10,019 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 Data Summarization in Well-Connected Networks
We study distributed algorithms for some fundamental problems in data summarization. Given a communication graph G of n nodes each of which may hold a value initially, we focus on computing sum_{i=1}^N g(f_i), where f_i is the number of occurrences of value i and g is some fixed function. This includes important statistics such as the number of distinct elements, frequency moments, and the empirical entropy of the data.
In the CONGEST~ model, a simple adaptation from streaming lower bounds shows that it requires Omega~(D+ n) rounds, where D is the diameter of the graph, to compute some of these statistics exactly. However, these lower bounds do not hold for graphs that are well-connected. We give an algorithm that computes sum_{i=1}^{N} g(f_i) exactly in {tau_{G}} * 2^{O(sqrt{log n})} rounds where {tau_{G}} is the mixing time of G. This also has applications in computing the top k most frequent elements.
We demonstrate that there is a high similarity between the GOSSIP~ model and the CONGEST~ model in well-connected graphs. In particular, we show that each round of the GOSSIP~ model can be simulated almost perfectly in O~({tau_{G}}) rounds of the CONGEST~ model. To this end, we develop a new algorithm for the GOSSIP~ model that 1 +/- epsilon approximates the p-th frequency moment F_p = sum_{i=1}^N f_i^p in O~(epsilon^{-2} n^{1-k/p}) roundsfor p >= 2, when the number of distinct elements F_0 is at most O(n^{1/(k-1)}). This result can be translated back to the CONGEST~ model with a factor O~({tau_{G}}) blow-up in the number of rounds
Design of testbed and emulation tools
The research summarized was concerned with the design of testbed and emulation tools suitable to assist in projecting, with reasonable accuracy, the expected performance of highly concurrent computing systems on large, complete applications. Such testbed and emulation tools are intended for the eventual use of those exploring new concurrent system architectures and organizations, either as users or as designers of such systems. While a range of alternatives was considered, a software based set of hierarchical tools was chosen to provide maximum flexibility, to ease in moving to new computers as technology improves and to take advantage of the inherent reliability and availability of commercially available computing systems
Randomized Initialization of a Wireless Multihop Network
Address autoconfiguration is an important mechanism required to set the IP
address of a node automatically in a wireless network. The address
autoconfiguration, also known as initialization or naming, consists to give a
unique identifier ranging from 1 to for a set of indistinguishable
nodes. We consider a wireless network where nodes (processors) are randomly
thrown in a square , uniformly and independently. We assume that the network
is synchronous and two nodes are able to communicate if they are within
distance at most of of each other ( is the transmitting/receiving
range). The model of this paper concerns nodes without the collision detection
ability: if two or more neighbors of a processor transmit concurrently at
the same time, then would not receive either messages. We suppose also that
nodes know neither the topology of the network nor the number of nodes in the
network. Moreover, they start indistinguishable, anonymous and unnamed. Under
this extremal scenario, we design and analyze a fully distributed protocol to
achieve the initialization task for a wireless multihop network of nodes
uniformly scattered in a square . We show how the transmitting range of the
deployed stations can affect the typical characteristics such as the degrees
and the diameter of the network. By allowing the nodes to transmit at a range
r= \sqrt{\frac{(1+\ell) \ln{n} \SIZE}{\pi n}} (slightly greater than the one
required to have a connected network), we show how to design a randomized
protocol running in expected time in order to assign a
unique number ranging from 1 to to each of the participating nodes
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