A Branch-and-Bound Algorithm for Building Optimal Data Gathering Tree in Wireless Sensor Networks

In this paper, we consider the maximum lifetime data gathering tree (MLDT) problem in sensor networks. A data gathering tree is a spanning tree rooted at a specified sink so that every node can send its messages to the sink along the tree. The lifetime of a tree is defined as the minimum lifetime among nodes where each node’s lifetime is determined by its initial energy and transmission load. The MLDT problem is NP-hard, and the state-of-the-art solution formulates a decision version of the problem as an integer linear program (ILP) and then solves it by conducting binary search over all possible lifetimes. In this paper, we first give an ILP for the optimization problem rather than its decision version, and then show that using ILP solvers to solve these programs could be highly inefficient. We then propose a branch-and-bound algorithm that incorporates two novel features. First, the bounding method takes into account integer flows, and contains a new set of constraints. Second, a special set of edges are deleted to reduce the number of subproblems generated by the branching process. Numerical simulations on randomly generated networks show that the proposed algorithm outperforms existing algorithms in terms of the number of solved problem instances in a fixed amount of time. Summary of Contribution: We study the maximum lifetime data gathering tree (MLDT) problem in the context of wireless sensor network. MLDT is a fundamental problem in both computer science and operations research. Since sensor nodes are often resource limited, the data gathering tree must be carefully constructed to prolong the network lifetime. In this paper, we first give an integer linear program for the optimization problem rather than its decision version, and then show that using ILP solvers to solve these programs could be highly inefficient. We then propose a branch and bound algorithm that incorporates two novel features.

Diameter-Aggregation Delay Tradeoff for Data Gathering Trees in Wireless Sensor Networks

We define the aggregation delay as the minimum number of time slots it takes for the data to be aggregated in a Data Gathering tree (DG tree) spanning all the nodes of the sensor network; the diameter of a DG tree is the maximum distance (number of hops) from a leaf node to the root node of the tree. We assume that intermediate nodes at the same level or different levels of a DG tree could simultaneously aggregate data from their respective child nodes using different CDMA (Code Division Multiple Access) codes; but, an intermediate node has to schedule non-overlapping time slots (one for each of its child nodes) to aggregate data from its own child nodes. We employ an algorithm to determine the minimum aggregation delay at every intermediate node of the Bottleneck Node Weight (BNW) and Bottleneck Link Weight (BLW)-based DG trees. We observe the BNW-DG trees to incur a smaller tree diameter, but a significantly larger aggregation delay; on the other hand, the BLW-DG trees incur a larger tree diameter and a relatively lower aggregation delay, especially with increase in node density.

Diameter-Aggregation Delay Tradeoff for Data Gathering Trees in Wireless Sensor Networks

We define the aggregation delay as the minimum number of time slots it takes for the data to be aggregated in a Data Gathering tree (DG tree) spanning all the nodes of the sensor network; the diameter of a DG tree is the maximum distance (number of hops) from a leaf node to the root node of the tree. We assume that intermediate nodes at the same level or different levels of a DG tree could simultaneously aggregate data from their respective child nodes using different CDMA (Code Division Multiple Access) codes; but, an intermediate node has to schedule non-overlapping time slots (one for each of its child nodes) to aggregate data from its own child nodes. We employ an algorithm to determine the minimum aggregation delay at every intermediate node of the Bottleneck Node Weight (BNW) and Bottleneck Link Weight (BLW)-based DG trees. We observe the BNW-DG trees to incur a smaller tree diameter, but a significantly larger aggregation delay; on the other hand, the BLW-DG trees incur a larger tree diameter and a relatively lower aggregation delay, especially with increase in node density.

Graph Intersection-Based Benchmarking Algorithm for Maximum Stability Data Gathering Trees in Wireless Mobile Sensor Networks

The authors propose a graph intersection-based benchmarking algorithm to determine the sequence of longest-living stable data gathering trees for wireless mobile sensor networks whose topology changes dynamically with time due to the random movement of the sensor nodes. Referred to as the Maximum Stability-based Data Gathering (Max.Stable-DG) algorithm, the algorithm assumes the availability of complete knowledge of future topology changes and is based on the following greedy principle coupled with the idea of graph intersections: Whenever a new data gathering tree is required at time instant t corresponding to a round of data aggregation, choose the longest-living data gathering tree from time t. The above strategy is repeated for subsequent rounds over the lifetime of the sensor network to obtain the sequence of longest-living stable data gathering trees spanning all the live sensor nodes in the network such that the number of tree discoveries is the global minimum. In addition to theoretically proving the correctness of the Max.Stable-DG algorithm (that it yields the lower bound for the number of discoveries for any network-wide communication topology like spanning trees), the authors also conduct exhaustive simulations to evaluate the performance of the Max.Stable-DG trees and compare to that of the minimum-distance spanning tree-based data gathering trees with respect to metrics such as tree lifetime, delay per round, node lifetime and network lifetime, under both sufficient-energy and energy-constrained scenarios.