Leader Election in a Smartphone Peer-to-Peer Network

In this paper, we study the fundamental problem of leader election in the mobile telephone model: a recently introduced variation of the classical telephone model modified to better describe the local peer-to-peer-communication services implemented in many popular smartphone operating systems. In more detail, the mobile telephone model differs from the classical telephone model in three ways: (1) each devicecan participate in at most one connection per round; (2) the network topology can undergo a parameterized rate of change; and (3) devices can advertise a parameterized number of bits to their neighbors in each round before connection attempts are initiated. We begin by describing and analyzing a new leader election algorithm in this model that works under the harshest possible parameter assumptions: maximum rate of topology changes and no advertising bits. We then apply this result to resolve an open question from [Ghaffari, 2016] on the efficiency of PUSH-PULL rumor spreading under these conditions. We then turn our attention to the slightly easier case where devices can advertise a single bit in each round. We demonstrate a large gap in time complexity between these zero bit and one bit cases. In more detail, we describe and analyze a new algorithm that solves leader election with a time complexity that includes the parameter bounding topology changes. For all values of this parameter, this algorithm is faster than the previous result, with a gap that grows quickly as the parameter increases (indicating lower rates of change). We conclude by describing and analyzing a modified version of this algorithm that does not require the assumptionthat all devices start during the same round. This new version has a similar time complexity (the rounds required differ only by a polylogarithmic factor),but now requires slightly larger advertisement tags.