Terminating Distributed Construction of Shapes and Patterns in a Fair Solution of Automata

In this work, we consider a solution of automata similar to Population Protocols and Network Constructors. The au-tomata, also called nodes, move passively in a well-mixed solution and can cooperate by interacting in pairs. Dur-ing every such interaction, the nodes, apart from updating their states, may also choose to connect to each other in order to start forming some required structure. The model introduced here is a more applied version of Network Con-structors, imposing geometrical constraints on the permissi-ble connections. Each node can connect to other nodes only via a very limited number of local ports, which implies that at any given time it has only a bounded number of neigh-bors. Connections are always made at unit distance and are perpendicular to connections of neighboring ports. Thoug

Fast Space Optimal Leader Election in Population Protocols

The model of population protocols refers to the growing in popularity theoretical framework suitable for studying pairwise interactions within a large collection of simple indistinguishable entities, frequently called agents. In this paper the emphasis is on the space complexity in fast leader election via population protocols governed by the random scheduler, which uniformly at random selects pairwise interactions within the population of n agents. The main result of this paper is a new fast and space optimal leader election protocol. The new protocol utilises O(log^2 n) parallel time (which is equivalent to O(n log^2 n) sequential pairwise interactions), and each agent operates on O(log log n) states. This double logarithmic space usage matches asymptotically the lower bound 1/2 log log n on the minimal number of states required by agents in any leader election algorithm with the running time o(n/polylog n). Our solution takes an advantage of the concept of phase clocks, a fundamental synchronisation and coordination tool in distributed computing. We propose a new fast and robust population protocol for initialisation of phase clocks to be run simultaneously in multiple modes and intertwined with the leader election process. We also provide the reader with the relevant formal argumentation indicating that our solution is always correct, and fast with high probability.Comment: 21 pages, 2 figures, published in SODA 2018 proceeding

Linear Support for Multi-Objective Coordination Graphs

Many real-world decision problems require making trade-offs among multiple objectives. However, in some cases, the relative importance of these objectives is not known when the problem is solved, precluding the use of single-objective methods. Instead, multi-objective methods, which compute the set of all potentially useful solutions, are required. This paper proposes variable elimination linear support (VELS), a new multi-objective algorithm for multi-agent coordina-tion that exploits loose couplings to compute the convex coverage set (CCS): the set of optimal solutions for all pos-sible weights for linearly weighted objectives. Unlike ex-isting methods, VELS exploits insights from POMDP solu-tion methods to build the CCS incrementally. We prove the correctness of VELS and show that for moderate numbers of objectives its complexity is better than that of previous methods. Furthermore, we present empirical results showing that VELS can tackle both random and realistic problems with many more agents than was previously feasible. The incremental nature of VELS also makes it an anytime al-gorithm, i.e., its intermediate results constitute ε-optimal approximations of the CCS, with ε decreasing the longer it runs. Our empirical results show that, by allowing even very small ε, VELS can enable large additional speedups