Team Formation and Applications

TL;DR

This paper introduces the Team Formation problem, a new distributed challenge, along with an efficient randomized algorithm, and demonstrates its broad applicability to many fundamental distributed problems, including leader election.

Contribution

The paper presents the first randomized algorithm for Team Formation in asynchronous networks with bounded messages, reducing many distributed problems to TF and breaking previous complexity bounds.

Findings

Breaks linear message complexity for asynchronous implicit leader election

Improves time complexity for message-optimal leader election algorithms

Establishes a tight lower bound on message complexity of TF algorithms

Abstract

A novel long-lived distributed problem, called Team Formation (TF), is introduced together with a message- and time-efficient randomized algorithm. The problem is defined over the asynchronous model with a complete communication graph, using bounded size messages, where a certain fraction of the nodes may experience a generalized, strictly stronger, version of initial failures. The goal of a TF algorithm is to assemble tokens injected by the environment, in a distributed manner, into teams of size $\sigma$, where $\sigma$ is a parameter of the problem. The usefulness of TF is demonstrated by using it to derive efficient algorithms for many distributed problems. Specifically, we show that various (one-shot as well as long-lived) distributed problems reduce to TF. This includes well-known (and extensively studied) distributed problems such as several versions of leader election and threshold detection. For example, we are the first to break the linear message complexity bound for asynchronous implicit leader election. We also improve the time complexity of message-optimal algorithms for asynchronous explicit leader election. Other distributed problems that reduce to TF are new ones, including matching players in online gaming platforms, a generalization of gathering, constructing a perfect matching in an induced subgraph of the complete graph, quorum sensing in message-passing networks, and more. To complement our positive contribution, we establish a tight lower bound on the message complexity of TF algorithms.