7,812 research outputs found
Fast Structuring of Radio Networks for Multi-Message Communications
We introduce collision free layerings as a powerful way to structure radio
networks. These layerings can replace hard-to-compute BFS-trees in many
contexts while having an efficient randomized distributed construction. We
demonstrate their versatility by using them to provide near optimal distributed
algorithms for several multi-message communication primitives.
Designing efficient communication primitives for radio networks has a rich
history that began 25 years ago when Bar-Yehuda et al. introduced fast
randomized algorithms for broadcasting and for constructing BFS-trees. Their
BFS-tree construction time was rounds, where is the network
diameter and is the number of nodes. Since then, the complexity of a
broadcast has been resolved to be rounds. On the other hand, BFS-trees have been used as a crucial building
block for many communication primitives and their construction time remained a
bottleneck for these primitives.
We introduce collision free layerings that can be used in place of BFS-trees
and we give a randomized construction of these layerings that runs in nearly
broadcast time, that is, w.h.p. in rounds for any constant . We then use these
layerings to obtain: (1) A randomized algorithm for gathering messages
running w.h.p. in rounds. (2) A randomized -message
broadcast algorithm running w.h.p. in rounds. These
algorithms are optimal up to the small difference in the additive
poly-logarithmic term between and . Moreover, they imply the
first optimal round randomized gossip algorithm
The Sparsest Additive Spanner via Multiple Weighted BFS Trees
Spanners are fundamental graph structures that sparsify graphs at the cost of small stretch. In particular, in recent years, many sequential algorithms constructing additive all-pairs spanners were designed, providing very sparse small-stretch subgraphs. Remarkably, it was then shown that the known (+6)-spanner constructions are essentially the sparsest possible, that is, larger additive stretch cannot guarantee a sparser spanner, which brought the stretch-sparsity trade-off to its limit. Distributed constructions of spanners are also abundant. However, for additive spanners, while there were algorithms constructing (+2) and (+4)-all-pairs spanners, the sparsest case of (+6)-spanners remained elusive.
We remedy this by designing a new sequential algorithm for constructing a (+6)-spanner with the essentially-optimal sparsity of O~(n^{4/3}) edges. We then show a distributed implementation of our algorithm, answering an open problem in [Keren Censor{-}Hillel et al., 2016].
A main ingredient in our distributed algorithm is an efficient construction of multiple weighted BFS trees. A weighted BFS tree is a BFS tree in a weighted graph, that consists of the lightest among all shortest paths from the root to each node. We present a distributed algorithm in the CONGEST model, that constructs multiple weighted BFS trees in |S|+D-1 rounds, where S is the set of sources and D is the diameter of the network graph
Distributed Constructions of Dual-Failure Fault-Tolerant Distance Preservers
Fault tolerant distance preservers (spanners) are sparse subgraphs that preserve (approximate) distances between given pairs of vertices under edge or vertex failures. So-far, these structures have been studied thoroughly mainly from a centralized viewpoint. Despite the fact fault tolerant preservers are mainly motivated by the error-prone nature of distributed networks, not much is known on the distributed computational aspects of these structures.
In this paper, we present distributed algorithms for constructing fault tolerant distance preservers and +2 additive spanners that are resilient to at most two edge faults. Prior to our work, the only non-trivial constructions known were for the single fault and single source setting by [Ghaffari and Parter SPAA\u2716].
Our key technical contribution is a distributed algorithm for computing distance preservers w.r.t. a subset S of source vertices, resilient to two edge faults. The output structure contains a BFS tree BFS(s,G ? {e?,e?}) for every s ? S and every e?,e? ? G. The distributed construction of this structure is based on a delicate balance between the edge congestion (formed by running multiple BFS trees simultaneously) and the sparsity of the output subgraph. No sublinear-round algorithms for constructing these structures have been known before
Fast Distributed Computation of Distances in Networks
This paper presents a distributed algorithm to simultaneously compute the
diameter, radius and node eccentricity in all nodes of a synchronous network.
Such topological information may be useful as input to configure other
algorithms. Previous approaches have been modular, progressing in sequential
phases using building blocks such as BFS tree construction, thus incurring
longer executions than strictly required. We present an algorithm that, by
timely propagation of available estimations, achieves a faster convergence to
the correct values. We show local criteria for detecting convergence in each
node. The algorithm avoids the creation of BFS trees and simply manipulates
sets of node ids and hop counts. For the worst scenario of variable start
times, each node i with eccentricity ecc(i) can compute: the node eccentricity
in diam(G)+ecc(i)+2 rounds; the diameter in 2*diam(G)+ecc(i)+2 rounds; and the
radius in diam(G)+ecc(i)+2*radius(G) rounds.Comment: 12 page
Distributed-Memory Breadth-First Search on Massive Graphs
This chapter studies the problem of traversing large graphs using the
breadth-first search order on distributed-memory supercomputers. We consider
both the traditional level-synchronous top-down algorithm as well as the
recently discovered direction optimizing algorithm. We analyze the performance
and scalability trade-offs in using different local data structures such as CSR
and DCSC, enabling in-node multithreading, and graph decompositions such as 1D
and 2D decomposition.Comment: arXiv admin note: text overlap with arXiv:1104.451
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