Subscribe to the gold package and get unlimited access to Shamra Academy
Register a new userComputability of Perpetual Exploration in Highly Dynamic Rings
67
0
0.0
(
0
)
Added by
Marjorie Bournat
Publication date
2016
fields
Informatics Engineering
and research's language is
English
Authors
Marjorie Bournat
Ask ChatGPT about the research
No Arabic abstract
We consider systems made of autonomous mobile robots evolving in highly dynamic discrete environment i.e., graphs where edges may appear and disappear unpredictably without any recurrence, stability, nor periodicity assumption. Robots are uniform (they execute the same algorithm), they are anonymous (they are devoid of any observable ID), they have no means allowing them to communicate together, they share no common sense of direction, and they have no global knowledge related to the size of the environment. However, each of them is endowed with persistent memory and is able to detect whether it stands alone at its current location. A highly dynamic environment is modeled by a graph such that its topology keeps continuously changing over time. In this paper, we consider only dynamic graphs in which nodes are anonymous, each of them is infinitely often reachable from any other one, and such that its underlying graph (i.e., the static graph made of the same set of nodes and that includes all edges that are present at least once over time) forms a ring of arbitrary size. In this context, we consider the fundamental problem of perpetual exploration: each node is required to be infinitely often visited by a robot. This paper analyzes the computability of this problem in (fully) synchronous settings, i.e., we study the deterministic solvability of the problem with respect to the number of robots. We provide three algorithms and two impossibility results that characterize, for any ring size, the necessary and sufficient number of robots to perform perpetual exploration of highly dynamic rings.
rate research
Read More
Gracefully degrading algorithms [Biely etal, TCS 2018] are designed to circumvent impossibility results in dynamic systems by adapting themselves to the dynamics. Indeed, such an algorithm solves a given problem under some dynamics and, moreover, guarantees that a weaker (but related) problem is solved under a higher dynamics under which the original problem is impossible to solve. The underlying intuition is to solve the problem whenever possible but to provide some kind of quality of service if the dynamics become (unpredictably) higher.In this paper, we apply for the first time this approach to robot networks. We focus on the fundamental problem of gathering a squad of autonomous robots on an unknown location of a dynamic ring. In this goal, we introduce a set of weaker variants of this problem. Motivated by a set of impossibility results related to the dynamics of the ring, we propose a gracefully degrading gathering algorithm.
We investigate a special case of hereditary property that we refer to as {em robustness}. A property is {em robust} in a given graph if it is inherited by all connected spanning subgraphs of this graph. We motivate this definition in different contexts, showing that it plays a central role in highly dynamic networks, although the problem is defined in terms of classical (static) graph theory. In this paper, we focus on the robustness of {em maximal independent sets} (MIS). Following the above definition, a MIS is said to be {em robust} (RMIS) if it remains a valid MIS in all connected spanning subgraphs of the original graph. We characterize the class of graphs in which {em all} possible MISs are robust. We show that, in these particular graphs, the problem of finding a robust MIS is {em local}; that is, we present an RMIS algorithm using only a sublogarithmic number of rounds (in the number of nodes $n$) in the ${cal LOCAL}$ model. On the negative side, we show that, in general graphs, the problem is not local. Precisely, we prove a $Omega(n)$ lower bound on the number of rounds required for the nodes to decide consistently in some graphs. This result implies a separation between the RMIS problem and the MIS problem in general graphs. It also implies that any strategy in this case is asymptotically (in order) as bad as collecting all the network information at one node and solving the problem in a centralized manner. Motivated by this observation, we present a centralized algorithm that computes a robust MIS in a given graph, if one exists, and rejects otherwise. Significantly, this algorithm requires only a polynomial amount of local computation time, despite the fact that exponentially many MISs and exponentially many connected spanning subgraphs may exist.
This paper provides an algorithmic framework for obtaining fast distributed algorithms for a highly-dynamic setting, in which *arbitrarily many* edge changes may occur in each round. Our algorithm significantly improves upon prior work in its combination of (1) having an $O(1)$ amortized time complexity, (2) using only $O(log{n})$-bit messages, (3) not posing any restrictions on the dynamic behavior of the environment, (4) being deterministic, (5) having strong guarantees for intermediate solutions, and (6) being applicable for a wide family of tasks. The tasks for which we deduce such an algorithm are maximal matching, $(degree+1)$-coloring, 2-approximation for minimum weight vertex cover, and maximal independent set (which is the most subtle case). For some of these tasks, node insertions can also be among the allowed topology changes, and for some of them also abrupt node deletions.
A task is a distributed problem for $n$ processes, in which each process starts with a private input value, communicates with other processes, and eventually decides an output value. A task is colorless if each process can adopt the input or output value of another process. Colorless tasks are well studied in the non-anonymous shared-memory model where each process has a distinct identifier that can be used to access a single-writer/multi-reader shared register. In the anonymous case, where processes have no identifiers and communicate through multi-writer/multi-reader registers, there is a recent topological characterization of the colorless tasks that are solvable when any number of asynchronous processes may crash. In this paper we study the case where at most $t$ processes may crash, where $1 le t < n$. We prove that a colorless task is $t$-resilient solvable non-anonymously if and only if it is $t$-resilient solvable anonymously. This implies a complete characterization of colorless anonymous t-resilient asynchronous task computability.
This paper introduces a new communication abstraction, called Set-Constrained Delivery Broadcast (SCD-broadcast), whose aim is to provide its users with an appropriate abstraction level when they have to implement objects or distributed tasks in an asynchronous message-passing system prone to process crash failures. This abstraction allows each process to broadcast messages and deliver a sequence of sets of messages in such a way that, if a process delivers a set of messages including a message m and later delivers a set of messages including a message m , no process delivers first a set of messages including m and later a set of message including m. After having presented an algorithm implementing SCD-broadcast, the paper investigates its programming power and its computability limits. On the power side it presents SCD-broadcast-based algorithms, which are both simple and efficient, building objects (such as snapshot and conflict-free replicated data), and distributed tasks. On the computability limits side it shows that SCD-broadcast and read/write registers are computationally equivalent.
Log in to be able to interact and post comments
comments
Fetching comments
Sign in to be able to follow your search criteria
