Optimal gathering protocols on paths under interference constraints

Abstract

We study the problem of gathering information from the nodes of a multi-hop radio network into a predefined destination node under reachability and interference constraints. In such a network, a node is able to send messages to other nodes within reception distance, but doing so it might create interference with other communications. Thus, a message can only be properly received if the receiver is reachable from the sender and there is no interference from another message being simultaneously transmitted. The network is modeled as a graph, where the vertices represent the nodes of the network and the edges, the possible communications. The interference constraint is modeled by a fixed integer d ≥ 1, which implies that nodes within distance d in the graph from one sender cannot receive messages from another node. In this paper, we suppose that each node has one unit-length message to transmit and, furthermore, we suppose that it takes one unit of time (slot) to transmit a unit-length message and during such a slot we can have only calls which do not interfere (called compatible calls). A set of compatible calls is referred to as a round. We give protocols and lower bounds on the minimum number of rounds for the gathering problem when the network is a path and the destination node is either at one end or at the center of the path. The protocols are shown to be optimal for any d in the first case, and for 1 ≤ d ≤ 4, in the second case.

Data gathering and personalized broadcasting in radio grids with interference

“…Other related results can be found in [1,2,6,7,10] (see [9] for a survey). In these articles data buffering is allowed at intermediate nodes, achieving a smaller makespan.…”

“…For simplicity we suppose that the grid is infinite; however it suffices to consider a grid slightly greater than the one containing all the destinations of messages. Note that our work does not include the case of the paths, already considered in [1,11,15].…”

Optimal Data Gathering Paths and Energy Balance Mechanisms in Wireless Networks

“…A heuristic on-line algorithm is proposed and the simulations show the good performances of the algorithm. In [6,8,7], the quantity that is optimized is the data latency. The authors compute tight bounds of the minimal number of rounds that are required for solving the problem.…”

“…An appropriate scheduling of the transmissions avoids collision. In [35,6,8,7], the authors discuss the problem of determining the optimal scheduling. In [35], the quantity that is optimized is the energy consumption.…”

The Distributed Wireless Gathering Problem

“…The wireless gathering problem in a centralized setting was studied by Bermond et al [4][5][6] and Bonifaci et al [7,8]. Bermond et al [5] showed that the problem of minimizing maximum completion time is NP-hard, even when all release times are zero.…”