Let G = (V, E) be an embedded connected graph with n vertices and m edges. Specifically, the vertex set V consists of points in R 2, and E consists

In a geocasting problem, a message is sent from one node to all the nodes located in a designated region. For example, monitoring center needs to contact all active sensors within a monitored area to either gather data from them periodically, or to provide its location to sensors covering certain area for event reporting. Intelligent flooding methods exist for this task when all active sensors belong to the monitored area. However, when a particular area containing only a small subset of active sensors needs to be monitored, the problem reduces to geocasting. Most existing geocasting solutions are shown not to guarantee delivery. We then describe three approaches to guarantee delivery. Two of them are face traversal schemes and are based on depthfirst search of the face tree and traversal of all faces that intersect the border of geocasting region, respectively. In the entrance zone multicasting based approach, the monitoring center divides entrance ring of geocast region into zones of diameter equal to the transmission radius. The problem is decomposed into multicasting toward centers of each zone, and flooding from these nodes. Improvements to all methods can be made by applying neighbor or area dominating sets and coverage, and converting nodes that are not selected to sleep mode. All solutions that guarantee delivery are reported here for the first time (except a message inefficient version of face tree traversal scheme). 1.

This paper concerns compact routing schemes with arbitrary node names. We present a compact name-independent routing scheme for unweighted networks with n nodes excluding a fixed minor. For any fixed minor, the scheme, constructible in polynomial time, has constant stretch factor and requires routing tables with poly-logarithmic number of bits at each node. For shortest-path labeled routing scheme in planar graphs, we prove an Ω(n ɛ) space lower bound for some constant ɛ>0. This lower bound holds even for bounded degree triangulations, and is optimal for polynomially weighted planar graphs (ɛ =1/2).

In this paper we study on-line local routing algorithms for communication networks. Our algorithms take advantage of the geometric properties of planar networks. We pay special attention to on-line local routing algorithms which guarantee that a message reaches its destination. A message cosists of packets of data that have to be sent to a destination node, i.e. the message itself plus a finite amount of space used to record a constant amount of data to aid it in its traversal, e.g. the address of the starting and destination nodes, a constant number of nodes visited, etc. Local means that at each site we have at our disposal only local information regarding a node and its neighbors, i.e. no global knowledge of the network is available at any time, other that the network is planar and connected. We then develop location aided local routing algorithms for wireless communication networks, in particularly cellular telephone networks.

We address the problem of designing compact routing tables for an unlabeled connected n-node planar network G. For each node r of G, the designer is given a routing spanning tree Tr of G rooted at r, which speci es the routes for sending packets from r to the rest of G.

We show that, given a set of randomly distributed wireless nodes with density n, when the transmission range r_n of wireless nodes satisfies #r log n+c(n) n , the localized Delaunay triangulation (LDel) [1] is the same as the Delaunay triangulation with high probability, where c(n) → ∞ as n goes infinity. Our experiments show that the delivery rates of existing localized routing protocols are increased when localized Delaunay triangulation is used instead of several previously proposed topologies, and the localized routing protocol based on Delaunay triangulation works well in practice.

In a geocasting problem in ad hoc networks, a message is sent from one node to all the nodes located in a designated region. For example, monitoring center needs to contact all active sensors within a monitored area to either gather data from them periodically, or to provide its location to sensors covering certain area for event reporting. Intelligent flooding methods exist for this task when all active sensors belong to the monitored area. However, when a particular area containing only a small subset of active sensors needs to be monitored, the problem reduces to geocasting. This article surveys existing solutions to the geocasting problem, with particular consideration on whether or not they guarantee delivery. Most existing solutions are shown not to guarantee delivery. Three approaches to guarantee delivery are then described. Two of them are face traversal schemes and are based on depth-first search of the face tree and traversal of all faces that intersect the border of geocasting region, respectively. In the entrance zone multicasting based approach, the monitoring center divides entrance ring of geocast region into zones of diameter equal to the transmission radius. The problem is decomposed into multicasting toward centers of each zone, and flooding from these nodes. Improvements to all methods can be made by applying neighbor or area dominating sets and coverage, and converting nodes that are not selected to sleep mode. 1.

Abstract — This paper addresses the problem of scat-ternet formation for single-hop Bluetooth based personal area and ad hoc networks, with minimal communication overhead. In a single-hop ad hoc network, all wireless devices are in the radio vicinity of each other, e.g., electronic devices in a laboratory, or laptops in a conference room. Recent scatternet formation schemes by Li, Stojmenovic and Wang [1] are position based and were applied for multi-hop networks. These schemes are localized and can construct degree limited and connected piconets, without parking any node. They also limit to 7 the number of slave roles in one piconet. The creation and maintenance require small overhead in addition to maintaining location infor-mation for one-hop neighbors. In this article we apply this method to single-hop networks, by showing that position information is then not needed. Each node can simply select a virtual position, and communicate it to all neighbors in the neighbor discovery phase. Nodes then act according to the scheme by Li, Stojmenovic and Wang using such virtual positions instead of real ones. In addition, in this paper we use Delaunay triangulation instead of partial Delaunay triangulation proposed in [1], since each node has all the information needed. Likewise, we can also apply Minimum Spanning Tree (MST) as the planar topology in our new schemes. Finally, we design experiments to study both the properties of formatted scatternet (such as number

Abstract — We investigate the use of distributed image sensing for network localization, dynamic routing, and load balancing in wireless sensor networks. In particular, the image sensors are first used to obtain angular bearing information between each network node and a set of other nodes, mobile agents, or targets. This data is used to construct the relative geographic topology of the network. The image sensors are then employed to make periodic measurements, which are reported to the destination via multihop routing. Nodes may also infrequently detect an event from which a set of image frames need to be reported. These high-bandwidth event reports may cause packet queues to develop at the routing nodes along paths to the destination. We propose a distributed routing scheme that employs a cost function based on location data, in-node queue sizes, and energy levels at neighboring nodes. Our scheme also implements a set of relative priority levels for the event-based and periodic data packets. Simulation results are presented and indicate improved network lifetime, lower end-to-end average and maximum delays, and significantly reduced buffer size requirements for the network nodes. I.

The detour and spanning ratio of a graph � embedded in �� � measure how well � approximates Euclidean space and the complete Euclidean graph, respectively. In this paper we describe �������������� � time algorithms for computing the detour and spanning ratio of a planar polygonal path. By generalizing these algorithms, we obtain ���������������� �-time algorithms for computing the detour or spanning ratio of planar trees and cycles. Finally, we develop subquadratic algorithms for computing the detour and spanning ratio for paths, cycles, and trees embedded in �� � , and show that computing the detour in �� � is at least as hard as Hopcroft’s problem.