94,877 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
Hierarchical Radio Resource Optimization for Heterogeneous Networks with Enhanced Inter-cell Interference Coordination (eICIC)
Interference is a major performance bottleneck in Heterogeneous Network
(HetNet) due to its multi-tier topological structure. We propose almost blank
resource block (ABRB) for interference control in HetNet. When an ABRB is
scheduled in a macro BS, a resource block (RB) with blank payload is
transmitted and this eliminates the interference from this macro BS to the pico
BSs. We study a two timescale hierarchical radio resource management (RRM)
scheme for HetNet with dynamic ABRB control. The long term controls, such as
dynamic ABRB, are adaptive to the large scale fading at a RRM server for
co-Tier and cross-Tier interference control. The short term control (user
scheduling) is adaptive to the local channel state information within each BS
to exploit the multi-user diversity. The two timescale optimization problem is
challenging due to the exponentially large solution space. We exploit the
sparsity in the interference graph of the HetNet topology and derive structural
properties for the optimal ABRB control. Based on that, we propose a two
timescale alternative optimization solution for the user scheduling and ABRB
control. The solution has low complexity and is asymptotically optimal at high
SNR. Simulations show that the proposed solution has significant gain over
various baselines.Comment: 14 pages, 8 figure
An Improved Distributed Algorithm for Maximal Independent Set
The Maximal Independent Set (MIS) problem is one of the basics in the study
of locality in distributed graph algorithms. This paper presents an extremely
simple randomized algorithm providing a near-optimal local complexity for this
problem, which incidentally, when combined with some recent techniques, also
leads to a near-optimal global complexity.
Classical algorithms of Luby [STOC'85] and Alon, Babai and Itai [JALG'86]
provide the global complexity guarantee that, with high probability, all nodes
terminate after rounds. In contrast, our initial focus is on the
local complexity, and our main contribution is to provide a very simple
algorithm guaranteeing that each particular node terminates after rounds, with probability at least
. The guarantee holds even if the randomness outside -hops
neighborhood of is determined adversarially. This degree-dependency is
optimal, due to a lower bound of Kuhn, Moscibroda, and Wattenhofer [PODC'04].
Interestingly, this local complexity smoothly transitions to a global
complexity: by adding techniques of Barenboim, Elkin, Pettie, and Schneider
[FOCS'12, arXiv: 1202.1983v3], we get a randomized MIS algorithm with a high
probability global complexity of ,
where denotes the maximum degree. This improves over the result of Barenboim et al., and gets close
to the lower bound of Kuhn et al.
Corollaries include improved algorithms for MIS in graphs of upper-bounded
arboricity, or lower-bounded girth, for Ruling Sets, for MIS in the Local
Computation Algorithms (LCA) model, and a faster distributed algorithm for the
Lov\'asz Local Lemma
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