A fast and simple randomized parallel algorithm for the maximal independent set problem
Journal of Algorithms
A simple parallel algorithm for the maximal independent set problem
SIAM Journal on Computing
ACM Transactions on Programming Languages and Systems (TOPLAS)
Self-stabilization by local checking and correction (extended abstract)
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
Locality in distributed graph algorithms
SIAM Journal on Computing
Sharing memory robustly in message-passing systems
Journal of the ACM (JACM)
Impossibility of distributed consensus with one faulty process
Journal of the ACM (JACM)
SIAM Journal on Computing
Unreliable failure detectors for reliable distributed systems
Journal of the ACM (JACM)
On the complexity of distributed network decomposition
Journal of Algorithms
The weakest failure detector for solving consensus
Journal of the ACM (JACM)
The local detection paradigm and its applications to self-stabilization
Theoretical Computer Science
Fast distributed construction of small k-dominating sets and applications
Journal of Algorithms
Distributed computing: a locality-sensitive approach
Distributed computing: a locality-sensitive approach
Self-stabilizing systems in spite of distributed control
Communications of the ACM
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
SIAM Journal on Computing
On the Distributed Complexity of Computing Maximal Matchings
SIAM Journal on Discrete Mathematics
Self-Stabilization by Local Checking and Global Reset (Extended Abstract)
WDAG '94 Proceedings of the 8th International Workshop on Distributed Algorithms
What cannot be computed locally!
Proceedings of the twenty-third annual ACM symposium on Principles of distributed computing
On the complexity of distributed graph coloring
Proceedings of the twenty-fifth annual ACM symposium on Principles of distributed computing
A faster distributed protocol for constructing a minimum spanning tree
Journal of Computer and System Sciences
Local MST computation with short advice
Proceedings of the nineteenth annual ACM symposium on Parallel algorithms and architectures
What can be approximated locally?: case study: dominating sets in planar graphs
Proceedings of the twentieth annual symposium on Parallelism in algorithms and architectures
Improved distributed approximate matching
Proceedings of the twentieth annual symposium on Parallelism in algorithms and architectures
Distributed (δ+1)-coloring in linear (in δ) time
Proceedings of the forty-first annual ACM symposium on Theory of computing
Weak graph colorings: distributed algorithms and applications
Proceedings of the twenty-first annual symposium on Parallelism in algorithms and architectures
Distributed Approximate Matching
SIAM Journal on Computing
Communication algorithms with advice
Journal of Computer and System Sciences
Local computation of nearly additive spanners
DISC'09 Proceedings of the 23rd international conference on Distributed computing
A new technique for distributed symmetry breaking
Proceedings of the 29th ACM SIGACT-SIGOPS symposium on Principles of distributed computing
Property testing: current research and surveys
Property testing: current research and surveys
Distributed verification and hardness of distributed approximation
Proceedings of the forty-third annual ACM symposium on Theory of computing
Toward more localized local algorithms: removing assumptions concerning global knowledge
Proceedings of the 30th annual ACM SIGACT-SIGOPS symposium on Principles of distributed computing
Proceedings of the 30th annual ACM SIGACT-SIGOPS symposium on Principles of distributed computing
Fast and compact self stabilizing verification, computation, and fault detection of an MST
Proceedings of the 30th annual ACM SIGACT-SIGOPS symposium on Principles of distributed computing
Locality and checkability in wait-free computing
DISC'11 Proceedings of the 25th international conference on Distributed computing
FOCS '11 Proceedings of the 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science
Distributed computing with advice: information sensitivity of graph coloring
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
The Locality of Distributed Symmetry Breaking
FOCS '12 Proceedings of the 2012 IEEE 53rd Annual Symposium on Foundations of Computer Science
Randomized distributed decision
DISC'12 Proceedings of the 26th international conference on Distributed Computing
What can be decided locally without identifiers?
Proceedings of the 2013 ACM symposium on Principles of distributed computing
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A central theme in distributed network algorithms concerns understanding and coping with the issue of locality. Yet despite considerable progress, research efforts in this direction have not yet resulted in a solid basis in the form of a fundamental computational complexity theory for locality. Inspired by sequential complexity theory, we focus on a complexity theory for distributed decision problems. In the context of locality, solving a decision problem requires the processors to independently inspect their local neighborhoods and then collectively decide whether a given global input instance belongs to some specified language. We consider the standard LOCAL model of computation and define LD(t) (for local decision) as the class of decision problems that can be solved in t communication rounds. We first study the intriguing question of whether randomization helps in local distributed computing, and to what extent. Specifically, we define the corresponding randomized class BPLD(t,p,q), containing all languages for which there exists a randomized algorithm that runs in t rounds, accepts correct instances with probability at least p, and rejects incorrect ones with probability at least q. We show that p2 + q = 1 is a threshold for the containment of LD(t) in BPLD(t,p,q). More precisely, we show that there exists a language that does not belong to LD(t) for any t=o(n) but does belong to BPLD(0,p,q) for any p,q ∈ (0,1) such that p2 + q ≤ 1. On the other hand, we show that, restricted to hereditary languages, BPLD(t,p,q)=LD(O(t)), for any function t, and any p, q ∈ (0,1) such that p2 + q 1. In addition, we investigate the impact of nondeterminism on local decision, and establish several structural results inspired by classical computational complexity theory. Specifically, we show that nondeterminism does help, but that this help is limited, as there exist languages that cannot be decided locally nondeterministically. Perhaps surprisingly, it turns out that it is the combination of randomization with nondeterminism that enables to decide all languages in constant time. Finally, we introduce the notion of local reduction, and establish a couple of completeness results.