23,897 research outputs found
Fast Graphical Population Protocols
Let be a graph on nodes. In the stochastic population protocol model,
a collection of indistinguishable, resource-limited nodes collectively
solve tasks via pairwise interactions. In each interaction, two randomly chosen
neighbors first read each other's states, and then update their local states. A
rich line of research has established tight upper and lower bounds on the
complexity of fundamental tasks, such as majority and leader election, in this
model, when is a clique. Specifically, in the clique, these tasks can be
solved fast, i.e., in pairwise interactions, with
high probability, using at most states per node.
In this work, we consider the more general setting where is an arbitrary
graph, and present a technique for simulating protocols designed for
fully-connected networks in any connected regular graph. Our main result is a
simulation that is efficient on many interesting graph families: roughly, the
simulation overhead is polylogarithmic in the number of nodes, and quadratic in
the conductance of the graph. As a sample application, we show that, in any
regular graph with conductance , both leader election and exact majority
can be solved in pairwise
interactions, with high probability, using at most states per node. This shows that there are fast and
space-efficient population protocols for leader election and exact majority on
graphs with good expansion properties. We believe our results will prove
generally useful, as they allow efficient technology transfer between the
well-mixed (clique) case, and the under-explored spatial setting.Comment: 47 pages, 5 figure
Distinguishing Views in Symmetric Networks: A Tight Lower Bound
The view of a node in a port-labeled network is an infinite tree encoding all
walks in the network originating from this node. We prove that for any integers
, there exists a port-labeled network with at most nodes and
diameter at most which contains a pair of nodes whose (infinite) views are
different, but whose views truncated to depth are
identical
Distributed Symmetry Breaking in Hypergraphs
Fundamental local symmetry breaking problems such as Maximal Independent Set
(MIS) and coloring have been recognized as important by the community, and
studied extensively in (standard) graphs. In particular, fast (i.e.,
logarithmic run time) randomized algorithms are well-established for MIS and
-coloring in both the LOCAL and CONGEST distributed computing
models. On the other hand, comparatively much less is known on the complexity
of distributed symmetry breaking in {\em hypergraphs}. In particular, a key
question is whether a fast (randomized) algorithm for MIS exists for
hypergraphs.
In this paper, we study the distributed complexity of symmetry breaking in
hypergraphs by presenting distributed randomized algorithms for a variety of
fundamental problems under a natural distributed computing model for
hypergraphs. We first show that MIS in hypergraphs (of arbitrary dimension) can
be solved in rounds ( is the number of nodes of the
hypergraph) in the LOCAL model. We then present a key result of this paper ---
an -round hypergraph MIS algorithm in
the CONGEST model where is the maximum node degree of the hypergraph
and is any arbitrarily small constant.
To demonstrate the usefulness of hypergraph MIS, we present applications of
our hypergraph algorithm to solving problems in (standard) graphs. In
particular, the hypergraph MIS yields fast distributed algorithms for the {\em
balanced minimal dominating set} problem (left open in Harris et al. [ICALP
2013]) and the {\em minimal connected dominating set problem}. We also present
distributed algorithms for coloring, maximal matching, and maximal clique in
hypergraphs.Comment: Changes from the previous version: More references adde
Gossip in a Smartphone Peer-to-Peer Network
In this paper, we study the fundamental problem of gossip in the mobile
telephone model: a recently introduced variation of the classical telephone
model modified to better describe the local peer-to-peer communication services
implemented in many popular smartphone operating systems. In more detail, the
mobile telephone model differs from the classical telephone model in three
ways: (1) each device can participate in at most one connection per round; (2)
the network topology can undergo a parameterized rate of change; and (3)
devices can advertise a parameterized number of bits about their state to their
neighbors in each round before connection attempts are initiated. We begin by
describing and analyzing new randomized gossip algorithms in this model under
the harsh assumption of a network topology that can change completely in every
round. We prove a significant time complexity gap between the case where nodes
can advertise bits to their neighbors in each round, and the case where
nodes can advertise bit. For the latter assumption, we present two
solutions: the first depends on a shared randomness source, while the second
eliminates this assumption using a pseudorandomness generator we prove to exist
with a novel generalization of a classical result from the study of two-party
communication complexity. We then turn our attention to the easier case where
the topology graph is stable, and describe and analyze a new gossip algorithm
that provides a substantial performance improvement for many parameters. We
conclude by studying a relaxed version of gossip in which it is only necessary
for nodes to each learn a specified fraction of the messages in the system.Comment: Extended Abstract to Appear in the Proceedings of the ACM Conference
on the Principles of Distributed Computing (PODC 2017
- âŠ