Results 1 
9 of
9
Distributed Algorithms for Ultrasparse Spanners and Linear Size Skeletons
"... We present efficient algorithms for computing very sparse low distortion spanners in distributed networks and prove some nontrivial lower bounds on the tradeoff between time, sparseness, and distortion. All of our algorithms assume a synchronized distributed network, where relatively short messages ..."
Abstract

Cited by 10 (0 self)
 Add to MetaCart
(Show Context)
We present efficient algorithms for computing very sparse low distortion spanners in distributed networks and prove some nontrivial lower bounds on the tradeoff between time, sparseness, and distortion. All of our algorithms assume a synchronized distributed network, where relatively short messages may be communicated in each time step. Our first result is a fast distributed algorithm for finding an O(2 log ∗ n log n)spanner with size O(n). Besides being nearly optimal in time and distortion, this algorithm appears to be the first that constructs an O(n)size skeleton without requiring unbounded length messages or time proportional to the diameter of the network. Our second result is a new class of efficiently constructible (α, β)spanners called Fibonacci spanners whose distortion improves with the distance being approximated. At their sparsest Fibonacci spanners can have nearly linear size O(n(log log n) φ) where φ = 1+ √ 5 2 is the golden ratio. As the distance increases the Fibonacci spanner’s multiplicative distortion passes through four discrete stages, moving from logarithmic to loglogarithmic, then into a period where it is constant, tending to 3, followed by another period tending to 1. On the lower bound side we prove that many recent sequential spanner constructions have no efficient counterparts in distributed networks, even if the desired distortion only needs to be achieved on the average or for a tiny fraction of the vertices. In particular, any distance preservers, purely additive spanners, or spanners with sublinear additive distortion must either be very dense, slow to construct, or have very weak guarantees on distortion.
Deterministic Distributed Construction of Linear Stretch Spanners in Polylogarithmic Time
, 2007
"... The paper presents a deterministic distributed algorithm that given an n node unweighted graph constructs an O(n 3/2) edge 3spanner for it in O(log n) time. This algorithm is then extended into a deterministic algorithm for computing an O(kn 1+1/k) edge O(k)spanner in O(log k−1 n) time for every i ..."
Abstract

Cited by 5 (2 self)
 Add to MetaCart
(Show Context)
The paper presents a deterministic distributed algorithm that given an n node unweighted graph constructs an O(n 3/2) edge 3spanner for it in O(log n) time. This algorithm is then extended into a deterministic algorithm for computing an O(kn 1+1/k) edge O(k)spanner in O(log k−1 n) time for every integer parameter k � 1. This establishes that the problem of the deterministic construction of a low stretch spanner with few edges can be solved in the distributed setting in polylogarithmic time. The paper also investigates the distributed construction of sparse spanners with almost pure additive stretch (1 + ɛ, β), i.e., such that the distance in the spanner is at most 1 + ɛ times the original distance plus β. It is shown, for every ɛ> 0, that in O(log n/ɛ) time one can deterministically construct a spanner with O(n 3/2) edges that is both a 3spanner and a (1 + ɛ, 8 log n)spanner. Furthermore, it is shown that in n O(1/ √ log n) + O(1/ɛ) time one can deterministically construct a spanner with O(n 3/2) edges which is both a 3spanner and a (1+ɛ, 4)spanner. (This algorithm can be transformed into a Las Vegas randomized algorithm with guarantees on the stretch and time, running in O(log n +1/ɛ) expected time).
IS
"... HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte p ..."
Abstract
 Add to MetaCart
(Show Context)
HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et a ̀ la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés. appor t de r ech er ch e
• Postdoctoral Students
, 2008
"... Searching and dissemination of information on largescale platforms ProjectTeam proposal – CR Bordeaux SudOuest ..."
Abstract
 Add to MetaCart
Searching and dissemination of information on largescale platforms ProjectTeam proposal – CR Bordeaux SudOuest
3.3. Theoretical Validation 7
"... c t i v it y e p o r t 2009 Table of contents 1. Team.................................................................................... 1 ..."
Abstract
 Add to MetaCart
(Show Context)
c t i v it y e p o r t 2009 Table of contents 1. Team.................................................................................... 1
3.3. Theoretical Validation 6
"... c t i v it y e p o r t 2008 Table of contents 1. Team.................................................................................... 1 ..."
Abstract
 Add to MetaCart
(Show Context)
c t i v it y e p o r t 2008 Table of contents 1. Team.................................................................................... 1
ProjectTeam DOLPHIN Discrete multiobjective Optimization for Large scale Problems with Hybrid
"... c t i v it y e p o r t ..."