# Distributed K-Backup Placement and Applications to Virtual Memory in Real-World Wireless Networks

The Backup Placement problem in networks in the CONGEST distributed setting considers a network graph G = (V,E), in which the goal of each vertex v ∈ V is selecting a neighbor, such that the maximum number of vertices in V that select the same vertex is minimized [Halldorsson et al., 2015]. Previous backup placement algorithms suffer from obliviousness to main factors of real-world heterogeneous wireless network. Specifically, there is no consideration of the nodes memory and storage capacities, and no reference to a case in which nodes have different energy capacity, and thus can leave (or join) the network at any time. These parameters are strongly correlated in wireless networks, as the load on different parts of the network can differ greatly, thus requiring more communication, energy, memory and storage. In order to fit the real-world attributes of wireless networks, this work addresses a generalized version of the original problem, namely K-Backup Placement, in which each vertex selects K neighbors, for a positive parameter K. Our K-Backup Placement algorithm terminates within just one round. In addition we suggest two complementary algorithms which employ K-Backup-Placement to obtain efficient virtual memory schemes for wireless networks. The first algorithm divides the memory of each node to many small parts. Each vertex is assigned the memories of a large subset of its neighbors. Thus more memory capacity for more vertices is gained, but with much fragmentation. The second algorithm requires greater round-complexity, but produces larger virtual memory for each vertex without any fragmentation.

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