Ad Hoc Networks 107 (2020) 102214 Contents lists available at ScienceDirect Ad Hoc Networks journal homepage: www.elsevier.com/locate/adhoc Towards optimal convergecast in wireless ad hoc networks Filipe Araujo a,∗ , André Gomes a , Rui P. Rocha b a University of Coimbra, Centre for Informatics and Systems of the University of Coimbra, Department of Informatics Engineering, Portugal b University of Coimbra, Institute of Systems and Robotics, Department of Electrical and Computer Engineering, Portugal a r t i c l e i n f o Article history: Received 26 February 2018 Revised 14 August 2019 Accepted 18 May 2020 Available online 6 June 2020 Keywords: Wireless ad hoc networks Convergecast Routing a b s t r a c t Sending data to a sink node is a crucial operation in wireless ad hoc networks serving humanitarian, environmental, industrial, military, or other purposes. While seemingly the inverse of broadcasting, this operation, known as “convergecast”, is more complex, because each node sends different data to the sink. Convergecast should minimize convergence time (i.e., the time at which the root hears from other nodes) and energy consumption, but since these two objectives are conflicting, most algorithms will set for one and disregard the other. In this paper, we propose a family of convergecast algorithms, called CHOPIN, offering a configuration parameter that explicitly trades convergence time for energy. Using closed-form analysis and simulation, we are able to show that CHOPIN can reach operation points that are either in, or very close to the Pareto frontier. This makes the network much more adaptable to changing external conditions. © 2020 Elsevier B.V. All rights reserved. 1. Introduction Wireless ad hoc networks, comprised of nodes that use radios to exchange direct messages, are quite useful in scenarios where the infrastructure might not exist, might not be available, or might be too expensive to use. In the last two decades, researchers have been working on multi-hop routing protocols for wireless ad hoc networks, in applications ranging from sensor networks, to mo- bile nodes in search and rescue teams (SaRTs) [3,43]. The interest in networks where nodes can self-organize, to share data or ac- cess the Internet, is also particularly important on the Internet of Things (IoT), as it promises to connect an unprecedented number of everyday devices, at homes, factories, and offices, via low-power, multi-hop protocols, like ZigBee [27]. For many of these networks, the most important communica- tion pattern involves the ability to send data from all the nodes to a special sink node, a process known as “convergecast”. This is the case of sensor networks, for example, as sensors must send and ag- gregate data towards the sink [29]. We observed the need for the same pattern in our own work with SaRTs [7]. While the problem initially seemed to be one of peer-to-peer communication between rescue agents in the terrain, we soon realized that communication in SaRTs is both highly hierarchical and, at the same time, geo- graphically constrained. Restricted message flooding might ensure ∗ Corresponding author. E-mail addresses: filipius@uc.pt (F. Araujo), afsg0@yahoo.com (A. Gomes), rprocha@isr.uc.pt (R.P. Rocha). group-wide peer-to-peer communication, but most other patterns involve exchanging messages with a Command Center, hereafter the “root”. A convergecast process is, therefore necessary, to let the root learn about every other node. While apparently similar to broadcast, in the sense that it seems to be a simple reversion of the process, convergecast re- quires participation of every single node, as these convey their own information to the root [28]. Information should get to the root in a timely and efficient manner: the root should get informa- tion as fast as possible, but nodes should minimize communication for the sake of preserving their batteries. This turns convergecast into a multi-criteria optimization problem: postponing and merg- ing messages towards the root will save battery, but delay informa- tion, whereas speeding information, incurs in a higher energy cost. These two metrics cannot be simultaneously optimized, as recog- nized before in the literature. For example, in distributed systems, authors usually express this relation in terms of running time vs. number of messages (e.g., Khan et al. [33]). In wireless networks, authors often express this relation in terms of latency vs. energy, where energy depends, not only, on the number of messages, but also on transmission ranges [41]. In convergecast, broadcast, multicast and other related prob- lems, like tree creation in wireless ad hoc networks, authors often strive for speed, as in [7,9,26,47], or for battery lifetime [1,2,35]. We argue that neither one of these goals is complete. Network admin- istrators must be aware of the inherent tradeoffs between the two and they should be able to explore such tradeoffs. Network proto- cols should expose sets of non-dominated points of operation (ide- https://doi.org/10.1016/j.adhoc.2020.102214 1570-8705/© 2020 Elsevier B.V. All rights reserved.