DCOSS)

2016

Self Cite

“…In fact, unlike in the previous approach, in this coordinate system we are able to perform rotation and detection of line segment intersection as in Euclidean space. Here we summarize the basics of this approach while a complete description of the algorithm can be found in [19] As illustrated in Figure 1b, a node divides the physical space into six sectors based on its coordinate value. Sectors are numbered according to the Figure 1b, and two of the components of the coordinates happen to be the borders of the sector.…”

Section: Face Switchingmentioning

confidence: 99%

Geographic routing on Virtual Raw Anchor Coordinate systems

Theoretical Computer Science

2016

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In this paper we present a novel combinatorial approach for geographic routing with delivery guarantees. Proposed algorithm can be seen as a variant of GFG (Greedy Face Greedy of Bose et.al) algorithm, but based on combinatorial properties derived in the Virtual Raw Anchor Coordinate system, which is the localization scheme of interest. We utilize a local planarization algorithm of a geometric graph, which is based on the Schnyder's characterization of planar graphs. The new approach is combinatorial in the sense that the nodes are ordered with respect to three distinct order relations satisfying suitable properties. The coordinate system that motivated the development of this routing algorithm is VRAC (Virtual Raw Anchor Coordinates), which localizes the nodes with the raw distances from three fixed anchors. Since the positions of the anchors are not known, the VRAC coordinate system does not correspond to the Euclidean location of nodes, yet leaving sufficient information to define necessary combinatorial constructs for routing with guaranteed delivery. In particular, the routing algorithm avoids the references to geographical arguments and makes use only of the order relations on the nodes. We expect that our approach will foster further research on building efficient order relations, that will prove to be useful in practical implementation of geographic routing algorithms. In particular, we expect that further work will prove that the combinatorial approach for geographic routing, based on a raw anchor based positioning system is more robust in the presence of distance measurement errors.

“…Huc et.al have proposed a similar virtual coordinate system which assigns raw distances from anchors as the coordinates; VRAC (Huc et al, 2010). A local routing strategy was proposed for VRAC in (Samarasinghe and Leone, 2012), where geographic primitives were identified (which can be performed locally) to perform classical algorithms like GFG and GPSR over VRAC. This proposal was based on a variant of original VRAC, where it assumed inter distances between anchors.…”

Section: Virtual Raw Anchor Coordinatesmentioning

confidence: 99%

Combinatorial Approach for Geographic Routing with Delivery Guarantees

Proceedings of the 3rd International Conference on Sensor Networks

2014

Abstract:In this paper we present a novel combinatorial approach for geographic routing with delivery guarantees. Proposed algorithm can be seen as a variant of GFG (Greedy Face Greedy of Bose et.al) algorithm, but based on the defined combinatorial properties of the graph. We utilize a distributed planarization algorithm of a geometric graph, which is based on the Schnyder's characterization of planar graphs. The new approach is combinatorial in the sense that the nodes are ordered with respect to three distinct order relations satisfying the suitable properties. The coordinate system motivated the development of this routing algorithm is VRAC (Virtual Raw Anchor Coordinates), which localizes nodes based on the raw distances from three fixed anchors.Since the positions of the anchors need not to be known, the nodes localized by the VRAC coordinate system does not correspond to the exact geographic location of nodes, yet leaving sufficient information to define necessary combinatorial constructs.