3,760 research outputs found
Optimal Dynamic Distributed MIS
Finding a maximal independent set (MIS) in a graph is a cornerstone task in
distributed computing. The local nature of an MIS allows for fast solutions in
a static distributed setting, which are logarithmic in the number of nodes or
in their degrees. The result trivially applies for the dynamic distributed
model, in which edges or nodes may be inserted or deleted. In this paper, we
take a different approach which exploits locality to the extreme, and show how
to update an MIS in a dynamic distributed setting, either \emph{synchronous} or
\emph{asynchronous}, with only \emph{a single adjustment} and in a single
round, in expectation. These strong guarantees hold for the \emph{complete
fully dynamic} setting: Insertions and deletions, of edges as well as nodes,
gracefully and abruptly. This strongly separates the static and dynamic
distributed models, as super-constant lower bounds exist for computing an MIS
in the former.
Our results are obtained by a novel analysis of the surprisingly simple
solution of carefully simulating the greedy \emph{sequential} MIS algorithm
with a random ordering of the nodes. As such, our algorithm has a direct
application as a -approximation algorithm for correlation clustering. This
adds to the important toolbox of distributed graph decompositions, which are
widely used as crucial building blocks in distributed computing.
Finally, our algorithm enjoys a useful \emph{history-independence} property,
meaning the output is independent of the history of topology changes that
constructed that graph. This means the output cannot be chosen, or even biased,
by the adversary in case its goal is to prevent us from optimizing some
objective function.Comment: 19 pages including appendix and reference
k-Inflation
It is shown that a large class of higher-order (i.e. non-quadratic) scalar
kinetic terms can, without the help of potential terms, drive an inflationary
evolution starting from rather generic initial conditions. In many models, this
kinetically driven inflation (or "k-inflation" for short) rolls slowly from a
high-curvature initial phase, down to a low-curvature phase and can exit
inflation to end up being radiation-dominated, in a naturally graceful manner.
We hope that this novel inflation mechanism might be useful in suggesting new
ways of reconciling the string dilaton with inflation.Comment: LaTeX, 20 pages including 3 figures. Submitted to Phys. Lett.
Strings And Colorings Of Topological Coding Towards Asymmetric Topology Cryptography
We, for anti-quantum computing, will discuss various number-based strings,
such as number-based super-strings, parameterized strings, set-based strings,
graph-based strings, integer-partitioned and integer-decomposed strings,
Hanzi-based strings, as well as algebraic operations based on number-based
strings. Moreover, we introduce number-based string-colorings, magic-constraint
colorings, and vector-colorings and set-colorings related with strings. For the
technique of encrypting the entire network at once, we propose graphic lattices
related with number-based strings, Hanzi-graphic lattices, string groups,
all-tree-graphic lattices. We study some topics of asymmetric topology
cryptography, such as topological signatures, Key-pair graphs, Key-pair
strings, one-encryption one-time and self-certification algorithms. Part of
topological techniques and algorithms introduced here are closely related with
NP-complete problems or NP-hard problems.Comment: Asymmetric topology encryption is a new topic of topological coding
towards the certificateless public key cryptograph
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