2,250 research outputs found
Distributed Computing on Core-Periphery Networks: Axiom-based Design
Inspired by social networks and complex systems, we propose a core-periphery
network architecture that supports fast computation for many distributed
algorithms and is robust and efficient in number of links. Rather than
providing a concrete network model, we take an axiom-based design approach. We
provide three intuitive (and independent) algorithmic axioms and prove that any
network that satisfies all axioms enjoys an efficient algorithm for a range of
tasks (e.g., MST, sparse matrix multiplication, etc.). We also show the
minimality of our axiom set: for networks that satisfy any subset of the
axioms, the same efficiency cannot be guaranteed for any deterministic
algorithm
A Simple Deterministic Distributed MST Algorithm, with Near-Optimal Time and Message Complexities
Distributed minimum spanning tree (MST) problem is one of the most central
and fundamental problems in distributed graph algorithms. Garay et al.
\cite{GKP98,KP98} devised an algorithm with running time , where is the hop-diameter of the input -vertex -edge
graph, and with message complexity . Peleg and Rubinovich
\cite{PR99} showed that the running time of the algorithm of \cite{KP98} is
essentially tight, and asked if one can achieve near-optimal running time
**together with near-optimal message complexity**.
In a recent breakthrough, Pandurangan et al. \cite{PRS16} answered this
question in the affirmative, and devised a **randomized** algorithm with time
and message complexity . They asked if
such a simultaneous time- and message-optimality can be achieved by a
**deterministic** algorithm.
In this paper, building upon the work of \cite{PRS16}, we answer this
question in the affirmative, and devise a **deterministic** algorithm that
computes MST in time , using messages. The polylogarithmic factors in the time
and message complexities of our algorithm are significantly smaller than the
respective factors in the result of \cite{PRS16}. Also, our algorithm and its
analysis are very **simple** and self-contained, as opposed to rather
complicated previous sublinear-time algorithms \cite{GKP98,KP98,E04b,PRS16}
Distributed Connectivity Decomposition
We present time-efficient distributed algorithms for decomposing graphs with
large edge or vertex connectivity into multiple spanning or dominating trees,
respectively. As their primary applications, these decompositions allow us to
achieve information flow with size close to the connectivity by parallelizing
it along the trees. More specifically, our distributed decomposition algorithms
are as follows:
(I) A decomposition of each undirected graph with vertex-connectivity
into (fractionally) vertex-disjoint weighted dominating trees with total weight
, in rounds.
(II) A decomposition of each undirected graph with edge-connectivity
into (fractionally) edge-disjoint weighted spanning trees with total
weight , in
rounds.
We also show round complexity lower bounds of
and
for the above two decompositions,
using techniques of [Das Sarma et al., STOC'11]. Moreover, our
vertex-connectivity decomposition extends to centralized algorithms and
improves the time complexity of [Censor-Hillel et al., SODA'14] from
to near-optimal .
As corollaries, we also get distributed oblivious routing broadcast with
-competitive edge-congestion and -competitive
vertex-congestion. Furthermore, the vertex connectivity decomposition leads to
near-time-optimal -approximation of vertex connectivity: centralized
and distributed . The former moves
toward the 1974 conjecture of Aho, Hopcroft, and Ullman postulating an
centralized exact algorithm while the latter is the first distributed vertex
connectivity approximation
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