SIAM Journal on Computing
Distributed computing: a locality-sensitive approach
Distributed computing: a locality-sensitive approach
Local and global properties in networks of processors (Extended Abstract)
STOC '80 Proceedings of the twelfth annual ACM symposium on Theory of computing
Compact and localized distributed data structures
Distributed Computing - Papers in celebration of the 20th anniversary of PODC
Proceedings of the twenty-fourth annual ACM symposium on Principles of distributed computing
Graph connectivity and monadic NP
SFCS '94 Proceedings of the 35th Annual Symposium on Foundations of Computer Science
Distributed computational complexities: are you volvo-addicted or nascar-obsessed?
Proceedings of the 29th ACM SIGACT-SIGOPS symposium on Principles of distributed computing
ICDCN'06 Proceedings of the 8th international conference on Distributed Computing and Networking
Distributed computing with advice: information sensitivity of graph coloring
ICALP'07 Proceedings of the 34th international conference on Automata, Languages and Programming
Locality and checkability in wait-free computing
DISC'11 Proceedings of the 25th international conference on Distributed computing
Decidability classes for mobile agents computing
LATIN'12 Proceedings of the 10th Latin American international conference on Theoretical Informatics
Randomized distributed decision
DISC'12 Proceedings of the 26th international conference on Distributed Computing
ACM Computing Surveys (CSUR)
What can be decided locally without identifiers?
Proceedings of the 2013 ACM symposium on Principles of distributed computing
Fast hamiltonicity checking via bases of perfect matchings
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
Exploiting locality in distributed SDN control
Proceedings of the second ACM SIGCOMM workshop on Hot topics in software defined networking
Towards a complexity theory for local distributed computing
Journal of the ACM (JACM)
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part I
Hi-index | 0.00 |
This work studies decision problems from the perspective of nondeterministic distributed algorithms. For a yes instance there must exist a proof that can be verified with a distributed algorithm: all nodes must accept a valid proof, and at least one node must reject an invalid proof. We focus on locally checkable proofs that can be verified with a constant-time distributed algorithm. For example, it is easy to prove that a graph is bipartite: the locally checkable proof gives a 2-colouring of the graph, which only takes 1 bit per node. However, it is more difficult to prove that a graph is not bipartite - it turns out that any locally checkable proof requires ©(log n) bits per node. In this work we classify graph problems according to their local proof complexity, i.e., how many bits per node are needed in a locally checkable proof. We establish tight or near-tight results for classical graph properties such as the chromatic number. We show that the proof complexities form a natural hierarchy of complexity classes: for many classical graph problems, the proof complexity is either 0, (1), (log n), or poly(n) bits per node. Among the most difficult graph properties are symmetric graphs, which require ©(n²) bits per node, and non-3-colourable graphs, which require ©(n²/log n) bits per node - any pure graph property admits a trivial proof of size O(n²).