1,897 research outputs found
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
Distributed Approximation Algorithms for Weighted Shortest Paths
A distributed network is modeled by a graph having nodes (processors) and
diameter . We study the time complexity of approximating {\em weighted}
(undirected) shortest paths on distributed networks with a {\em
bandwidth restriction} on edges (the standard synchronous \congest model). The
question whether approximation algorithms help speed up the shortest paths
(more precisely distance computation) was raised since at least 2004 by Elkin
(SIGACT News 2004). The unweighted case of this problem is well-understood
while its weighted counterpart is fundamental problem in the area of
distributed approximation algorithms and remains widely open. We present new
algorithms for computing both single-source shortest paths (\sssp) and
all-pairs shortest paths (\apsp) in the weighted case.
Our main result is an algorithm for \sssp. Previous results are the classic
-time Bellman-Ford algorithm and an -time
-approximation algorithm, for any integer
, which follows from the result of Lenzen and Patt-Shamir (STOC 2013).
(Note that Lenzen and Patt-Shamir in fact solve a harder problem, and we use
to hide the O(\poly\log n) term.) We present an -time -approximation algorithm for \sssp. This
algorithm is {\em sublinear-time} as long as is sublinear, thus yielding a
sublinear-time algorithm with almost optimal solution. When is small, our
running time matches the lower bound of by Das Sarma
et al. (SICOMP 2012), which holds even when , up to a
\poly\log n factor.Comment: Full version of STOC 201
Message Reduction in the LOCAL Model Is a Free Lunch
A new spanner construction algorithm is presented, working under the LOCAL model with unique edge IDs. Given an n-node communication graph, a spanner with a constant stretch and O(n^{1 + epsilon}) edges (for an arbitrarily small constant epsilon > 0) is constructed in a constant number of rounds sending O(n^{1 + epsilon}) messages whp. Consequently, we conclude that every t-round LOCAL algorithm can be transformed into an O(t)-round LOCAL algorithm that sends O(t * n^{1 + epsilon}) messages whp. This improves upon all previous message-reduction schemes for LOCAL algorithms that incur a log^{Omega (1)} n blow-up of the round complexity
Rational Fair Consensus in the GOSSIP Model
The \emph{rational fair consensus problem} can be informally defined as
follows. Consider a network of (selfish) \emph{rational agents}, each of
them initially supporting a \emph{color} chosen from a finite set .
The goal is to design a protocol that leads the network to a stable
monochromatic configuration (i.e. a consensus) such that the probability that
the winning color is is equal to the fraction of the agents that initially
support , for any . Furthermore, this fairness property must
be guaranteed (with high probability) even in presence of any fixed
\emph{coalition} of rational agents that may deviate from the protocol in order
to increase the winning probability of their supported colors. A protocol
having this property, in presence of coalitions of size at most , is said to
be a \emph{whp\,--strong equilibrium}. We investigate, for the first time,
the rational fair consensus problem in the GOSSIP communication model where, at
every round, every agent can actively contact at most one neighbor via a
\emph{pushpull} operation. We provide a randomized GOSSIP protocol that,
starting from any initial color configuration of the complete graph, achieves
rational fair consensus within rounds using messages of
size, w.h.p. More in details, we prove that our protocol is a
whp\,--strong equilibrium for any and, moreover, it
tolerates worst-case permanent faults provided that the number of non-faulty
agents is . As far as we know, our protocol is the first solution
which avoids any all-to-all communication, thus resulting in message
complexity.Comment: Accepted at IPDPS'1
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