We propose a novel localized algorithm that constructs a bounded degree and planar spanner for wireless ad hoc networks modeled by unit disk graph (UDG). Every node only has to know its 2-hop neighbors to find the edges in this new structure. Our method applies the Yao structure on the local Delaunay graph [21] in an ordering that are computed locally. This new structure has the following attractive properties: (1) it is a planar graph; (2) its node degree is bounded from above by a positive constant 19 + ⌈ 2π α ⌉; (3) it is a t-spanner (given any two nodes u and v, there is a path connecting them in the structure such that its length is no more than t ≤ max { π α,πsin 2 2 +1}·Cdel times of the shortest path in UDG); (4) it can be constructed locally and is easy to maintain when the nodes move around; (5) moreover, we show that the total communication cost is O(n), where n is the number of wireless nodes, and the computation cost of each node is at most O(d log d), where d is its 2-hop neighbors in the original unit disk graph. Here Cdel is the spanning ratio of the Delaunay triangulation, which is at most 4 √ 3 9 π. And the adjustable parameter α satisfies 0 <α<π/3. In addition, experiments are conducted to show this topology is efficient in practice, compared with other well-known topologies used in wireless ad hoc networks. Previously, only centralized method [5] of constructing bounded degree planar spanner is known, with degree bound 27 and spanning ratio t ≃ 10.02. The distributed implementation of their centralized method takes O(n 2) communications in the worst case. No localized methods were known previously for constructing bounded degree planar spanner.

In ad hoc wireless networks, it is crucial to minimize power consumption while maintaining key network properties. This work studies power assignments of wireless devices that minimize power while maintaining k-fault tolerance. Specifically, we require all links established by this power setting be symmetric and form a k-vertex connected subgraph of the network graph. This problem is known to be NP-hard. We show current heuristic approaches can use arbitrarily more power than the optimal solution. Hence, we seek approximation algorithms for this problem. We present three approximation algorithms. The first algorithm gives an O(kα)-approximation where α is the best approximation factor for the related problem in wired networks (the best α so far is O(log k).) With a more careful analysis, we show our second (slightly more complicated) algorithm is an O(k)-approximation. Our third algorithm assumes that the edge lengths of the network graph form a metric. In this case, we present simple and practical distributed algorithms for the cases of 2- and 3-connectivity with constant approximation factors. We generalize this algorithm to obtain an O(k 2c+2)-approximation for general k-connectivity (2 ≤ c ≤ 4 is the power attenuation exponent). Finally, we show that these approximation algorithms compare favorably with existing heuristics. We note that all algorithms presented in this paper can be used to minimize power while maintaining k-edge connectivity with guaranteed approximation factors.

This paper investigate fault tolerance for wireless ad hoc networks. We consider a large-scale of wireless networks whose nodes are distributed randomly in a unit-area square region. Given n wireless nodes V , each with transmission range rn , the wireless networks are often modeled by graph G(V,rn ) in which two nodes are connected if their Euclidean distance is no more than rn .

We consider the problem of deploying or repairing a sensor network to guarantee a specified level of multi-path connectivity (k-connectivity) between all nodes. Such a guarantee simultaneously provides fault tolerance against node failures and high overall network capacity (by the max-flow min-cut theorem). We design and analyze the first algorithms that place an almostminimum number of additional sensors to augment an existing network into a k-connected network, for any desired parameter k. Our algorithms have provable guarantees on the quality of the solution. Specifically, we prove that the number of additional sensors is within a constant factor of the absolute minimum, for any fixed k. We have implemented greedy and distributed versions of this algorithm, and demonstrate in simulation that they produce high-quality placements for the additional sensors.

In most existing localized topology control protocols for mobile ad hoc networks (MANETs), each node selects a few logical neighbors based on location information, and uses a small transmission range to cover those logical neighbors. Transmission range reduction conserves energy and bandwidth consumption, while still maintaining network connectivity. However, the majority of these approaches assume a static network without mobility. In a mobile environment network connectivity can be com-promised by two types of “bad ” location information: inconsistent information, which makes a node select too few logical neighbors, and outdated information, which makes a node use too small a trans-mission range. In this paper, we first show some issues in existing topology control. Then we propose a mobility-sensitive topology control method that extends many existing mobility-insensitive protocols. Two mechanisms are introduced: consistent local views that avoid inconsistent information, and delay and mobility management that tolerate outdated information. The effectiveness of the proposed approach is confirmed through an extensive simulation study.

An important problem in wireless ad hoc and sensor networks is to select a few nodes to form a virtual backbone that supports routing and other tasks such as area monitoring. Previous work in this area has focused on selecting a small vir-tual backbone for high efficiency. In this paper, we propose the construction of a k-connected k-dominating set (k-CDS) as a backbone to balance efficiency and fault tolerance. Four localized k-CDS construction protocols are proposed. The first pro-tocol randomly selects virtual backbone nodes with a given probability pk, where pk depends on the value of k and network condition, such as network size and node density. The second one maintains a fixed backbone node degree of Bk, where Bk also depends on the network condition. The third protocol is a deterministic ap-proach. It extends Wu and Dai’s coverage condition, which is originally designed for 1-CDS construction, to ensure the formation of a k-CDS. The last protocol is a hybrid of probabilistic and deterministic approaches. It provides a generic frame-work that can convert many existing CDS algorithms into k-CDS algorithms. These protocols are evaluated via a simulation study. Key words: Connected dominating set (CDS), k-vertex connectivity, localized algorithms, simulation, wireless ad hoc and sensor networks. PACS: Preprint submitted to Elsevier Science 23 September 2005

Many routing protocols have been proposed for wireless ad hoc networks, and most of them are based on some variants of flooding. Thus many routing messages are propagated through the network unnecessarily despite various optimizations. Gossip based routing method has been used and re-investigated to reduce the number of messages in both wired networks and wireless ad hoc networks. However, the global gossiping still generates many unnecessary messages in the area that could be far away from the line between sender node and receiver node. We propose a regional gossip approach, where only the nodes within some region forward a message with some probability, to reduce the overhead of the route discovery in the network. We show how to set the forwarding probability based on the region and the network density both by theoretical analysis and by extensive simulations. Our simulations show that the number of messages generated using this approach is much less than the simple global gossiping method, which already saves many messages compared with global flooding. We expect that the improvement should be even more significant in larger networks.

Given a graph with costs on the edges, the power of a node is the maximum cost of an edge leaving it, and the power of the graph is the sum of the powers of the nodes of this graph. Motivated by applications in wireless multi-hop networks, we consider four fundamental problems under the power minimization criteria: the Min-Power b-Edge-Cover problem (MPb-EC) where the goal is to find a min-power subgraph so that the degree of every node v is at least some given integer b(v), the Min-Power k-node Connected Spanning Subgraph problem (MPk-CSS), Min-Power k-edge Connected Spanning Subgraph problem (MPk-ECSS), and finally the Min-Power k-Edge-Disjoint Paths problem in directed graphs (MPk-EDP). We give an O(log 4 n)-approximation algorithm for MPb-EC. This gives an O(log 4 n)-approximation algorithm for MPk-CSS for most values of k, improving the best previously known O(k)-approximation guarantee. In contrast, we obtain an O ( √ n) approximation algorithm for MPk-ECSS, and for its variant in directed graphs (i.e., MPk-EDP), we establish the following inap-proximability threshold: MPk-EDP cannot be approximated within O(2 log1−ε n) for any fixed ε> 0, unless NP-hard problems can be solved in quasi-polynomial time.

Topology control, wherein nodes adjust their transmission ranges to conserve en-ergy and reduce interference, is an important feature in wireless ad hoc networks. Contrary to most of the literature on topology control which focuses on reducing en-ergy consumption, in this paper we tackle the topology control problem with the goal of limiting interference as much as possible, while keeping the communication graph connected with high probability. Our approach is based on the principle of maintaining the number of physical neighbors of every node equal to or slightly below a specific value k. As we will discuss in this paper, having a non-trivially bounded physical node degree allows a network topology with bounded interference to be generated. The proposed approach enforces symmetry on the resulting communication graph, thereby easing the operation of higher layer protocols. To evaluate the performance of our approach, we estimate the value of k that guarantees connectivity of the communica-tion graph with high probability both theoretically and through simulation. We then define k-Neigh, a fully distributed, asynchronous, and localized protocol that uses distance estimation. k-Neigh guarantees logarithmically bounded physical degree at every node, is the most efficient known protocol (requiring 2n messages in total, where

Abstract- Ad hoc network normally has critical connectivity properties before partitioning. The timely recognition is important in order to perform some data or service replication. Several existing centralized or globalized algorithms declare an edge or a node as critical if their removal will separate the network into several components. We introduce several localized definitions of critical nodes and critical links, using topological or positional information. A node is critical if the subgraph of k-hop neighbours of node (without the node itself) is disconnected. We propose three definitions of critical links, based on verifying common k-hop neighbours, loop length, and critical status of link endpoints, respectively. The experiments with random unit graph model of ad hoc networks show high correspondence of local and global decisions. For instance, in experiments with 500 nodes in connected random unit graphs (using a novel graph generation method from [6], first published here), over half of locally estimated critical nodes and links were indeed globally critical even for k=1 (the accuracy increases to over 70 % for k=2 and over 80% for k=3), for average number of neighbours ranging from 3 to 15. The errors mostly occur when alternative routes exist but are relatively long, and therefore may not provide satisfactory service in applications. Therefore our localized protocols provide faster and often more reliable partition warnings for possible timely replication decisions. I.