Geographic Routing without Planarization Ben Leong, Barbara Liskov, and Robert Morris MIT Computer Science and Artificial Intelligence Laboratory {benleong, liskov, rtm}@csail.mit.edu Abstract data-centric applications [21, 28]. Even when physical locations are not available, geographic routing can still We present a new geographic routing algorithm, Greedy be applied using virtual coordinates [22, 26]. Distributed Spanning Tree Routing (GDSTR), that finds All previously proposed geographic routing algo- shorter routes and generates less maintenance traffic than rithms are based on face routing [15], which guarantees previous algorithms. While geographic routing poten- packet delivery by routing on a planar subgraph of the tially scales well, it faces the problem of what to do at network. It turns out that distributed planarization is dif- local dead ends where greedy forwarding fails. Existing ficult for real wireless networks [11] and the problem geographic routing algorithms handle dead ends by pla- was only solved recently by Kim et al. with the Cross- narizing the node connectivity graph and then using the Link Detection Protocol (CLDP) [13]. However, CLDP right-hand rule to route around the resulting faces. is complex and somewhat costly, while face routing re- GDSTR handles this situation differently by switch- quires the handling of many subtle corner cases [14]. ing instead to routing on a spanning tree until it reaches a While practical distributed planarization is now a solved point where greedy forwarding can again make progress. problem, the high maintenance costs and complexities In order to choose a direction on the tree that is most associated with the deployment of face routing algo- likely to make progress towards the destination, each rithms (with CLDP) make it worthwhile to consider an GDSTR node maintains a summary of the area covered alternative approach to face routing. by the subtree below each of its tree neighbors. While We have developed a new geographic routing algo- GDSTR requires only one tree for correctness, it uses rithm, the Greedy Distributed Spanning Tree Routing two for robustness and to give it an additional forward- (GDSTR) algorithm, that does not require planarization. ing choice. GDSTR is better than existing geographic face routing Our simulations show that GDSTR finds shorter routes algorithms in the following respects: than geographic face routing algorithms: GDSTR’s stretch is up to 20% less than the best existing algorithm • It requires significantly less maintenance bandwidth in situations where dead ends are common. In addition, than CLDP; we show that GDSTR requires an order of magnitude less • It achieves lower path and hop stretch than existing bandwidth to maintain its trees than CLDP, the only dis- geographic face routing algorithms; and tributed planarization algorithm that is known to work with practical radio networks. • It is simpler and easier to understand and imple- ment. 1 Introduction Like existing geographic routing algorithms, we as- sume that nodes have assigned coordinates and that links Geographic routing algorithms [2, 12, 16, 17, 20] are an are bi-directional. Unlike some previous work, we do attractive alternative to traditional ad hoc routing algo- not require radio ranges to be uniform and to cover unit rithms [8, 23, 24] for wireless networks, because they disks [2, 12]. scale better: the routing state maintained per node is de- Geographic routing algorithms forward packets greed- pendent only on local network density and not on net- ily whenever possible, by routing through a directly con- work size [10, 13]. Recently, geographic routing algo- nected neighbor in the direction of the ultimate destina- rithms have also been proposed as a routing primitive for tion. When there is no such neighbor, face routing algo- USENIX Association NSDI ’06: 3rd Symposium on Networked Systems Design & Implementation 339 rithms avoid the obstacle by forwarding around the faces latest addition to the family is GPVFR, which im- of a planar subgraph of the network graph. GDSTR, proves routing efficiency by exploiting local face infor- in contrast, switches to forwarding along the edges of mation [20]. While GOAFR+ is asymptotically optimal a spanning tree. and bounds worst-case performance with an expanding A common technique for achieving scalability in tradi- ellipse search, GPVFR generally achieves the best aver- tional networking is the aggregation of information about age case stretch performance among existing geographic the address space. A key insight of our work is that face routing algorithms. GDSTR can apply the same principle to help it route The planarization algorithms that were initially avail- along its spanning tree by aggregating the locations cov- able [5, 33] relied on the assumption that the underly- ered by subtrees using convex hulls. We call a tree an- ing network is a Unit Disk Graph (UDG) for correct- notated with convex hulls a hull tree. GDSTR uses the ness and were unusable in practical networks. A ma- convex hulls to decide which direction in the tree is most jor breakthrough was made by Kim et al. in developing likely to make progress towards a given geographic des- the Cross-Link Detection Protocol (CLDP) [13], which tination. produces a subgraph on which face-routing-based algo- GDSTR requires only one hull tree for correctness. rithms are guaranteed to work correctly. Their key in- However, we use a second tree because doing so pro- sight is that starting from a connected graph, nodes can vides better robustness in the event of node failures and independently probe each of their links using a right- an additional routing choice. hand rule to determine if the link crosses some other link A simulation evaluation shows that GDSTR achieves in the network. CLDP uses a two-phase locking proto- a peak improvement of about 20% in terms of path and col to ensure that no more than one link is removed at hop stretch over the best available geographic face rout- any time from any given face; in this way it guarantees ing algorithm in situations where dead ends are common, that the removal of a crossed link will not disconnect the and that GDSTR performance is consistently good over network. While CLDP is able to planarize an arbitrary a wide range of network densities and sizes. graph, every single link in the network has to be probed Simulation also shows that GDSTR generates sig- multiple times and it has a high cost. nificantly less maintenance traffic than CLDP. GDSTR There are previous routing algorithms for ad hoc net- sends two orders of magnitude fewer messages to build works that also use spanning trees, though none of them its trees initially than what CLDP sends to construct a leverages location information like GDSTR. Radhakr- planar subgraph, and GDSTR’s communication when ishnan et al. first proposed the use of a set of dis- maintaining existing trees is one order of magnitude less tributed spanning trees for routing in ad hoc wireless than CLDP. networks [25]. Their algorithm constructs the spanning The remainder of this paper is organized as follows: trees in an ad hoc manner and messages are delivered in Section 2, we provide a review of existing and re- using a flooding-based algorithm. lated work. In Section 3, we describe the maintenance Newsome and Song proposed an approach for rout- of hull trees and the GDSTR routing algorithm in detail, ing in sensor networks called GEM, which embeds a la- and explain why hull trees work in practice. We describe beled graph in the network topology [22]. They proposed our simulation methodology in Section 4 and present our Virtual Polar Coordinate Routing (VPCR), which routes simulation results in Sections 5 and 6. Finally, we con- packets on an embedded ringed tree graph. VPCR was clude in Section 7. evaluated in a regime where average node degree is about 15 and was found to achieve a stretch (which the authors refer to as dilation) of about 1.2. This does not com- 2 Related Work pare favorably with geographic routing algorithms, since in the same regime, geographic routing algorithms are The early proposals for geographic routing were simple able to achieve unit stretch almost all the time. How- greedy forwarding schemes that did not guarantee packet ever, considering that VPCR does not require nodes to delivery in a connected network [3, 7, 31]. Packets are have access to location information because it assigns its simply dropped when greedy forwarding causes them to own virtual polar coordinates, the achieved performance end up at a local minimum. is reasonably good. The first geographic (or geometric) routing algorithm Beacon Vector Routing (BVR) [4] and HopID [35] are to provide guaranteed delivery was face routing [15] routing algorithms that employ a set of landmark nodes (originally called Compass Routing II). Several practi- (beacons). Coordinates are assigned to nodes based on cal algorithms that are variations of face routing have their hop count distances to the beacons. Routing is done since been developed, including GFG [2], GPSR [12] by minimizing a distance function to these coordinates. and the GOAFR+ family of algorithms [16, 17]. The When a packet is trapped at a local minimum, they resort 340 NSDI ’06: 3rd Symposium on Networked Systems Design & Implementation USENIX Association to scoped flooding. The major drawback of this approach n1 is that it requires a large number of beacons (about 40) to n1 achieve routing performance comparable to geographic n2 n3 routing algorithms. It is also somewhat cumbersome to n2 n3 n4 n have to specify a destination with a large set of distance 5 n vectors, and it may be costly to keep updating a node’s n4 5 coordinates when distance vectors change over time un- der network churn. A common application of the spanning tree in the wired domain is the Ethernet spanning tree.