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## Domination games played on line graphs of complete multipartite graphs

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 01/05/2014
Português

Relevância na Pesquisa

47.002534%

The domination game on a graph $G$ (introduced by B. Bre\v{s}ar, S.
Klav\v{z}ar, D.F. Rall \cite{BKR2010}) consists of two players, Dominator and
Staller, who take turns choosing a vertex from $G$ such that whenever a vertex
is chosen by either player, at least one additional vertex is dominated.
Dominator wishes to dominate the graph in as few steps as possible, and Staller
wishes to delay this process as much as possible. The game domination number
$\gamma _{{\small g}}(G)$ is the number of vertices chosen when Dominator
starts the game; when Staller starts, it is denoted by $\gamma _{{\small
g}}^{\prime }(G).$
In this paper, the domination game on line graph $L\left(
K_{\overline{m}}\right) $ of complete multipartite graph $K_{\overline{m}}$
$(\overline{m}\equiv (m_{1},...,m_{n})\in \mathbb{N} ^{n})$ is considered, the
exact values for game domination numbers are obtained and optimal strategy for
both players is described. Particularly, it is proved that for $m_{1}\leq
m_{2}\leq ...\leq m_{n}$ both $\gamma _{{\small g}}\left( L\left(
K_{\overline{m}}\right) \right) =\min \left\{ \left\lceil \frac{2}{3}\left\vert
V\left( K_{\overline{m}}\right) \right\vert \right\rceil ,\right.$ $\left.
2\max \left\{ \left\lceil \frac{1}{2}\left( m_{1}+...+m_{n-1}\right)
\right\rceil ...

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## Lower bounds for on-line graph colorings

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

Relevância na Pesquisa

47.204395%

We propose two strategies for Presenter in on-line graph coloring games. The
first one constructs bipartite graphs and forces any on-line coloring algorithm
to use $2\log_2 n - 10$ colors, where $n$ is the number of vertices in the
constructed graph. This is best possible up to an additive constant. The second
strategy constructs graphs that contain neither $C_3$ nor $C_5$ as a subgraph
and forces $\Omega(\frac{n}{\log n}^\frac{1}{3})$ colors. The best known
on-line coloring algorithm for these graphs uses $O(n^{\frac{1}{2}})$ colors.

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## On-Line Difference Maximization

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Português

Relevância na Pesquisa

47.34445%

#Computer Science - Data Structures and Algorithms#Computer Science - Discrete Mathematics#F.2.2#G.1.6#G.2.1#G.2.3#G.3

In this paper we examine problems motivated by on-line financial problems and
stochastic games. In particular, we consider a sequence of entirely arbitrary
distinct values arriving in random order, and must devise strategies for
selecting low values followed by high values in such a way as to maximize the
expected gain in rank from low values to high values.
First, we consider a scenario in which only one low value and one high value
may be selected. We give an optimal on-line algorithm for this scenario, and
analyze it to show that, surprisingly, the expected gain is n-O(1), and so
differs from the best possible off-line gain by only a constant additive term
(which is, in fact, fairly small -- at most 15).
In a second scenario, we allow multiple nonoverlapping low/high selections,
where the total gain for our algorithm is the sum of the individual pair gains.
We also give an optimal on-line algorithm for this problem, where the expected
gain is n^2/8-\Theta(n\log n). An analysis shows that the optimal expected
off-line gain is n^2/6+\Theta(1), so the performance of our on-line algorithm
is within a factor of 3/4 of the best off-line strategy.

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## Combining Peer-to-Peer and Cloud Computing for Large Scale On-line Games

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 29/10/2015
Português

Relevância na Pesquisa

67.325596%

This thesis investigates the combination of Peer-to-Peer (P2P) and Cloud
Computing to support Massively Multiplayer On- line Games (MMOGs). MMOGs are
large-scale distributed applications where a large number of users concurrently
share a real-time virtual environment. Commercial MMOG infrastructures are
sized to support peak loads, incurring in high economical cost. Cloud Computing
represents an attractive solution, as it lifts MMOG operators from the burden
of buying and maintaining hardware, while offering the illusion of infinite
machines. However, it requires balancing the tradeoff between resource
provisioning and operational costs. P2P- based solutions present several
advantages, including the inherent scalability, self-repairing, and natural
load distribution capabilities. They require additional mechanisms to suit the
requirements of a MMOG, such as backup solutions to cope with peer
unreliability and heterogeneity. We propose mechanisms that integrate P2P and
Cloud Computing combining their advantages. Our techniques allow operators to
select the ideal tradeoff between performance and economical costs. Using
realistic workloads, we show that hybrid infrastructures can reduce the
economical effort of the operator, while offering a level of service comparable
with centralized architectures.

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## Strategy correlations and timing of adaptation in Minority Games

Fonte: Universidade Cornell
Publicador: Universidade Cornell

Tipo: Artigo de Revista Científica

Publicado em 31/03/2005
Português

Relevância na Pesquisa

47.794414%

We study the role of strategy correlations and timing of adaptation for the
dynamics of Minority Games, both simulationally and analytically. Using the
exact generating functional approach a la De Dominicis we compute the phase
diagram and the behaviour of batch and on-line games with correlated
strategies, complementing exisiting replica studies of their statics. It is
shown that the timing of adaptation can be relevant; while conventional games
with uncorrelated strategies are nearly insensitive to the choice of on-line
versus batch learning, we find qualitative differences when anti-correlations
are present in the strategy assignments. The available standard approximations
for the volatility in terms of persistent order parameters in the stationary
ergodic states become unreliable in batch games under such circumstances. We
then comment on the role of oscillations and the relation to the breakdown of
ergodicity. Finally, it is discussed how the generating functional formalism
can be used to study mixed populations of so-called `producers' and
`speculators' in the context of the batch minority games.; Comment: 15 pages, 13 figures, EPJ style

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