51 research outputs found
Distributed Strong Diameter Network Decomposition
For a pair of positive parameters , a partition of the
vertex set of an -vertex graph into disjoint clusters of
diameter at most each is called a network decomposition, if the
supergraph , obtained by contracting each of the clusters
of , can be properly -colored. The decomposition is
said to be strong (resp., weak) if each of the clusters has strong (resp.,
weak) diameter at most , i.e., if for every cluster and
every two vertices , the distance between them in the induced graph
of (resp., in ) is at most .
Network decomposition is a powerful construct, very useful in distributed
computing and beyond. It was shown by Awerbuch \etal \cite{AGLP89} and
Panconesi and Srinivasan \cite{PS92}, that strong network decompositions can be computed in
distributed time. Linial and Saks \cite{LS93} devised an
ingenious randomized algorithm that constructs {\em weak} network decompositions in time. It was however open till now
if {\em strong} network decompositions with both parameters can be constructed in distributed time.
In this paper we answer this long-standing open question in the affirmative,
and show that strong network decompositions can be
computed in time. We also present a tradeoff between parameters
of our network decomposition. Our work is inspired by and relies on the
"shifted shortest path approach", due to Blelloch \etal \cite{BGKMPT11}, and
Miller \etal \cite{MPX13}. These authors developed this approach for PRAM
algorithms for padded partitions. We adapt their approach to network
decompositions in the distributed model of computation
Robust and Listening-Efficient Contention Resolution
This paper shows how to achieve contention resolution on a shared
communication channel using only a small number of channel accesses -- both for
listening and sending -- and the resulting algorithm is resistant to
adversarial noise.
The shared channel operates over a sequence of synchronized time slots, and
in any slot agents may attempt to broadcast a packet. An agent's broadcast
succeeds if no other agent broadcasts during that slot. If two or more agents
broadcast in the same slot, then the broadcasts collide and both broadcasts
fail. An agent listening on the channel during a slot receives ternary
feedback, learning whether that slot had silence, a successful broadcast, or a
collision. Agents are (adversarially) injected into the system over time. The
goal is to coordinate the agents so that each is able to successfully broadcast
its packet.
A contention-resolution protocol is measured both in terms of its throughput
and the number of slots during which an agent broadcasts or listens. Most prior
work assumes that listening is free and only tries to minimize the number of
broadcasts.
This paper answers two foundational questions. First, is constant throughput
achievable when using polylogarithmic channel accesses per agent, both for
listening and broadcasting? Second, is constant throughput still achievable
when an adversary jams some slots by broadcasting noise in them? Specifically,
for packets arriving over time and jammed slots, we give an algorithm
that with high probability in guarantees throughput and
achieves on average channel accesses against an
adaptive adversary. We also have per-agent high-probability guarantees on the
number of channel accesses -- either or , depending on how quickly the adversary can react to what
is being broadcast
Modeling the Small-World Phenomenon with Road Networks
Dating back to two famous experiments by the social-psychologist, Stanley
Milgram, in the 1960s, the small-world phenomenon is the idea that all people
are connected through a short chain of acquaintances that can be used to route
messages. Many subsequent papers have attempted to model this phenomenon, with
most concentrating on the "short chain" of acquaintances rather than their
ability to efficiently route messages. In this paper, we study the small-world
navigability of the U.S. road network, with the goal of providing a model that
explains how messages in the original small-world experiments could be routed
along short paths using U.S. roads. To this end, we introduce the Neighborhood
Preferential Attachment model, which combines elements from Kleinberg's model
and the Barab\'asi-Albert model, such that long-range links are chosen
according to both the degrees and (road-network) distances of vertices in the
network. We empirically evaluate all three models by running a decentralized
routing algorithm, where each vertex only has knowledge of its own neighbors,
and find that our model outperforms both of these models in terms of the
average hop length. Moreover, our experiments indicate that similar to the
Barab\'asi-Albert model, networks generated by our model are scale-free, which
could be a more realistic representation of acquaintanceship links in the
original small-world experiment
Peer to peer multidimensional overlays: Approximating complex structures
Peer to peer overlay networks have proven to be a good support for storing and retrieving data in a fully decentralized way. A sound approach is to structure them in such a way that they reflect the structure of the application. Peers represent objects of the application so that neighbours in the peer to peer network are objects having similar characteristics from the application's point of view. Such structured peer to peer overlay networks provide a natural support for range queries. While some complex structures such as a Voronoï tessellation, where each peer is associated to a cell in the space, are clearly relevant to structure the objects, the associated cost to compute and maintain these structures is usually extremely high for dimensions larger than 2. We argue that an approximation of a complex structure is enough to provide a native support of range queries. This stems fromthe fact that neighbours are importantwhile the exact space partitioning associated to a given peer is not as crucial. In this paper we present the design, analysis and evaluation of RayNet, a loosely structured Voronoï-based overlay network. RayNet organizes peers in an approximation of a Voronoï tessellation in a fully decentralized way. It relies on a Monte-Carlo algorithm to estimate the size of a cell and on an epidemic protocol to discover neighbours. In order to ensure efficient (polylogarithmic) routing, RayNet is inspired from the Kleinberg's small world model where each peer gets connected to close neighbours (its approximate Voronoï neighbours in Raynet) and shortcuts, long range neighbours, implemented using an existing Kleinberg-like peer sampling
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
On the Tree Conjecture for the Network Creation Game
Selfish Network Creation focuses on modeling real world networks from a game-theoretic point of view. One of the classic models by Fabrikant et al.[PODC\u2703] is the network creation game, where agents correspond to nodes in a network which buy incident edges for the price of alpha per edge to minimize their total distance to all other nodes. The model is well-studied but still has intriguing open problems. The most famous conjectures state that the price of anarchy is constant for all alpha and that for alpha >= n all equilibrium networks are trees.
We introduce a novel technique for analyzing stable networks for high edge-price alpha and employ it to improve on the best known bounds for both conjectures. In particular we show that for alpha > 4n-13 all equilibrium networks must be trees, which implies a constant price of anarchy for this range of alpha. Moreover, we also improve the constant upper bound on the price of anarchy for equilibrium trees
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