66 research outputs found
Irrational guards are sometimes needed
In this paper we study the art gallery problem, which is one of the
fundamental problems in computational geometry. The objective is to place a
minimum number of guards inside a simple polygon such that the guards together
can see the whole polygon. We say that a guard at position sees a point
if the line segment is fully contained in the polygon.
Despite an extensive study of the art gallery problem, it remained an open
question whether there are polygons given by integer coordinates that require
guard positions with irrational coordinates in any optimal solution. We give a
positive answer to this question by constructing a monotone polygon with
integer coordinates that can be guarded by three guards only when we allow to
place the guards at points with irrational coordinates. Otherwise, four guards
are needed. By extending this example, we show that for every , there is
polygon which can be guarded by guards with irrational coordinates but
need guards if the coordinates have to be rational. Subsequently, we show
that there are rectilinear polygons given by integer coordinates that require
guards with irrational coordinates in any optimal solution.Comment: 18 pages 10 Figure
Heuristic algorithms for the min-max edge 2-coloring problem
In multi-channel Wireless Mesh Networks (WMN), each node is able to use
multiple non-overlapping frequency channels. Raniwala et al. (MC2R 2004,
INFOCOM 2005) propose and study several such architectures in which a computer
can have multiple network interface cards. These architectures are modeled as a
graph problem named \emph{maximum edge -coloring} and studied in several
papers by Feng et. al (TAMC 2007), Adamaszek and Popa (ISAAC 2010, JDA 2016).
Later on Larjomaa and Popa (IWOCA 2014, JGAA 2015) define and study an
alternative variant, named the \emph{min-max edge -coloring}.
The above mentioned graph problems, namely the maximum edge -coloring and
the min-max edge -coloring are studied mainly from the theoretical
perspective. In this paper, we study the min-max edge 2-coloring problem from a
practical perspective. More precisely, we introduce, implement and test four
heuristic approximation algorithms for the min-max edge -coloring problem.
These algorithms are based on a \emph{Breadth First Search} (BFS)-based
heuristic and on \emph{local search} methods like basic \emph{hill climbing},
\emph{simulated annealing} and \emph{tabu search} techniques, respectively.
Although several algorithms for particular graph classes were proposed by
Larjomaa and Popa (e.g., trees, planar graphs, cliques, bi-cliques,
hypergraphs), we design the first algorithms for general graphs.
We study and compare the running data for all algorithms on Unit Disk Graphs,
as well as some graphs from the DIMACS vertex coloring benchmark dataset.Comment: This is a post-peer-review, pre-copyedit version of an article
published in International Computing and Combinatorics Conference
(COCOON'18). The final authenticated version is available online at:
http://www.doi.org/10.1007/978-3-319-94776-1_5
Complexity and Inapproximability Results for Parallel Task Scheduling and Strip Packing
We study the Parallel Task Scheduling problem with a
constant number of machines. This problem is known to be strongly NP-complete
for each , while it is solvable in pseudo-polynomial time for each . We give a positive answer to the long-standing open question whether
this problem is strongly -complete for . As a second result, we
improve the lower bound of for approximating pseudo-polynomial
Strip Packing to . Since the best known approximation algorithm
for this problem has a ratio of , this result
narrows the gap between approximation ratio and inapproximability result by a
significant step. Both results are proven by a reduction from the strongly
-complete problem 3-Partition
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Consensus Paper: Cerebellum and Emotion
Over the past three decades, insights into the role of the cerebellum in emotional processing have substantially increased. Indeed, methodological refinements in cerebellar lesion studies and major technological advancements in the field of neuroscience are in particular responsible to an exponential growth of knowledge on the topic. It is timely to review the available data and to critically evaluate the current status of the role of the cerebellum in emotion and related domains. The main aim of this article is to present an overview of current facts and ongoing debates relating to clinical, neuroimaging, and neurophysiological findings on the role of the cerebellum in key aspects of emotion. Experts in the field of cerebellar research discuss the range of cerebellar contributions to emotion in nine topics. Topics include the role of the cerebellum in perception and recognition, forwarding and encoding of emotional information, and the experience and regulation of emotional states in relation to motor, cognitive, and social behaviors. In addition, perspectives including cerebellar involvement in emotional learning, pain, emotional aspects of speech, and neuropsychiatric aspects of the cerebellum in mood disorders are briefly discussed. Results of this consensus paper illustrate how theory and empirical research have converged to produce a composite picture of brain topography, physiology, and function that establishes the role of the cerebellum in many aspects of emotional processing
Reordering buffer management with advice
In the reordering buffer management problem, a sequence of colored items arrives at a service station to be processed. Each color change between two consecutively processed items generates some cost. A reordering buffer of capacity k items can be used to preprocess the input sequence in order to decrease the number of color changes. The goal is to find a scheduling strategy that, using the reordering buffer, minimizes the number of color changes in the given sequence of items. We consider the problem in the setting of online computation with advice. In this model, the color of an item becomes known only at the time when the item enters the reordering buffer. Additionally, together with each item entering the buffer, we get a fixed number of advice bits, which can be seen as information about the future or as information about an optimal solution (or an approximation thereof) for the whole input sequence. We show that for any ε>0 there is a (1+ε)-competitive algorithm for the problem which uses only a constant (depending on ε) number of advice bits per input item. This also immediately implies a (1+ε)-approximation algorithm which has 2O(nlog1/ε) running time (this should be compared to the trivial optimal algorithm which has a running time of kO(n)). We complement the above result by presenting a lower bound of Ω(logk) bits of advice per request for any 1-competitive algorithm
Competitive Tendering In The Netherlands: Central Planning Or Functional Specifications?
Institute of Transport and Logistics Studies. Faculty of Economics and Business. The University of Sydne
The mystery of the cerebellum: clues from experimental and clinical observations
Abstract The cerebellum has a striking homogeneous cytoarchitecture and participates in both motor and non-motor domains. Indeed, a wealth of evidence from neuroanatomical, electrophysiological, neuroimaging and clinical studies has substantially modified our traditional view on the cerebellum as a sole calibrator of sensorimotor functions. Despite the major advances of the last four decades of cerebellar research, outstanding questions remain regarding the mechanisms and functions of the cerebellar circuitry. We discuss major clues from both experimental and clinical studies, with a focus on rodent models in fear behaviour, on the role of the cerebellum in motor control, on cerebellar contributions to timing and our appraisal of the pathogenesis of cerebellar tremor. The cerebellum occupies a central position to optimize behaviour, motor control, timing procedures and to prevent body oscillations. More than ever, the cerebellum is now considered as a major actor on the scene of disorders affecting the CNS, extending from motor disorders to cognitive and affective disorders. However, the respective roles of the mossy fibres, the climbing fibres, cerebellar cortex and cerebellar nuclei remains unknown or partially known at best in most cases. Research is now moving towards a better definition of the roles of cerebellar modules and microzones. This will impact on the management of cerebellar disorders
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