Yukiko Yamauchi

Distance and time based node selection for probabilistic coverage in People-Centric Sensing

Aiming to achieve sensing coverage for a given Area of Interest (AoI) in a People-Centric Sensing (PCS) manner, we propose a concept of (α, T)-coverage of the target field where each point in the field is sensed by at least one node with probability of at least α during the time period T. Our goal is to achieve (α, T)-coverage by a minimal set of mobile sensor nodes for a given AoI, coverage ratio α, and time period T. We model pedestrians as mobile sensor nodes moving according to a discrete Markov chain. Based on this model, we propose two algorithms: the inter-location and inter-meeting-time algorithms, to meet a coverage ratio α in time period T. These algorithms estimate the expected coverage of the specified AoI for a set of selected nodes. The inter-location algorithm selects a minimal number of mobile sensor nodes from nodes inside the AoI taking into account the distance between them. The inter-meeting-time selects nodes taking into account the expected meeting time between the nodes. We conducted a simulation study to evaluate the performance of the proposed algorithms for various parameter setting including a realistic scenario on a specific city map. The simulation results show that our algorithms achieve (α, T)-coverage with good accuracy for various values of α, T, and AoI size.

Asynchronous pattern formation by anonymous oblivious mobile robots

We present an oblivious pattern formation algorithm for anonymous mobile robots in the asynchronous model. The robots obeying the algorithm, starting from any initial configuration I, always form a given pattern F, if I and F do not contain multiplicities and ρ(I) divides ρ(F), where ρ(·) denotes the geometric symmetricity. Our algorithm substantially outdoes an algorithm by Dieudonne et al. proposed in DISC 2010, which is dedicated to ρ(I)=1. Our algorithm is best possible (as long as I and F do not contain multiplicities), since there is no algorithm that always forms F from I when ρ(F) is not divisible by ρ(I). All known pattern formation algorithms are constructed from scratch. We instead use a bipartite matching algorithm (between the robots and the points in F) we proposed in OPODIS 2011 as a core subroutine, to make the description of algorithm concise and easy to understand.

Plane Formation by Synchronous Mobile Robots in the Three-Dimensional Euclidean Space

Creating a swarm of mobile computing entities, frequently called robots, agents, or sensor nodes, with self-organization ability is a contemporary challenge in distributed computing. Motivated by this, we investigate the plane formation problem that requires a swarm of robots moving in the three-dimensional Euclidean space to land on a common plane. The robots are fully synchronous and endowed with visual perception. But they do not have identifiers, nor access to the global coordinate system, nor any means of explicit communication with each other. Though there are plenty of results on the agreement problem for robots in the two-dimensional plane, for example, the point formation problem, the pattern formation problem, and so on, this is the first result for robots in the three-dimensional space. This article presents a necessary and sufficient condition for fully synchronous robots to solve the plane formation problem that does not depend on obliviousness, i.e., the availability of local memory at robots. An implication of the result is somewhat counter-intuitive: The robots cannot form a plane from most of the semi-regular polyhedra, while they can form a plane from every regular polyhedron (except a regular icosahedron), whose symmetry is usually considered to be higher than any semi-regular polyhedron.

Pattern Formation by Mobile Robots with Limited Visibility

We investigate the pattern formation problem by mobile robots with limited visibility that can observe the positions of robots within limited distance. For robots with unlimited visibility, Fujinaga et al. (DISC 2012) showed that asynchronous oblivious robots have the same formation power as fully-synchronous non-oblivious robots, that is, starting from any initial configuration I, target pattern F is formable if and only if i¾?(I) divides i¾?(F) where i¾?(·) is the geometric symmetricity. We first show that fully-synchronous oblivious robots with limited visibility cannot form F even when i¾?(I) divides i¾?(F). Hence, limited visibility substantially weakens the formation power of oblivious robots. Secondly, we show that despite limited visibility, semi-synchronous robots with rigid moves, and fully-synchronous robots with non-rigid moves have the same formation power as robots with unlimited visibility. Consequently, local memory is necessary and sufficient for these robots.

Randomized Pattern Formation Algorithm for Asynchronous Oblivious Mobile Robots

We present a randomized pattern formation algorithm for asynchronous oblivious (i.e., memory-less) mobile robots that enables formation of any target pattern. As for deterministic pattern formation algorithms, the class of patterns formable from an initial configuration I is characterized by the symmetricity (i.e., the order of rotational symmetry) of I, and in particular, every pattern is formable from I if its symmetricity is 1. The randomized pattern formation algorithm ψ PF we present in this paper consists of two phases: The first phase transforms a given initial configuration I into a configuration I′ such that its symmetricity is 1, and the second phase invokes a deterministic pattern formation algorithm ψ CWM by Fujinaga et al. (DISC 2012) for asynchronous oblivious mobile robots to finally form the target pattern.

Mobile Byzantine Agreement on Arbitrary Network

The mobile Byzantine agreement problem on general network is investigated for the first time. We first show that the problem is unsolvable on any network with the order n and the vertex connectivity d, if n ≤ 6t or d ≤ 4t, where t is an upper bound on the number of faulty processes. Assuming full synchronization and the existence of a permanently non-faulty process, we next propose two t-resilient mobile Byzantine agreement algorithms for some families of not fully connected networks. They are optimal on some networks, in the sense that they correctly work if n > 6t and d > 4t.

Loosely-stabilizing leader election in a population protocol model

A self-stabilizing protocol guarantees that starting from any arbitrary initial configuration, a system eventually comes to satisfy its specification and keeps the specification forever. Although self-stabilizing protocols show excellent fault-tolerance against any transient faults (e.g. memory crash), designing self-stabilizing protocols is difficult and, what is worse, might be impossible due to the severe requirements. To circumvent the difficulty and impossibility, we introduce a novel notion of loose-stabilization, that relaxes the closure requirement of self-stabilization; starting from any arbitrary configuration, a system comes to satisfy its specification in a relatively short time, and it keeps the specification not forever but for a long time. To show the effectiveness and feasibility of this new concept, we present a probabilistic loosely-stabilizing leader election protocol in the Probabilistic Population Protocol (PPP) model of complete networks. Starting from any configuration, the protocol elects a unique leader within O(nNlogn) expected steps and keeps the unique leader for @W(Ne^N) expected steps, where n is the network size (not known to the protocol) and N is a known upper bound of n. This result proves that introduction of the loose-stabilization circumvents the already-known impossibility result; the self-stabilizing leader election problem in the PPP model of complete networks cannot be solved without the knowledge of the exact network size.

Deterministic Random Walks for Rapidly Mixing Chains

The rotor-router model is a deterministic process analogous to a simple random walk on a graph. This paper is concerned with a generalized model, functional-router model, which imitates a Markov chain possibly containing irrational transition probabilities. We investigate the discrepancy of the number of tokens at a single vertex between the functional-router model and its corresponding Markov chain, and give an upper bound in terms of the mixing time of the Markov chain.

Brief Announcement: Pattern Formation Problem for Synchronous Mobile Robots in the Three Dimensional Euclidean Space

We investigate the pattern formation problem that requires a swarm of autonomous mobile robots to form a given target pattern in the three-dimensional Euclidean space. We show a necessary and sufficient condition for synchronous robots to form a given target pattern from an initial configuration. We give a pattern formation algorithm for solvable instances that does not need any local memory at each robot.

Composition of fault-containing protocols based on recovery waiting fault-containing composition framework

Self-stabilizing protocols provide autonomous recovery from finite number of transient faults. Fault-containing self-stabilizing protocols promise not only self-stabilization but also quick recovery from and small effect of a small number of faults. However, existing composition techniques of self-stabilizing protocols (e.g. fair composition) cannot preserve the fault-containment property when composing fault-containing protocols. In this paper, we present Recovery Waiting Fault-containing Composition (RWFC) framework that preserves the faultcontainment property of the composed protocol. We show an example of fault-containing composition of a minimum spanning tree protocol on arbitrary weighted graphs and a median finding protocol on trees via RWFC.