A PTAS for geometric 2-FTP

Moezkarimi, Zahra; Bagheri, Alireza

doi:10.1016/j.ipl.2014.06.017

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Cited by 4 publications

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“…If there exist more than one initial awake robot, we denote the problem by k-FTP, where k is the number of initially awake robots. A PTAS is presented for 2-FTP in Euclidean space [2]. It is proved that FTP in 2D and 3D Euclidean space is NP-hard in [6] and [7], respectively.…”

Section: Introductionmentioning

confidence: 99%

Approximation algorithms for the freeze tag problem inside polygons

Rajabi-Alni

Bagheri

2022

Preprint

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Section: Introductionmentioning

confidence: 99%

Approximation algorithms for the freeze tag problem inside polygons

Rajabi-Alni

Bagheri

2022

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“…Further work has mostly centered around approximation algorithms such as in [2] and [6]. No PTAS for general metric spaces has been found, though much progress has been made for Euclidean metrics in [5] and [7], finding a linear-time PTAS in some cases. In [1] it is shown that 5/3-approximation is NP-hard for general metrics arising from weighted graphs, so a PTAS does not exists assuming P = NP .…”

Section: Introductionmentioning

confidence: 99%

An Optimal Algorithm for Online Freeze-tag

Brunner,

Wellman

2019

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In the freeze-tag problem, one active robot must wake up many frozen robots. The robots are considered as points in a metric space, where active robots move at a constant rate and activate other robots by visiting them. In the (time-dependent) online variant of the problem, frozen robots are not revealed until a specified time. Hammar, Nilsson, and Persson have shown that no online algorithm can achieve a competitive ratio better than 7/3 for online freeze-tag, and asked whether there is any O(1)-competitive algorithm. In this paper, we provide a (1 + √ 2)-competitive algorithm for online time-dependent freeze-tag, and show that no algorithm can achieve a lower competitive ratio on every metric space.

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