Distributed transforms for efficient data gathering in arbitrary networks

Abstract

In this paper we present a simple distributed transform for datagathering applications for arbitrary networks that achieves significant gains over raw data transmission, while requiring minimal coordination between nodes. In most spatial compression schemes some nodes (i.e., raw nodes) need to transmit raw data before spatial compression can be performed. Nodes that receive raw data (i.e., aggregating nodes) can then perform spatial compression. Thus, most spatial compression schemes require some raw-aggregating node assignment (RANA) to enable compression. Since transmitting raw data usually requires more bits than transmitting compressed data, we seek to find RANAs that select raw nodes in order to minimize overall energy consumption in the network. We formulate the problem of optimally selecting raw nodes as a set cover problem and propose distributed solutions for a variety of scenarios, including single-sink, multi-sink and gossip-based networks.

Optimized Update/Prediction Assignment for Lifting Transforms on Graphs

“…While straightforward UPAs have been proposed for these specific examples, optimizing the UPA for arbitrary weighted non-planar graphs of practical interest becomes a complex problem, and just a few solutions have been proposed in the literature. The UPA proposed in [32], [33] to minimize the total energy consumption in a wireless sensor network is equivalent to solving a Set-Covering (SC) problem, i.e., minimizing the number of U nodes while guaranteeing that every P node has at least one U neighbor, as in the example in Figure 2(e). [19] and [34] find techniques that minimize the number of discarded edges (i.e., the percentage of direct neighbors in the graph that have the same label), proving that the UPA that minimizes the error between the transform in the original graph and in the simplified graph (i.e., after edges are discarded) corresponds to the solution to the classical Weighted Maximum-Cut (WMC) problem (i.e., finding the UPA which maximizes the sum of weights over the edges between U and P sets, as in Figure 2(f)).…”