88,176 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
Distributed Edge Connectivity in Sublinear Time
We present the first sublinear-time algorithm for a distributed
message-passing network sto compute its edge connectivity exactly in
the CONGEST model, as long as there are no parallel edges. Our algorithm takes
time to compute and a
cut of cardinality with high probability, where and are the
number of nodes and the diameter of the network, respectively, and
hides polylogarithmic factors. This running time is sublinear in (i.e.
) whenever is. Previous sublinear-time
distributed algorithms can solve this problem either (i) exactly only when
[Thurimella PODC'95; Pritchard, Thurimella, ACM
Trans. Algorithms'11; Nanongkai, Su, DISC'14] or (ii) approximately [Ghaffari,
Kuhn, DISC'13; Nanongkai, Su, DISC'14].
To achieve this we develop and combine several new techniques. First, we
design the first distributed algorithm that can compute a -edge connectivity
certificate for any in time .
Second, we show that by combining the recent distributed expander decomposition
technique of [Chang, Pettie, Zhang, SODA'19] with techniques from the
sequential deterministic edge connectivity algorithm of [Kawarabayashi, Thorup,
STOC'15], we can decompose the network into a sublinear number of clusters with
small average diameter and without any mincut separating a cluster (except the
`trivial' ones). Finally, by extending the tree packing technique from [Karger
STOC'96], we can find the minimum cut in time proportional to the number of
components. As a byproduct of this technique, we obtain an -time
algorithm for computing exact minimum cut for weighted graphs.Comment: Accepted at 51st ACM Symposium on Theory of Computing (STOC 2019
Parallel and Distributed Algorithms for the Housing Allocation Problem
We give parallel and distributed algorithms for the housing allocation
problem. In this problem, there is a set of agents and a set of houses. Each
agent has a strict preference list for a subset of houses. We need to find a
matching such that some criterion is optimized. One such criterion is Pareto
Optimality. A matching is Pareto optimal if no coalition of agents can be
strictly better off by exchanging houses among themselves. We also study the
housing market problem, a variant of the housing allocation problem, where each
agent initially owns a house. In addition to Pareto optimality, we are also
interested in finding the core of a housing market. A matching is in the core
if there is no coalition of agents that can be better off by breaking away from
other agents and switching houses only among themselves.
In the first part of this work, we show that computing a Pareto optimal
matching of a house allocation is in {\bf CC} and computing the core of a
housing market is {\bf CC}-hard. Given a matching, we also show that verifying
whether it is in the core can be done in {\bf NC}. We then give an algorithm to
show that computing a maximum Pareto optimal matching for the housing
allocation problem is in {\bf RNC}^2 and quasi-{\bf NC}^2. In the second part
of this work, we present a distributed version of the top trading cycle
algorithm for finding the core of a housing market. To that end, we first
present two algorithms for finding all the disjoint cycles in a functional
graph: a Las Vegas algorithm which terminates in rounds with high
probability, where is the length of the longest cycle, and a deterministic
algorithm which terminates in rounds, where is the
number of nodes in the graph. Both algorithms work in the synchronous
distributed model and use messages of size
Asymptotically Faster Quantum Distributed Algorithms for Approximate Steiner Trees and Directed Minimum Spanning Trees
The CONGEST and CONGEST-CLIQUE models have been carefully studied to
represent situations where the communication bandwidth between processors in a
network is severely limited. Messages of only bits of information
each may be sent between processors in each round. The quantum versions of
these models allow the processors instead to communicate and compute with
quantum bits under the same bandwidth limitations. This leads to the following
natural research question: What problems can be solved more efficiently in
these quantum models than in the classical ones? Building on existing work, we
contribute to this question in two ways. Firstly, we present two algorithms in
the Quantum CONGEST-CLIQUE model of distributed computation that succeed with
high probability; one for producing an approximately optimal Steiner Tree, and
one for producing an exact directed minimum spanning tree, each of which uses
rounds of communication and messages,
where is the number of nodes in the network. The algorithms thus achieve a
lower asymptotic round and message complexity than any known algorithms in the
classical CONGEST-CLIQUE model. At a high level, we achieve these results by
combining classical algorithmic frameworks with quantum subroutines. An
existing framework for using distributed version of Grover's search algorithm
to accelerate triangle finding lies at the core of the asymptotic speedup.
Secondly, we carefully characterize the constants and logarithmic factors
involved in our algorithms as well as related algorithms, otherwise commonly
obscured by notation. The analysis shows that some improvements are
needed to render both our and existing related quantum and classical algorithms
practical, as their asymptotic speedups only help for very large values of .Comment: 23 pages, 0 figure
Storage and Search in Dynamic Peer-to-Peer Networks
We study robust and efficient distributed algorithms for searching, storing,
and maintaining data in dynamic Peer-to-Peer (P2P) networks. P2P networks are
highly dynamic networks that experience heavy node churn (i.e., nodes join and
leave the network continuously over time). Our goal is to guarantee, despite
high node churn rate, that a large number of nodes in the network can store,
retrieve, and maintain a large number of data items. Our main contributions are
fast randomized distributed algorithms that guarantee the above with high
probability (whp) even under high adversarial churn:
1. A randomized distributed search algorithm that (whp) guarantees that
searches from as many as nodes ( is the stable network size)
succeed in -rounds despite churn, for
any small constant , per round. We assume that the churn is
controlled by an oblivious adversary (that has complete knowledge and control
of what nodes join and leave and at what time, but is oblivious to the random
choices made by the algorithm).
2. A storage and maintenance algorithm that guarantees (whp) data items can
be efficiently stored (with only copies of each data item)
and maintained in a dynamic P2P network with churn rate up to
per round. Our search algorithm together with our
storage and maintenance algorithm guarantees that as many as nodes
can efficiently store, maintain, and search even under churn per round. Our algorithms require only polylogarithmic in bits to
be processed and sent (per round) by each node.
To the best of our knowledge, our algorithms are the first-known,
fully-distributed storage and search algorithms that provably work under highly
dynamic settings (i.e., high churn rates per step).Comment: to appear at SPAA 201
A Review of the Energy Efficient and Secure Multicast Routing Protocols for Mobile Ad hoc Networks
This paper presents a thorough survey of recent work addressing energy
efficient multicast routing protocols and secure multicast routing protocols in
Mobile Ad hoc Networks (MANETs). There are so many issues and solutions which
witness the need of energy management and security in ad hoc wireless networks.
The objective of a multicast routing protocol for MANETs is to support the
propagation of data from a sender to all the receivers of a multicast group
while trying to use the available bandwidth efficiently in the presence of
frequent topology changes. Multicasting can improve the efficiency of the
wireless link when sending multiple copies of messages by exploiting the
inherent broadcast property of wireless transmission. Secure multicast routing
plays a significant role in MANETs. However, offering energy efficient and
secure multicast routing is a difficult and challenging task. In recent years,
various multicast routing protocols have been proposed for MANETs. These
protocols have distinguishing features and use different mechanismsComment: 15 page
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