Rendezvous with constant memory

Flocchini, Paola; Santoro, Nicola; Viglietta, Giovanni; Yamashita, Masafumi

doi:10.1016/j.tcs.2016.01.025

Cited by 40 publications

(34 citation statements)

References 9 publications

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“…Fault-tolerant Gathering has been investigated in [13,16] for oblivious robots with unlimited visibility. Rendezvous has been investigated also when the robots have a constant amount of "visible memory" [22].…”

Section: Related Workmentioning

confidence: 99%

Meeting in a polygon by anonymous oblivious robots

et al. 2019

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The Meeting problem for k ≥ 2 searchers in a polygon P (possibly with holes) consists in making the searchers move within P , according to a distributed algorithm, in such a way that at least two of them eventually come to see each other, regardless of their initial positions. The polygon is initially unknown to the searchers, and its edges obstruct both movement and vision. Depending on the shape of P , we minimize the number of searchers k for which the Meeting problem is solvable. Specifically, if P has a rotational symmetry of order σ (where σ = 1 corresponds to no rotational symmetry), we prove that k = σ +1 searchers are sufficient, and the bound is tight. Furthermore, we give an improved algorithm that optimally solves the Meeting problem with k = 2 searchers in all polygons whose barycenter is not in a hole (which includes the polygons with no holes). Our algorithms can be implemented in a variety of standard models of mobile robots operating in Look-Compute-Move cycles. For instance, if the searchers have memory but are anonymous, asynchronous, and have no agreement on a coordinate system or a notion of clockwise direction, then our algorithms work even if the initial memory contents of the searchers are arbitrary and possibly misleading. Moreover, oblivious searchers can execute our algorithms as well, encoding information by carefully positioning themselves within the polygon. This code is computable with basic arithmetic operations (provided that the coordinates of the polygon's vertices are algebraic real numbers in some global coordinate system), and each searcher can geometrically construct its own destination point at each cycle using only a compass. We stress that such memoryless searchers may be located anywhere in the polygon when the execution begins, and hence the information they initially encode is arbitrary. Our algorithms use a self-stabilizing map construction subroutine which is of independent interest.

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Section: Related Workmentioning

confidence: 99%

Meeting in a polygon by anonymous oblivious robots

et al. 2019

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“…The robot is endowed with O(1) bits of persistent memory. This model is known in literature as FState [16], where the internal state of the robot can assume a finite number of 'colors'. S will denote the set of all possible states of the robot.…”

Section: Model and Definitionsmentioning

confidence: 99%

Positional Encoding by Robots with Non-rigid Movements

Bose

Adhikary

Kundu

et al. 2019

Structural Information and Communication Complexity

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Consider a set of autonomous computational entities, called robots, operating inside a polygonal enclosure (possibly with holes), that have to perform some collaborative tasks. The boundary of the polygon obstructs both visibility and mobility of a robot. Since the polygon is initially unknown to the robots, the natural approach is to first explore and construct a map of the polygon. For this, the robots need an unlimited amount of persistent memory to store the snapshots taken from different points inside the polygon. However, it has been shown by Di Luna et al. [DISC 2017] that map construction can be done even by oblivious robots by employing a positional encoding strategy where a robot carefully positions itself inside the polygon to encode information in the binary representation of its distance from the closest polygon vertex. Of course, to execute this strategy, it is crucial for the robots to make accurate movements. In this paper, we address the question whether this technique can be implemented even when the movements of the robots are unpredictable in the sense that the robot can be stopped by the adversary during its movement before reaching its destination. However, there exists a constant δ > 0, unknown to the robot, such that the robot can always reach its destination if it has to move by no more than δ amount. This model is known in literature as non-rigid movement. We give a partial answer to the question in the affirmative by presenting a map construction algorithm for robots with non-rigid movement, but having O(1) bits of persistent memory and ability to make circular moves.

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“…Das et al [4] extend the classical model with persistent memory, called lights, to reveal the relationship between ASYNC and SSYNC and they show that asynchronous robots equipped with lights and a constant number of colors, are strictly more powerful than semi-synchronous robots without lights. In order to solve Rendezvous without any other additional assumptions, robots with lights have been introduced [4,9,22]. Table 1 shows previous results including ours to solve Rendezvous by robots with lights, for each scheduler and movement restriction.…”

Section: Background and Motivationmentioning

confidence: 99%

“…Algorithm 1 SS-Rendezvous-with-3-colors (scheduler, movement, initialcolor) [9] Parameters: scheduler, movement-restriction, initial-color A time t c is called a cycle start time (cs-time, for short), if the next performed operations of both r and s after t are both Look , or otherwise, the robots performing the operations neither change their colors of lights nor move. In the latter case, we can consider that these operations can be performed before t c and the subsequent Look operation can be performed as the first operation after t c .…”

Section: Rendezvous L-algorithms For Robots With Three Colors Of Extementioning

confidence: 99%

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Rendezvous of Asynchronous Mobile Robots with Lights

Okumura

Wada

Katayama

2018

Adventures Between Lower Bounds and Higher Altitudes

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We study the Rendezvous problem for 2 autonomous mobile robots in asynchronous settings with persistent memory called light. It is well known that Rendezvous is impossible in a basic model when robots have no lights, even if the system is semi-synchronous. On the other hand, Rendezvous is possible if robots have lights of various types with a constant number of colors [9,22]. If robots can observe not only their own lights but also other robots' lights, their lights are called full-light. If robots can only observe the state of other robots' lights, the lights are called external-light. In this paper, we focus on robots with external-lights in asynchronous settings and a particular class of algorithms (called L-algorithms), where an L-algorithm computes a destination based only on the current colors of observable lights. When considering L-algorithms, Rendezvous can be solved by robots with full-lights and 3 colors in general asynchronous settings (called ASYNC) and the number of colors is optimal under these assumptions. In contrast, there exists no L-algorithms in ASYNC with external-lights regardless of the number of colors [9]. In this paper, we consider a fairly large subclass of ASYNC in which Rendezvous can be solved by L-algorithms using external-lights with a finite number of colors, and we show that the algorithms are optimal in the number of colors they use.

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Rendezvous with constant memory

Cited by 40 publications

References 9 publications

Meeting in a polygon by anonymous oblivious robots

Meeting in a polygon by anonymous oblivious robots

Positional Encoding by Robots with Non-rigid Movements

Rendezvous of Asynchronous Mobile Robots with Lights

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