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ETH Zurich – Distributed Computing Group Roger Wattenhofer 1ETH Zurich – Distributed Computing – www.disco.ethz.ch
Christoph LenzenRoger Wattenhofer
Exponential Speed-Upof Local Algorithms
using Non-Local Communication
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Christoph Lenzen@PODC 2010
"classical"local model
distributed systemswith "non-local"communication
abstracting
communication
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Christoph Lenzen@PODC 2010
Local vs. Non-Local Communication
local non-local
communication range
neighbors anyone
limiting factor locality bandwidth
strength highly concurrent algorithms known
global information
exchange
Can we combine it?
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Christoph Lenzen@PODC 2010
MIS, MDS,max. matching, coloring, etc.
Model
Communication:
• |V| = n nodes that may exchange messages directly
• bandwidth and memory limitation of n² (² constant)
Task:
• graph problem on G = (V,E)
• maximum degree ¢ of G polylogarithmic
• nodes know neighbors in G
large degrees implied small
diameter anyway
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Christoph Lenzen@PODC 2010
Idea
• collect entire (multi-hop) neighorhoods in G• distance to which graph is known grows exponentially• simulate multiple rounds of local algorithm in one
v
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Christoph Lenzen@PODC 2010
Results
Theorem:
Given that inputs are of size at most n²/2,any local algorithm terminating within r 2 O(log n) roundscan be simulated within O(log r) rounds.
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Christoph Lenzen@PODC 2010
Examples
problem running timemaximal
independent setO(log log n)
w.h.p.O(log ¢)-approx. of min.
dominating setO(log log ¢)
µ O(log log log n)
(2+±)-approx. of max. weighted matching
O(log log n)
2-approx.of min. vertex cover
O(log log n)
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ETH Zurich – Distributed Computing Group Roger Wattenhofer 8ETH Zurich – Distributed Computing – www.disco.ethz.ch
Christoph LenzenRoger Wattenhofer
Thank You!Questions & Comments?