Some of my favorite “lesser known” problems

Rosenfeld, Moshe

doi:10.26493/1855-3974.25.7bd

Cited by 4 publications

(5 citation statements)

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“…Since bouncing robots do not have any control over their movements, it might seem that in most configurations all the robots must die. We prove that this is not always the case, thus answering an open question first posed in [46] for the case of robots of equal masses and speeds.…”

Section: Survivability Of Bouncing Robotsmentioning

confidence: 54%

“…The configuration from Theorem 4 is the first correct example of surviving subset of robots. We argue below that the example from [46], represented in Table 1, which supposedly contains a swarm of five robots with four survivors is not correct. The Although it is correct that the first robot to die is r 1 , it is easy to check that robot r 3 or robot r 2 must die as well.…”

Section: Proofmentioning

confidence: 96%

“…The following −120 −92 +55 +41 +51 110 die −102 +100 +0 −74 123 +115 −87 −115 +87 Table 1. Example given in [46] theorem states that there are no swarms of smaller size than the swarm of Theorem 4 with survivors.…”

Section: Proofmentioning

confidence: 99%

“…A somewhat similar problem for very simple mobile robots was introduced by Moshe Rosenfeld in [46] in what he calls the salmon problem. The salmon problem is inspired by the life cycle of salmons: a salmon after being hatched lives in the ocean for a period of several years, then it returns to its place of birth to spawn and die.…”

Section: Survivability Of Mobile Robotsmentioning

confidence: 99%

“…The salmon problem is stated in [46] as follows: Consider n salmon fries distributed on a ring, each fry moving with constant speed either clockwise or counterclockwise.…”

Section: Survivability Of Mobile Robotsmentioning

confidence: 99%

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Swarms of Bouncing Robots

Pacheco¹

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We study models of mobile robots with limited capabilities that are deployed either on a cycle or an infinite line or on a segment. Robots start moving at the same time and when two robots collide their speeds and movement directions are instantaneously updated. Each of them possesses a collision detector and a clock to measure the times of its collisions. They do not have any knowledge on the total number of robots and do not have a common sense of direction. Besides, they neither have visibility nor control over their movements.We investigate the feasibility of the localization task in the cycle and the segment by bouncing robots: every robot should figure out the starting position and initial velocity of all the other robots. We consider two different scenarios when robots have common masses and speeds and robots of arbitrary masses and speeds. We give complete characterizations of all feasible configurations for the cycle in both scenarios.We study the survivability of bouncing robots. We say a robot survives if it never returns to its starting position. Non-surviving robots disappear from the environment.We provide sufficient and necessary conditions to have surviving robots in the cycle and in the segment. Finally we investigate communication protocols for bouncing robots that only communicate at the time of their collisions. We establish necessary and sufficient conditions for bouncing robots to perform gossiping, broadcasting and convergecast.iii ContentsAbstract iii List of Figures viiChapter 1. Introduction Computing the kth level of a set of lines 83vii CHAPTER 1 similarities with some models of gas particles, for instance in [36]. We also address related problems that we came to encounter after we proposed our model like the salmon problem and study communications protocols performed by these robots.Outline. In Chapter 2, we survey some models of mobile robots and we provide an overview of the state of the art of the field. We also motivate the models that we propose. In Chapter 3, we introduce our model of mobile robots that we call bouncing robots in two different flavors. We then study the task of localization also known as position discovery by bouncing robots. In our first model, robots move with the same speed while in the second one they have arbitrary speeds. We study the localization for one dimensional environments. We give algorithms to carry out localization and provide full characterizations of all feasible configurations. In Chapter 4, we study the survivability of bouncing robots that are deployed in a dangerous environment with deadly locations. When a robot visits some of such locations it is destroyed.In all those chapters we assume that robots can not communicate by any means however in Chapter 5 we allow bouncing robots to communicate and study different communication protocols carried out by them.In this section, we review some of the most relevant and related literature of mobile robots. We discuss different models of mobile robots, their environment, and the different timing ass...

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Section: Survivability Of Bouncing Robotsmentioning

confidence: 54%

Section: Proofmentioning

confidence: 96%

Section: Proofmentioning

confidence: 99%

Section: Survivability Of Mobile Robotsmentioning

confidence: 99%

“…The salmon problem is stated in [46] as follows: Consider n salmon fries distributed on a ring, each fry moving with constant speed either clockwise or counterclockwise.…”

Section: Survivability Of Mobile Robotsmentioning

confidence: 99%

See 3 more Smart Citations