Jaroslav Opatrny

Bio: Jaroslav Opatrny is an academic researcher from Concordia University. The author has contributed to research in topics: Unit disk graph & Destination-Sequenced Distance Vector routing. The author has an hindex of 26, co-authored 116 publications receiving 1839 citations. Previous affiliations of Jaroslav Opatrny include Concordia University Wisconsin & Rutgers University.

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

Abstract: 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 © 2003 John Wiley & Sons, Ltd.

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

Abstract: 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.

On Minimizing the Sum of Sensor Movements for Barrier Coverage of a Line Segment

Abstract: 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

Abstract: 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.

Multicommodity max-flow min-cut theorems and their use in designing approximation algorithms

Abstract: In this paper, we establish max-flow min-cut theorems for several important classes of multicommodity flow problems. In particular, we show that for any n-node multicommodity flow problem with uniform demands, the max-flow for the problem is within an O(log n) factor of the upper bound implied by the min-cut. The result (which is existentially optimal) establishes an important analogue of the famous 1-commodity max-flow min-cut theorem for problems with multiple commodities. The result also has substantial applications to the field of approximation algorithms. For example, we use the flow result to design the first polynomial-time (polylog n-times-optimal) approximation algorithms for well-known NP-hard optimization problems such as graph partitioning, min-cut linear arrangement, crossing number, VLSI layout, and minimum feedback arc set. Applications of the flow results to path routing problems, network reconfiguration, communication in distributed networks, scientific computing and rapidly mixing Markov chains are also described in the paper. Categories and Subject Descriptors: F.2.2 (Analysis of Algorithms and Problem Complexity):