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n 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 assumption that 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.
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Gossip in a Smartphone Peer-to-Peer Network
In this paper, we study the fundamental problem of gossip 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 device can 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 about their state to their neighbors in each round before connection attempts are initiated. We begin by describing and analyzing new randomized gossip algorithms in this model under the harsh assumption of a network topology that can change completely in every round. We prove a significant time complexity gap between the case where nodes can advertise 0 bits to their neighbors in each round, and the case where nodes can advertise 1 bit. For the latter assumption, we present two solutions: the first depends on a shared randomness source, while the second eliminates this assumption using a pseudorandomness generator we prove to exist with a novel generalization of a classical result from the study of two-party communication complexity. We then turn our attention to the easier case where the topology graph is stable, and describe and analyze a new gossip algorithm that provides a substantial performance improvement for many parameters. We conclude by studying a relaxed version of gossip in which it is only necessary for nodes to each learn a specified fraction of the messages in the system. We prove that our existing algorithms for dynamic network topologies and a single advertising bit solve this relaxed version up to a polynomial factor faster (in network size) for many parameters. These are the first known gossip results for the mobile telephone model, and they significantly expand our understanding of how to communicate and coordinate in this increasingly relevant setting.
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- Award ID(s):
- 1733842
- PAR ID:
- 10067142
- Date Published:
- Journal Name:
- Proceedings of the ACM Symposium on the Principles of Distributed Computing (PODC)
- Page Range / eLocation ID:
- 43 to 52
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.1145/3087801.3087813
