STOC '87 Proceedings of the nineteenth annual ACM symposium on Theory of computing
Introduction to algorithms
Memory-efficient self stabilizing protocols for general networks
Proceedings of the 4th international workshop on Distributed algorithms
Locality in distributed graph algorithms
SIAM Journal on Computing
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
Improvements in the time complexity of two message-optimal election algorithms
Proceedings of the fourth annual ACM symposium on Principles of distributed computing
Distributed computing: a locality-sensitive approach
Distributed computing: a locality-sensitive approach
A Distributed Algorithm for Minimum-Weight Spanning Trees
ACM Transactions on Programming Languages and Systems (TOPLAS)
Distributed MST for constant diameter graphs
Proceedings of the twentieth annual ACM symposium on Principles of distributed computing
A Near-Tight Lower Bound on the Time Complexity of Distributed MST Construction
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
A faster distributed protocol for constructing a minimum spanning tree
SODA '04 Proceedings of the fifteenth annual ACM-SIAM symposium on Discrete algorithms
STOC '04 Proceedings of the thirty-sixth annual ACM symposium on Theory of computing
What cannot be computed locally!
Proceedings of the twenty-third annual ACM symposium on Principles of distributed computing
Proceedings of the twenty-fourth annual ACM symposium on Principles of distributed computing
Distributed verification of minimum spanning trees
Proceedings of the twenty-fifth annual ACM symposium on Principles of distributed computing
Oracle size: a new measure of difficulty for communication tasks
Proceedings of the twenty-fifth annual ACM symposium on Principles of distributed computing
Labeling schemes for tree representation
IWDC'05 Proceedings of the 7th international conference on Distributed Computing
Label-guided graph exploration by a finite automaton
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
Tree exploration with an oracle
MFCS'06 Proceedings of the 31st international conference on Mathematical Foundations of Computer Science
What can be approximated locally?: case study: dominating sets in planar graphs
Proceedings of the twentieth annual symposium on Parallelism in algorithms and architectures
Trade-offs between the size of advice and broadcasting time in trees
Proceedings of the twentieth annual symposium on Parallelism in algorithms and architectures
Label-guided graph exploration by a finite automaton
ACM Transactions on Algorithms (TALG)
Fast Radio Broadcasting with Advice
SIROCCO '08 Proceedings of the 15th international colloquium on Structural Information and Communication Complexity
r3: Resilient Random Regular Graphs
DISC '08 Proceedings of the 22nd international symposium on Distributed Computing
Information and Computation
Theoretical Computer Science
Online Computation with Advice
ICALP '09 Proceedings of the 36th International Colloquium on Automata, Languages and Programming: Part I
Fast radio broadcasting with advice
Theoretical Computer Science
Communication algorithms with advice
Journal of Computer and System Sciences
DISC'10 Proceedings of the 24th international conference on Distributed computing
Online computation with advice
Theoretical Computer Science
Toward more localized local algorithms: removing assumptions concerning global knowledge
Proceedings of the 30th annual ACM SIGACT-SIGOPS symposium on Principles of distributed computing
Randomized distributed decision
DISC'12 Proceedings of the 26th international conference on Distributed Computing
Towards a complexity theory for local distributed computing
Journal of the ACM (JACM)
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We use the recently introduced advising scheme framework for measuring the difficulty of locally distributively computing a Minimum Spanning Tree (MST). An (m,t)-advising scheme for a distributed problem P is a way, for every possible input I of P, to provide an "advice" (i.e., a bit string) about I to each node so that: (1) the maximum size of the advices is at most m bits, and (2) the problem P can be solved distributively in at most t rounds using the advices as inputs. In case of MST, the output returned by each node of a weighted graph G is the edge leading to its parent in some rooted MST T of G. Clearly, there is a trivial (log n,0)-advising scheme for MST (each node is given the local port number of the edge leading to the root of some MST T), and it is known that any (0,t)-advising scheme satisfies t ≥ Ω (√n). Our main result is the construction of an (O(1),O(log n))-advising scheme for MST. That is, by only giving a constant number of bits of advice to each node, one can decrease exponentially the distributed computation time of MST in arbitrary graph, compared to algorithms dealing with the problem in absence of any a priori information. We also consider the average size of the advices. On the one hand, we show that any (m,0)-advising scheme for MST gives advices of average size Ω(log n). On the other hand we design an (m,1)-advising scheme for MST with advices of constant average size, that is one round is enough to decrease the average size of the advices from log(n) to constant.