3,061 research outputs found
The Visibility Freeze-Tag Problem
In the Freeze-Tag Problem, we are given a set of robots at points inside some metric space. Initially, all the robots are frozen except one. That robot can awaken (or “unfreeze”) another robot by moving to its position, and once a robot is awakened, it can move and help to awaken other robots. The goal is to awaken all the robots in the shortest time. The Freeze-Tag Problem has been studied in different metric spaces: graphs and Euclidean spaces.
In this thesis, we look at the Freeze-Tag Problem in polygons, and we introduce the Visibility Freeze-Tag Problem, where one robot can awaken another robot by “seeing” it. Furthermore, we introduce a variant of the Visibility Freeze-Tag Problem, called the Line/Point Freeze Tag Problem, where each robot lies on an awakening line, and one robot can awaken another robot by touching its awakening line.
We survey the current results for the Freeze-Tag Problem in graphs, Euclidean spaces and polygons. Since the Visibility Freeze-Tag Problem bears some resemblance to the Watchman Route Problem, we also survey the background literature on the Watchman Route Problem. We show that the Freeze-Tag Problem in polygons and the Visibility Freeze-Tag Problem are NP-hard, and we present an O(n)-approximation algorithm for the Visibility Freeze-Tag Problem. For the Line/Point Freeze-Tag Problem, we give a polynomial time algorithm for the special case where all the awakening lines are parallel to each other. We prove that the general case is NP-hard, and we present an O(1)- approximation algorithm
An Optimal Algorithm for Online Freeze-Tag
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, each frozen robot is 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 posed the question of whether an O(1)-competitive algorithm exists. We provide a (1+?2)-competitive algorithm for online time-dependent freeze-tag, and show that this is the best possible: there does not exist an algorithm which achieves a lower competitive ratio on every metric space
Feedback control optimisation of ESR experiments
Numerically optimised microwave pulses are used to increase excitation
efficiency and modulation depth in electron spin resonance experiments
performed on a spectrometer equipped with an arbitrary waveform generator. The
optimisation procedure is sample-specific and reminiscent of the magnet
shimming process used in the early days of nuclear magnetic resonance -- an
objective function (for example, echo integral in a spin echo experiment) is
defined and optimised numerically as a function of the pulse waveform vector
using noise-resilient gradient-free methods. We found that the resulting shaped
microwave pulses achieve higher excitation bandwidth and better echo modulation
depth than the pulse shapes used as the initial guess. Although the method is
theoretically less sophisticated than simulation based quantum optimal control
techniques, it has the advantage of being free of the linear response
approximation; rapid electron spin relaxation also means that the optimisation
takes only a few seconds. This makes the procedure fast, convenient, and easy
to use. An important application of this method is at the final stage of the
implementation of theoretically designed pulse shapes: compensation of pulse
distortions introduced by the instrument. The performance is illustrated using
spin echo and out-of-phase electron spin echo envelope modulation experiments.
Interface code between Bruker SpinJet arbitrary waveform generator and Matlab
is included in versions 2.2 and later of the Spinach library
Approximating the Degree-Bounded Minimum Diameter Spanning Tree Problem
We consider the problem of finding a minimum diameter spanning treewith maximum node degree in a complete undirected edge-weightedgraph. We provide an -approximation algorithm for theproblem. Our algorithm is purely combinatorial, and relies on acombination of filtering and divide and conquer.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/41348/1/453_2004_Article_1121.pd
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