Jean-Claude König

Scheduling algorithms for parallel Gaussian elimination with communication costs

We consider a graph theoretical model and study a parallel implementation of the well-known Gaussian elimination method on parallel distributed memory architectures, where the communication delay for the transmission of an elementary data is higher than the computation time of an elementary instruction. We propose and analyze two low-complexity algorithms for scheduling the tasks of the parallel Gaussian elimination on an unbounded number of completely connected processors. We compare these two algorithms with a higher-complexity general-purpose scheduling algorithm, the DSC heuristic, proposed by A. Gerasoulis and T. Yang (1993).

On the complexity of scheduling with large communication delays

Abstract Given a directed acyclic graph (dag) with unit execution time tasks and constant communication delays c ⩾ 2, we are interested in deciding if there is a schedule for the dag of length at most L. We prove that the problem is polynomial when L is equal to (c + 1), or (c + 2) for the special case of c = 2, and that it is NP-complete for (c + 3) for any value of c, even in the case of a bipartite dag of depth one.

Optimal schedules for d-D grid graphs with communication delays

We consider a task graph model taking into account the communication among tasks of a parallel system. First, we assume that the available number of processors is adequate for dealing with the whole width of the task graph (i.e. the number of processors is unbounded), and we propose a schedule, called Line-Schedule, which executes the tasks of a d-dimensional grid graph (d-D grid in short) in the optimal time. We continue by proving that Line-Schedule is the only strategy able to execute a d-D grid in the optimal time. Furthermore, we compute the minimum number of processors required to execute a d-D grid optimally.

Complexity and approximation for the precedence constrained scheduling problem with large communication delays

We investigate the problem of minimizing the makespan for the multiprocessor scheduling problem. We show that there is no hope of finding a ρ-approximation with

Ellipse Routing: A Geographic Routing Protocol for Mobile Sensor Networks with Uncertain Positions

\displaystyle \rho < 1+ 1/(c+4)

A Distributed Method to Localization for Mobile Sensor Networks

(unless

MuR : A Distributed Preliminary Method For Location Techniques in Sensor Networks

{\cal{P}}={\cal{NP}}

A distributed method for dynamic resolution of BGP oscillations

) for the case where all the tasks of the precedence graph have unit execution times, where the multiprocessor is composed of an unrestricted number of machines, and where c denotes the communication delay between two tasks i and j submitted to a precedence constraint and to be processed by two different machines. The problem becomes polynomial whenever the makespan is at the most (c+1). The (c+2) case is still partially opened.

A LOW OVERHEAD SCHEDULE FOR A 3D-GRID GRAPH

Several routing protocols have been proposed for mobile wireless sensor networks. Some are based on variants of flooding algorithms leading to redundant copies of message unnecessarily. Despite various optimizations, such routing methods still remain inefficient. This paper deals with region-based routing which has been introduced to reduce the number of messages in the network. We propose an energy efficient routing algorithm, called Ellipse-routing, which is based on region-based routing. A virtual ellipse is built thanks to source and destination positions. So, only nodes within this region forward a message. For a given energy consumption model, we select a suitable ellipse factor and a transmission range, leading to a delivery rate close to 100% while minimizing energy consumption. Then, we extend the proposed scheme to take into account position errors. Performances of proposed algorithms are shown thanks to simulations.

AT-Angle: A distributed method for localization using angles in sensor networks

Mobile wireless sensors need to know their localizations in many control and monitoring applications. Among all sensors, some know their exact position (i.e., they are equipped with GPS or they are positioned by human intervention). These sensors are called anchors. Some sensors can have different capabilities allowing them to calculate either distances or angles when they receive messages from others nodes. So, they only use anchor positions to obtain an estimated position. However, when sensors are mobile they cannot continuously calculate their position because of the energy constraints. This paper concerns the localization problem in the case where all nodes in the network (anchors and others sensors) are mobile. The authors propose three techniques following the capabilities of nodes. Thus, each node obtains either an exact position or an approximate position with the knowledge of the maximal error born. Also, the authors adapt the periods where nodes invoke their localization. Simulation results show the performances of our methods in term of accuracy and determinate the technique the more adapted related to the network configurations.