Wake up and join me! An energy-efficient algorithm for maximal matching in radio networks

• Published in: Distributed computing Vol. 36; no. 3; pp. 373 - 384
• Main Authors: Dani, Varsha, Gupta, Aayush, Hayes, Thomas P., Pettie, Seth
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.09.2023; Springer Nature B.V
• Subjects: Algorithms; Complexity; Computer Communication Networks; Computer Hardware; Computer Science; Computer Systems Organization and Communication Networks; Energy; Energy consumption; Energy costs; Matching; Network topologies; Nodes; Optimization; Software Engineering/Programming and Operating Systems; Theory of Computation; Upper bounds; Sensor networks; Radio networks; Maximal matching; Distributed algorithms; Energy-aware computation
• ISSN: 0178-2770; 1432-0452
• DOI: 10.1007/s00446-022-00426-w

We consider networks of small, autonomous devices that communicate with each other wirelessly. Minimizing energy usage is an important consideration in designing algorithms for such networks, as battery life is a crucial and limited resource. Working in a model where both sending and listening for messages deplete energy, we consider the problem of finding a maximal matching of the nodes in a radio network of arbitrary and unknown topology. We present a distributed randomized algorithm that produces, with high probability, a maximal matching. The maximum energy cost per node is O ( ( log n ) ( log Δ ) ) , and the time complexity is O ( Δ log n ) . Here n is any upper bound on the number of nodes, and Δ is any upper bound on the maximum degree; n and Δ are parameters of our algorithm that we assume are known a priori to all the processors. We note that there exist families of graphs for which our bounds on energy cost and time complexity are simultaneously optimal up to polylog factors, so any significant improvement would need additional assumptions about the network topology. We also consider the related problem of assigning, for each node in the network, a neighbor to back up its data in case of eventual node failure. Here, a key goal is to minimize the maximum load , defined as the number of nodes assigned to a single node. We present an efficient decentralized low-energy algorithm that finds a neighbor assignment whose maximum load is at most a polylog ( n ) factor bigger that the optimum.