## 1 Introduction  
Wireless Sensor Networks (WSNs) are typically deployed for monitoring environmental data such as temperature, pressure, humidity, _etc_. Sensor nodes operate under limited battery charge and transmission range. Hence, the data sensed at one or more sensor nodes cannot be directly propagated to the control center (a.k.a. sink); multi-hop data propagation is the norm. Various algorithms for determining communication topologies (like cluster [1], grid [2], chain [3], connected dominating set [4], tree [5], _etc._) that support the many-to-one reporting style have been proposed in the literature. Among these, the data gathering trees (DG trees) have been considered energy-efficient due to the use of the minimum number of links for data transmission and reception [5; 6; 7]. In this research, we focus on the delay incurred for data aggregation along the edges of a DG tree. 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 network. Various algorithms (e.g., [8; 9; 10; 11; 12; 13]) have been proposed to determine the aggregation delay for DG trees and all of these assume limited availability of the communication channels and focus on scheduling the channels for the different nodes to minimize the aggregation delay. In this paper, we consider a channel availability model such that the intermediate nodes at the same level or different levels could simultaneously aggregate data from their respective child nodes using different CDMA (Code Division Multiple Access) codes [14]. An intermediate node has to schedule non-overlapping time slots (one for each of its child nodes: Time Division Multiple Access, TDMA) to aggregate data from its child nodes. Given a DG tree with sufficient availability of communication channels with unique CDMA codes, we propose a benchmarking algorithm to determine the minimum aggregation delay at every intermediate node (including the root node) of the DG tree. We run the proposed algorithm on four broad categories of DG trees typically used for data aggregation in WSNs [5; 15; 16; 17; 18; 19; 20]: The Maximum Bottleneck Node Weight-based Data Gathering trees (MaxBNW-DG trees) are the ones for which the bottleneck node weight (minimum node weight) of the path from any node to the root node is the maximum; the Minimum Bottleneck Node Weight-based Data Gathering trees (MinBNW-DG trees) are the ones for which the bottleneck node weight (maximum node weight) of the path from any node to the root node is the minimum. The Maximum Bottleneck Link Weight-based Data Gathering trees (MaxBLW-DG trees) are the ones for which the bottleneck link weight (minimum link weight) of the bottleneck link weight (maximum link weight) of the constituent links of a path from any node to the root node is the minimum. MaxBNW-DG trees could be used to determine DG trees with a larger residual energy per intermediate node such that the minimum node energy of the path from any node to the root node is the maximum (e.g., [15; 16]). The MinBNW-DG trees could be used to determine DG trees in mobile sensor networks with lower velocity for the intermediate nodes such that the maximum node velocity of the path from any node to the root node is the minimum (e.g., [17]). MaxBLW-DG trees could be used to determine DG trees with a larger trust score for each link on the tree such that the minimum trust score for any of the constituent links of a path from any node to the root node is the maximum (e.g., [18]); the MinBLW-DG trees could be used to determine DG trees with maximum of the square of the link distance (measureof the transmission energy loss) for any of the constituent links for a path from any node to the root node is the minimum (e.g., [19]). Most of the work conducted in the literature focus on deriving bounds for the aggregation delay for the data gathering trees as a function of various networking parameters (like density, diameter, node degree, _etc._).