arXiv subjects

Paola Flocchini

Publications and source records attributed to Paola Flocchini.

32 records · Page 2Linked to original sources

arXiv2017

Gathering in Dynamic Rings

The gathering problem requires a set of mobile agents, arbitrarily positioned at different nodes of a network to group within finite time at the same location, not fixed in advanced. The extensive existing literature on this problem shares the same fundamental assumption: the topological structure does not change during the rendezvous or the gathering; this is true also for those investigations that consider faulty nodes. In other words, they only consider static graphs. In this paper we start the investigation of gathering in dynamic graphs, that is networks where the topology changes continuously and at unpredictable locations. We study the feasibility of gathering mobile agents, identical and without explicit communication capabilities, in a dynamic ring of anonymous nodes; the class of dynamics we consider is the classic 1-interval-connectivity. We focus on the impact that factors such as chirality (i.e., a common sense of orientation) and cross detection (i.e., the ability to detect, when traversing an edge, whether some agent is traversing it in the other direction), have on the solvability of the problem. We provide a complete characterization of the classes of initial configurations from which the gathering problem is solvable in presence and in absence of cross detection and of chirality. The feasibility results of the characterization are all constructive: we provide distributed algorithms that allow the agents to gather. In particular, the protocols for gathering with cross detection are time optimal. We also show that cross detection is a powerful computational element. We prove that, without chirality, knowledge of the ring size is strictly more powerful than knowledge of the number of agents; on the other hand, with chirality, knowledge of n can be substituted by knowledge of k, yielding the same classes of feasible initial configurations.

cs.DC↗

arXiv2017

Distributed Computing by Mobile Robots: Uniform Circle Formation

Consider a set of $n$ simple autonomous mobile robots (asynchronous, no common coordinate system, no identities, no central coordination, no direct communication, no memory of the past, non-rigid, deterministic) initially in distinct locations, moving freely in the plane and able to sense the positions of the other robots. We study the primitive task of the robots arranging themselves on the vertices of a regular $n$-gon not fixed in advance (Uniform Circle Formation). In the literature, the existing algorithmic contributions are limited to conveniently restricted sets of initial configurations of the robots and to more powerful robots. The question of whether such simple robots could deterministically form a uniform circle has remained open. In this paper, we constructively prove that indeed the Uniform Circle Formation problem is solvable for any initial configuration in which the robots are in distinct locations, without any additional assumption (if two robots are in the same location, the problem is easily seen to be unsolvable). In addition to closing a long-standing problem, the result of this paper also implies that, for pattern formation, asynchrony is not a computational handicap, and that additional powers such as chirality and rigidity are computationally irrelevant.

cs.DC↗

arXiv2016

Population Protocols with Faulty Interactions: the Impact of a Leader

We consider the problem of simulating traditional population protocols under weaker models of communication, which include one-way interactions (as opposed to two-way interactions) and omission faults (i.e., failure by an agent to read its partner's state during an interaction), which in turn may be detectable or undetectable. We focus on the impact of a leader, and we give a complete characterization of the models in which the presence of a unique leader in the system allows the construction of simulators: when simulations are possible, we give explicit protocols; when they are not, we give proofs of impossibility. Specifically, if each agent has only a finite amount of memory, the simulation is possible only if there are no omission faults. If agents have an unbounded amount of memory, the simulation is possible as long as omissions are detectable. If an upper bound on the number of omissions involving the leader is known, the simulation is always possible, except in the one-way model in which one side is unable to detect the interaction.

cs.DC↗

arXiv2016

On the Power of Weaker Pairwise Interaction: Fault-Tolerant Simulation of Population Protocols

In this paper we investigate the computational power of Population Protocols (PP) under some unreliable and/or weaker interaction models. More precisely, we focus on two features related to the power of interactions: omission failures and one-way communications. An omission failure, a notion that this paper introduces for the first time in the context of PP, is the loss by one or both parties of the information transmitted in an interaction. The failure may or may not be detected by either party. On the other hand, in one-way models, communication happens only in one direction: only one of the two agents can change its state depending on both agents' states, and the other agent may or may not be aware of the interaction. These notions can be combined, obtaining one-way protocols with (possibly detectable) omission failures. A general question is what additional power is necessary and sufficient to completely overcome the weakness of one-way protocols and enable them to simulate two-way protocols, with and without omission failures. As a basic feature, a simulator needs to implement an atomic communication of states between two agents; this task is further complicated by the anonymity of the agents, their lack of knowledge of the system, and the limited amount of memory that they may have. We provide the first answers to these questions by presenting and analyzing several simulators, i.e., wrapper protocols converting any protocol for the standard two-way model into one running on a weaker one.

cs.DC↗

arXiv2016

Universal Systems of Oblivious Mobile Robots

An oblivious mobile robot is a stateless computational entity located in a spatial universe, capable of moving in that universe. When activated, the robot observes the universe and the location of the other robots, chooses a destination, and moves there. The computation of the destination is made by executing an algorithm, the same for all robots, whose sole input is the current observation. No memory of all these actions is retained after the move. When the universe is a graph, distributed computations by oblivious mobile robots have been intensively studied focusing on the conditions for feasibility of basic problems (e.g., gathering, exploration) in specific classes of graphs under different schedulers. In this paper, we embark on a different, more general, type of investigation. With their movements from vertices to neighboring vertices, the robots make the system transition from one configuration to another. Viewing this transition as the computation of an abstract function, we ask which functions are computed by which systems. Our main interest is on identifying sets of systems that are "universal", in the sense that they can collectively compute all finite functions. We are able to identify several such classes of fully synchronous systems. In particular, among other results, we prove the universality of the set of all graphs with at least one robot, of any set of graphs with at least two robots whose quotient graphs contain arbitrarily long paths, and of any set of graphs with at least three robots and arbitrarily large finite girths. We then focus on the minimum size that a network must have for the robots to be able to compute all functions on a given finite set. We are able to approximate the minimum size of such a network up to a factor that tends to 2 as $n$ goes to infinity.

cs.DC↗

arXiv2015

Tempus Fugit: The Impact of Time in Knowledge Mobilization Networks

The temporal component of social networks is often neglected in their analysis, and statistical measures are typically performed on a "static" representation of the network. As a result, measures of importance (like betweenness centrality) cannot reveal any temporal role of the entities involved. Our goal is to start filling this limitation by proposing a form of temporal betweenness measure, and by using it to analyse a knowledge mobilization network. We show that this measure, which takes time explicitly into account, allows us to detect centrality roles that were completely hidden in the classical statistical analysis. In particular, we uncover nodes whose static centrality was considered negligible, but whose temporal role is instead important to accelerate mobilization flow in the network. We also observe the reverse behaviour by detecting nodes with high static centrality, whose role as temporal bridges is instead very low. By revealing important temporal roles, this study is a first step towards a better understanding of the impact of time in social networks, and opens the road to further investigation.

cs.SI↗

arXiv2014

Shortest, Fastest, and Foremost Broadcast in Dynamic Networks

Highly dynamic networks rarely offer end-to-end connectivity at a given time. Yet, connectivity in these networks can be established over time and space, based on temporal analogues of multi-hop paths (also called {\em journeys}). Attempting to optimize the selection of the journeys in these networks naturally leads to the study of three cases: shortest (minimum hop), fastest (minimum duration), and foremost (earliest arrival) journeys. Efficient centralized algorithms exists to compute all cases, when the full knowledge of the network evolution is given. In this paper, we study the {\em distributed} counterparts of these problems, i.e. shortest, fastest, and foremost broadcast with termination detection (TDB), with minimal knowledge on the topology. We show that the feasibility of each of these problems requires distinct features on the evolution, through identifying three classes of dynamic graphs wherein the problems become gradually feasible: graphs in which the re-appearance of edges is {\em recurrent} (class R), {\em bounded-recurrent} (B), or {\em periodic} (P), together with specific knowledge that are respectively $n$ (the number of nodes), $Δ$ (a bound on the recurrence time), and $p$ (the period). In these classes it is not required that all pairs of nodes get in contact -- only that the overall {\em footprint} of the graph is connected over time. Our results, together with the strict inclusion between $P$, $B$, and $R$, implies a feasibility order among the three variants of the problem, i.e. TDB[foremost] requires weaker assumptions on the topology dynamics than TDB[shortest], which itself requires less than TDB[fastest]. Reversely, these differences in feasibility imply that the computational powers of $R_n$, $B_Δ$, and $P_p$ also form a strict hierarchy.

cs.DC↗

arXiv2013

Rendezvous of Two Robots with Constant Memory

We study the impact that persistent memory has on the classical rendezvous problem of two mobile computational entities, called robots, in the plane. It is well known that, without additional assumptions, rendezvous is impossible if the entities are oblivious (i.e., have no persistent memory) even if the system is semi-synchronous (SSynch). It has been recently shown that rendezvous is possible even if the system is asynchronous (ASynch) if each robot is endowed with O(1) bits of persistent memory, can transmit O(1) bits in each cycle, and can remember (i.e., can persistently store) the last received transmission. This setting is overly powerful. In this paper we weaken that setting in two different ways: (1) by maintaining the O(1) bits of persistent memory but removing the communication capabilities; and (2) by maintaining the O(1) transmission capability and the ability to remember the last received transmission, but removing the ability of an agent to remember its previous activities. We call the former setting finite-state (FState) and the latter finite-communication (FComm). Note that, even though its use is very different, in both settings, the amount of persistent memory of a robot is constant. We investigate the rendezvous problem in these two weaker settings. We model both settings as a system of robots endowed with visible lights: in FState, a robot can only see its own light, while in FComm a robot can only see the other robot's light. We prove, among other things, that finite-state robots can rendezvous in SSynch, and that finite-communication robots are able to rendezvous even in ASynch. All proofs are constructive: in each setting, we present a protocol that allows the two robots to rendezvous in finite time.

cs.MA↗

arXiv2012

On the Parity Problem in One-Dimensional Cellular Automata

We consider the parity problem in one-dimensional, binary, circular cellular automata: if the initial configuration contains an odd number of 1s, the lattice should converge to all 1s; otherwise, it should converge to all 0s. It is easy to see that the problem is ill-defined for even-sized lattices (which, by definition, would never be able to converge to 1). We then consider only odd lattices. We are interested in determining the minimal neighbourhood that allows the problem to be solvable for any initial configuration. On the one hand, we show that radius 2 is not sufficient, proving that there exists no radius 2 rule that can possibly solve the parity problem from arbitrary initial configurations. On the other hand, we design a radius 4 rule that converges correctly for any initial configuration and we formally prove its correctness. Whether or not there exists a radius 3 rule that solves the parity problem remains an open problem.

cs.FL↗

arXiv2012

Expressivity of Time-Varying Graphs and the Power of Waiting in Dynamic Networks

In infrastructure-less highly dynamic networks, computing and performing even basic tasks (such as routing and broadcasting) is a very challenging activity due to the fact that connectivity does not necessarily hold, and the network may actually be disconnected at every time instant. Clearly the task of designing protocols for these networks is less difficult if the environment allows waiting (i.e., it provides the nodes with store-carry-forward-like mechanisms such as local buffering) than if waiting is not feasible. No quantitative corroborations of this fact exist (e.g., no answer to the question: how much easier?). In this paper, we consider these qualitative questions about dynamic networks, modeled as time-varying (or evolving) graphs, where edges exist only at some times. We examine the difficulty of the environment in terms of the expressivity of the corresponding time-varying graph; that is in terms of the language generated by the feasible journeys in the graph. We prove that the set of languages $L_{nowait}$ when no waiting is allowed contains all computable languages. On the other end, using algebraic properties of quasi-orders, we prove that $L_{wait}$ is just the family of regular languages. In other words, we prove that, when waiting is no longer forbidden, the power of the accepting automaton (difficulty of the environment) drops drastically from being as powerful as a Turing machine, to becoming that of a Finite-State machine. This (perhaps surprisingly large) gap is a measure of the computational power of waiting. We also study bounded waiting; that is when waiting is allowed at a node only for at most $d$ time units. We prove the negative result that $L_{wait[d]} = L_{nowait}$; that is, the expressivity decreases only if the waiting is finite but unpredictable (i.e., under the control of the protocol designer and not of the environment).

cs.DC↗

arXiv2012

Building Fastest Broadcast Trees in Periodically-Varying Graphs

Delay-tolerant networks (DTNs) are characterized by a possible absence of end-to-end communication routes at any instant. Still, connectivity can generally be established over time and space. The optimality of a temporal path (journey) in this context can be defined in several terms, including topological (e.g. {\em shortest} in hops) and temporal (e.g. {\em fastest, foremost}). The combinatorial problem of computing shortest, foremost, and fastest journeys {\em given full knowledge} of the network schedule was addressed a decade ago (Bui-Xuan {\it et al.}, 2003). A recent line of research has focused on the distributed version of this problem, where foremost, shortest or fastest {\em broadcast} are performed without knowing the schedule beforehand. In this paper we show how to build {\em fastest} broadcast trees (i.e., trees that minimize the global duration of the broadcast, however late the departure is) in Time-Varying Graphs where intermittent edges are available periodically (it is known that the problem is infeasible in the general case even if various parameters of the graph are know). We address the general case where contacts between nodes can have arbitrary durations and thus fastest routes may consist of a mixture of {\em continuous} and {\em discontinuous} segments (a more complex scenario than when contacts are {\em punctual} and thus routes are only discontinuous). Using the abstraction of \tclocks to compute the temporal distances, we solve the fastest broadcast problem by first learning, at the emitter, what is its time of {\em minimum temporal eccentricity} (i.e. the fastest time to reach all the other nodes), and second by building a {\em foremost} broadcast tree relative to this particular emission date.

cs.DC↗

arXiv2012

Time-Varying Graphs and Dynamic Networks

The past few years have seen intensive research efforts carried out in some apparently unrelated areas of dynamic systems -- delay-tolerant networks, opportunistic-mobility networks, social networks -- obtaining closely related insights. Indeed, the concepts discovered in these investigations can be viewed as parts of the same conceptual universe; and the formal models proposed so far to express some specific concepts are components of a larger formal description of this universe. The main contribution of this paper is to integrate the vast collection of concepts, formalisms, and results found in the literature into a unified framework, which we call TVG (for time-varying graphs). Using this framework, it is possible to express directly in the same formalism not only the concepts common to all those different areas, but also those specific to each. Based on this definitional work, employing both existing results and original observations, we present a hierarchical classification of TVGs; each class corresponds to a significant property examined in the distributed computing literature. We then examine how TVGs can be used to study the evolution of network properties, and propose different techniques, depending on whether the indicators for these properties are a-temporal (as in the majority of existing studies) or temporal. Finally, we briefly discuss the introduction of randomness in TVGs.

cs.DC↗

arXiv2011

Time-Varying Graphs and Social Network Analysis: Temporal Indicators and Metrics

Most instruments - formalisms, concepts, and metrics - for social networks analysis fail to capture their dynamics. Typical systems exhibit different scales of dynamics, ranging from the fine-grain dynamics of interactions (which recently led researchers to consider temporal versions of distance, connectivity, and related indicators), to the evolution of network properties over longer periods of time. This paper proposes a general approach to study that evolution for both atemporal and temporal indicators, based respectively on sequences of static graphs and sequences of time-varying graphs that cover successive time-windows. All the concepts and indicators, some of which are new, are expressed using a time-varying graph formalism.

cs.SI↗

arXiv2009

Exploration of Periodically Varying Graphs

We study the computability and complexity of the exploration problem in a class of highly dynamic graphs: periodically varying (PV) graphs, where the edges exist only at some (unknown) times defined by the periodic movements of carriers. These graphs naturally model highly dynamic infrastructure-less networks such as public transports with fixed timetables, low earth orbiting (LEO) satellite systems, security guards' tours, etc. We establish necessary conditions for the problem to be solved. We also derive lower bounds on the amount of time required in general, as well as for the PV graphs defined by restricted classes of carriers movements: simple routes, and circular routes. We then prove that the limitations on computability and complexity we have established are indeed tight. In fact we prove that all necessary conditions are also sufficient and all lower bounds on costs are tight. We do so constructively presenting two worst case optimal solution algorithms, one for anonymous systems, and one for those with distinct nodes ids. An added benefit is that the algorithms are rather simple.

cs.DS↗