Data gathering and personalized broadcasting in radio grids with interference

In 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 d I 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 d I ? { 0 , 1 , 2 } . In particular, we present an algorithm that achieves the optimal makespan up to an additive constant 2 when d I = 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 d I = 0 , 4 when d I = 2 , and 3 when both d I = 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.

[1]  Hervé Rivano,et al.  Minimum Delay Data Gathering in Radio Networks , 2009, ADHOC-NOW.

[2]  Stéphane Pérennes,et al.  Optimal time data gathering in wireless networks with multidirectional antennas , 2013, Theor. Comput. Sci..

[3]  Michael Segal,et al.  Real-time data gathering in sensor networks , 2010, Discret. Appl. Math..

[4]  Jean-Claude Bermond,et al.  Gathering with Minimum Completion Time in Sensor Tree Networks , 2010, J. Interconnect. Networks.

[5]  Stéphane Pérennes,et al.  Hardness and approximation of gathering in static radio networks , 2006, Fourth Annual IEEE International Conference on Pervasive Computing and Communications Workshops (PERCOMW'06).

[6]  Michael Segal,et al.  Improved Algorithms for Data-Gathering Time in Sensor Networks II: Ring, Tree and Grid Topologies , 2007, International Conference on Networking and Services (ICNS '07).

[7]  Massimo Franceschetti,et al.  Lower bounds on data collection time in sensory networks , 2004, IEEE Journal on Selected Areas in Communications.

[8]  Stéphane Pérennes,et al.  From Balls and Bins to Points and Vertices , 2005, Algorithmic Oper. Res..

[9]  Jean-Claude Bermond,et al.  Optimal gathering protocols on paths under interference constraints , 2009, Discret. Math..

[10]  Michael Segal,et al.  Improved bounds for data-gathering time in sensor networks , 2008, Comput. Commun..

[11]  Michael Segal,et al.  Improved Algorithms for Data-Gathering Time in Sensor Networks II: Ring, Tree, and Grid Topologies , 2009, Int. J. Distributed Sens. Networks.

[12]  Bin Tang,et al.  Delay Efficient Data Gathering in Sensor Networks , 2005, MSN.

[13]  Luisa Gargano,et al.  Optimally Fast Data Gathering in Sensor Networks , 2006, MFCS.

[14]  Stéphane Pérennes,et al.  Optimal Time Data Gathering in Wireless Networks with Omni-Directional Antennas , 2011, SIROCCO.

[15]  Jean-Claude Bermond,et al.  Optimal gathering in radio grids with interference , 2012, Theor. Comput. Sci..

[16]  Jean-Claude Bermond,et al.  Optimal Gathering Algorithms in Multi-Hop Radio Tree-Networks with Interferences , 2010, Ad Hoc Sens. Wirel. Networks.

[17]  Stéphane Pérennes,et al.  Bandwidth Allocation in Radio Grid Networks , 2008 .

[18]  Luisa Gargano,et al.  Collision-free path coloring with application to minimum-delay gathering in sensor networks , 2009, Discret. Appl. Math..

[19]  Leen Stougie,et al.  An approximation algorithm for the wireless gathering problem , 2008, Oper. Res. Lett..

[20]  Leen Stougie,et al.  Data Gathering in Wireless Networks , 2010, Graphs and Algorithms in Communication Networks.