Data gathering and personalized broadcasting in radio grids with interference

International audienceIn the gathering problem, a particular node in a graph, the base station , aims at receiving messages from some nodes in the graph. At each step, a node can send one message to one of its neighbors (such an action is called a call ). However, a node cannot send and receive a message during the same step. Moreover, the communication is subject to interference constraints, more precisely, two calls interfere in a step, if one sender is at distance at most dI from the other receiver. Given a graph with a base station and a set of nodes having some messages, the goal of the gathering problem is to compute a schedule of calls for the base station to receive all messages as fast as possible, i.e., minimizing the number of steps (called makespan). The gathering problem is equivalent to the personalized broadcasting problem where the base station has to send messages to some nodes in the graph, with same transmission constraints.In this paper, we focus on the gathering and personalized broadcasting problem in grids. Moreover, we consider the non-buffering model: when a node receives a message at some step, it must transmit it during the next step. In this setting, though the problem of determining the complexity of computing the optimal makespan in a grid is still open, we present linear (in the number of messages) algorithms that compute schedules for gathering with dI∈{0,1,2}. In particular, we present an algorithm that achieves the optimal makespan up to an additive constant 2 when dI=0. If no messages are “close” to the axes (the base station being the origin), our algorithms achieve the optimal makespan up to an additive constant 1 when dI=0, 4 when dI=2, and 3 when both dI=1 and the base station is in a corner. Note that, the approximation algorithms that we present also provide approximation up to a ratio 2 for the gathering with buffering. All our results are proved in terms of personalized broadcasting

Minimum delay Data Gathering in Radio Networks

International audienceThe aim of this paper is to design efficient gathering algorithms (data collection) in a Base Station of a wireless multi hop grid network when interferences constraints are present. We suppose the time is slotted and that during one time slot (step) each node can transmit to one of its neighbours at most one data item. Each device is equipped with a half duplex interface; so a node cannot both receive and transmit simultaneously. During a step only non interfering transmissions can be done. In other words, the non interfering calls done during a step will form a matching. The aim is to minimize the number of steps needed to send to the base station a set of messages generated by the nodes, this completion time is also denoted makespan of the call scheduling. The best known algorithm for open-grids was a multiplicative 1.5-approximation algorithm [Revah, Segal 07]. In such topologies, we give a very simple +2 approximation algorithm and then a more involved +1 approximation algorithm. Moreover, our algorithms work when no buffering is allowed in intermediary nodes, i.e., when a node receives a message at some step, it must transmit it during the next step