Jaroslav Opatrny

Robust position-based routing in wireless ad hoc networks with irregular transmission ranges†

Several papers considered the problem of routing in ad hoc wireless networks using the positions of the mobile hosts. Perimeter routing1, 2 gives an algorithm that guarantees delivery of messages in such networks without the use of flooding of control packets. However, this protocol is likely to fail if the transmission ranges of the mobile hosts vary because of natural or man-made obstacles. It may fail because either some connections are not considered, which effectively results in a disconnection of the network, or because some crossing connections are used, which could misdirect the message. In this paper, we describe a robust routing protocol, a variant of perimeter routing, which tolerates up to 40% of variation in the transmission ranges of the mobile hosts. More precisely, our protocol guarantees message delivery in a connected ad hoc wireless network without the use of message flooding whenever the ratio of the maximum transmission range to the minimum transmission range is at most √2. Copyright

On minimizing the sum ofensor movements for barrier coverage of a line segment

A set of sensors establishes barrier coverage of a given line segment if every point of the segment is within the sensing range of a sensor. Given a line segment I, n mobile sensors in arbitrary initial positions on the line (not necessarily inside I) and the sensing ranges of the sensors, we are interested in finding final positions of sensors which establish a barrier coverage of I so that the sum of the distances traveled by all sensors from initial to final positions is minimized. It is shown that the problem is NP complete even to approximate up to constant factor when the sensors may have different sensing ranges. When the sensors have an identical sensing range we give several efficient algorithms to calculate the final destinations so that the sensors either establish a barrier coverage or maximize the coverage of the segment if complete coverage is not feasible while at the same time the sum of the distances traveled by all sensors is minimized. Some open problems are also mentioned.

A Position Based Ant Colony Routing Algorithm for Mobile Ad-hoc Networks

Position based routing algorithms use the knowledge of the position of nodes for routing of packets in mobile ad-hoc networks. Previously proposed position based routing algorithms may fail to find a route from a source to a destination in some types of ad-hoc networks and if they find a route, it may be much longer than the shortest path. On the other hand, routing algorithms which are based on ant colony optimization find routing paths that are close in length to the shortest paths. The drawback of these algorithms is the large number of control messages that needs to be sent or the long delay before the routes are established from a source to a destination. In this paper we propose a new reactive routing algorithm for mobile ad hoc networks, called POSANT (Position based Ant Colony Routing Algorithm), which combines the idea of ant colony optimization with information about the position of nodes. In contrast to the other ant colony optimization based routing algorithms, our simulations show that POSANT has a relatively short route establishment time while using a small number of control messages which makes it a scalable reactive routing algorithm.

Embeddings of complete binary trees into grids and extended grids with total vertex-congestion

Abstract Let G and H be two simple, undirected graphs. An embedding of the graph G into the graph H is an injective mapping f from the vertices of G to the vertices of H, together with a mapping which assigns to each edge [u,v] of G a path between f(u) and f(v) in H. The grid M(r,s) is the graph whose vertex set is the set of pairs on nonnegative integers, {(i,j) : 0⩽i 0⩽j , in which there is an edge between vertices (i,j) and (k,l) if either |i−k|=1 and j=l or i=k and |j−l|=1. The extended grid EM(r,s) is the graph whose vertex set is the set of pairs on nonnegative integers, {(i,j) : 0⩽i 0⩽j , in which there is an edge between vertices (i,j) and (k,l) if and only if |i−k|⩽1 and |j−l|⩽1. In this paper, we give embeddings of complete binary trees into square grids and extended grids with total vertex-congestion 1, i.e., for any vertex x of the extended grid we have load(x)+vertex-congestion(x)⩽1. Depending on the parity of the height of the tree, the expansion of these embeddings is approaching 1.606 or 1.51 for grids, and 1.208 or 1.247 for extended grids.

POSANT: A Position Based Ant Colony Routing Algorithm for Mobile Ad-hoc Networks

Availability of cheap positioning instruments like GPS receivers makes it possible for routing algorithms to use the position of nodes in an ad hoc mobile network. Regular position based routing algorithms fail to find a route from a source to a destination in some cases when the network contains nodes with irregular transmission ranges or they find a route that is much longer than the shortest path. On the other hand, routing algorithms based on ant colony optimization find routing paths that are close to the shortest paths even if the nodes in the network have different transmission ranges. The drawback of these algorithms is the large number of messages that needs to be sent or the long delay before the routes are established. In this paper we propose POSANT, a reactive routing algorithm for mobile ad hoc networks which combines the idea of ant colony optimization with information about the position of nodes. Our simulations show that POSANT has a shorter route establishment time while using a smaller number of control messages than other ant colony routing algorithms.

Minimizing the number of sensors moved on line barriers

We study the problem of achieving maximum barrier coverage by sensors on a barrier modeled by a line segment, by moving the minimum possible number of sensors, initially placed at arbitrary positions on the line containing the barrier. We consider several cases based on whether or not complete coverage is possible, and whether non-contiguous coverage is allowed in the case when complete coverage is impossible. When the sensors have unequal transmission ranges, we show that the problem of finding a minimum-sized subset of sensors to move in order to achieve maximum contiguous or non-contiguous coverage on a finite line segment barrier is NP-complete. In contrast, if the sensors all have the same range, we give efficient algorithms to achieve maximum contiguous as well as non-contiguous coverage. For some cases, we reduce the problem to finding a maximum-hop path of a certain minimum (maximum) weight on a related graph, and solve it using dynamic programming.

Local algorithms for dominating and connected dominating sets of unit disk graphs with location aware nodes

Many protocols in ad-hoc networks use dominating and connected dominating sets, for example for broadcasting and routing. For large ad hoc networks the construction of such sets should be local in the sense that each node of the network should make decisions based only on the information obtained from nodes located a constant number of hops from it. In this paper we use the location awareness of the network, i.e. the knowledge of position of nodes in the plane to provide local, constant approximation, deterministic algorithms for the construction of dominating and connected dominating sets of a Unit Disk Graph (UDG). The size of the constructed set, in the case of the dominating set, is shown to be 5 times the optimal, while for the connected dominating set 7.453 + Ɛ the optimal, for any arbitrarily small Ɛ > 0. These are to our knowledge the first local algorithms whose time complexities and approximation bounds are independent of the size of the network.

High delivery rate position-based routing algorithms for 3D ad hoc networks

Position-based routing algorithms use the geographic position of the nodes in a network to make the forwarding decisions. Recent research in this field primarily addresses such routing algorithms in two dimensional (2D) space. However, in real applications, nodes may be distributed in three dimensional (3D) environments. In this paper, we propose several randomized position-based routing algorithms and their combination with restricted directional flooding-based algorithms for routing in 3D environments. The first group of algorithms AB3D are extensions of previous randomized routing algorithms from 2D space to 3D space. The second group ABLAR chooses m neighbors according to a space-partition heuristic and forwards the message to all these nodes. The third group T-ABLAR-T uses progress-based routing until a local minimum is reached. The algorithm then switches to ABLAR for one step after which the algorithm switches back to the progress-based algorithm again. The fourth group AB3D-ABLAR uses an algorithm from the AB3D group until a threshold is passed in terms of number of hops. The algorithm then switches to an ABLAR algorithm. The algorithms are evaluated and compared with current routing algorithms. The simulation results on unit disk graphs (UDG) show a significant improvement in delivery rate (up to 99%) and a large reduction of the traffic.

Compact Routing on Chordal Rings of Degree 4

Abstract. A chordalringG(n;c) of degree 4 is a ring of n nodes with chords connecting each vertex i to the vertex (i + c) mod n . In this paper we investigate compact routing schemes on such networks. We show an optimal boolean routing scheme for any such network that requires O( log n) bits of storage at each node, and O(1) time to compute a shortest path to any destination. This improves on the results of [16] which gives a linear time algorithm for such networks and [6] where efficient routing schemes for certain fixed values of c were developed. Further, we show several bounds on interval routing schemes for such networks. We show that while every chordal ring has an optimal interval routing scheme with at most

Local construction of planar spanners in unit disk graphs with irregular transmission ranges

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