Lata Narayanan

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

Robust position-based routing in wireless Ad Hoc networks with unstable transmission ranges

Several papers showed how to perform routing in ad hoc wireless networks based on the positions of the mobile hosts. However, all these protocols are likely to fail if the transmission ranges of the mobile hosts vary due to natural or man-made obstacles or weather conditions. These protocols may fail because in routing either some connections are not considered which effectively results in disconnecting the network, or the use of some connections causes livelocks. In this paper, we describe a robust routing protocol that tolerates up to roughly 40% of variation in the transmission ranges of the mobile hosts. More precisely, our protocol guarantees message delivery in a connected adhoc network whenever the ratio of the maximum transmission range to the minimum transmission range is at most √2.

Static Frequency Assignment in Cellular Networks

Abstract. A cellular network is generally modeled as a subgraph of the triangular lattice. In the static frequency assignment problem, each vertex of the graph is a base station in the network, and has associated with it an integer weight that represents the number of calls that must be served at the vertex by assigning distinct frequencies per call. The edges of the graph model interference constraints for frequencies assigned to neighboring stations. The static frequency assignment problem can be abstracted as a graph multicoloring problem. We describe an efficient algorithm to multicolor optimally any weighted even or odd length cycle representing a cellular network. This result is further extended to any outerplanar graph. For the problem of multicoloring an arbitrary connected subgraph of the triangular lattice, we demonstrate an approximation algorithm which guarantees that no more than 4/3 times the minimum number of required colors are used. Further, we show that this algorithm can be implemented in a distributed manner, where each station needs to have knowledge only of the weights at a small neighborhood.

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.

Distributed Online Frequency Assignment in Cellular Networks

A cellular network is generally modeled as a subgraph of the triangular lattice. The distributed online frequency assignment problem can be abstracted as a multicoloring problem on a weighted graph, where the weight vector associated with the vertices models the number of calls to be served at the vertices and is assumed to change over time. In this paper, we develop a framework for studying distributed online frequency assignment in cellular networks. We present the first distributed online algorithms for this problem with proven bounds on their competitive ratios. We show a series of algorithms that use at each vertex information about increasingly larger neighborhoods of the vertex, and that achieve better competitive ratios. In contrast, we show lower bounds on the competitive ratios of some natural classes of online algorithms.

On routing with guaranteed delivery in three-dimensional ad hoc wireless networks

We study routing algorithms for three-dimensional ad hoc networks that guarantee delivery and are k-local, i.e., each intermediate node υs routing decision only depends on knowledge of the labels of the source and destination nodes, of the subgraph induced by nodes within distance k of υ, and of the neighbour of υ from which the message was received. We model a three-dimensional ad hoc network by a unit ball graph, where nodes are points in R3, and nodes u and υ are joined by an edge if and only if the distance between u and v is at most one. The question of whether there is a simple local routing algorithm that guarantees delivery in unit ball graphs has been open for some time. In this paper, we answer this question in the negative: we show that for any fixed k, there can be no k-local routing algorithm that guarantees delivery on all unit ball graphs. This result is in contrast with the two-dimensional case, where 1-local routing algorithms that guarantee delivery are known. Specifically, we show that guaranteed delivery is possible if the nodes of the unit ball graph are contained in a slab of thickness 1/√2. However, there is no k-local routing algorithm that guarantees delivery for the class of unit ball graphs contained in thicker slabs, i.e., slabs of thickness 1/√2+Ɛ for some Ɛ > 0. The algorithm for routing in thin slabs derives from a transformation of unit ball graphs contained in thin slabs into quasi unit disc graphs, which yields a 2-local routing algorithm. We also show several results that further elaborate on the relationship between these two classes of graphs.

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.

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

Complexity of barrier coverage with relocatable sensors in the plane

2\sqrt{n}

Evacuating Robots from a Disk Using Face-to-Face Communication Extended Abstract

intervals on any edge, there exist chordal rings for which any optimal interval routing scheme that labels the vertices around the ring in the graph requires